The design of efficient flapping wings for human engineered micro aerial vehicles (MAVs) has long been an elusive goal, in part because of the large size of the design space. One strategy for overcoming this difficulty is to use a multifidelity simulation strategy that appropriately balances computation time and accuracy. We compare two models with different geometric and physical fidelity. The low-fidelity model is an inviscid doublet lattice method with infinitely thin lifting surfaces. The high-fidelity model is a high-order accurate discontinuous Galerkin Navier–Stokes solver, which uses an accurate representation of the flapping wing geometry. To compare the performance of the two methods, we consider a model flapping wing with an elliptical planform and an analytically prescribed spanwise wing twist, at size scales relevant to MAVs. Our results show that in many cases, including those with mild separation, low-fidelity simulations can accurately predict integrated forces, provide insight into the flow structure, indicate regions of likely separation, and shed light on design–relevant quantities. But for problems with significant levels of separation, higher-fidelity methods are required to capture the details of the flow field. Inevitably high-fidelity simulations are needed to establish the limits of validity of the lower fidelity simulations.Copyright © 2012 John Wiley & Sons, Ltd.

An explicit integration algorithm for computations of discontinuous wave propagation in heterogeneous solids is presented, which is aimed at minimizing spurious oscillations when the wave fronts pass through several zones of different wave speeds. The essence of the present method is a combination of two wave capturing characteristics: a new integration formula that is obtained by pushforward–pullback operations in time designed to filter post-shock oscillations, and the central difference method that intrinsically filters front-shock oscillations. It is shown that a judicious combination of these two characteristics substantially reduces both spurious front-shock and post-shock oscillations. The performance of the new method is demonstrated as applied to wave propagation through a uniform bar with varying courant numbers, then to heterogeneous bars. Copyright © 2012 John Wiley & Sons, Ltd.

A new indirect way of producing all-quad meshes is presented. The method takes advantage of a well-known algorithm of the graph theory, namely the Blossom algorithm, that computes the minimum-cost perfect matching in a graph in polynomial time. The new Blossom-Quad algorithm is compared with standard indirect procedures. Meshes produced by the new approach are better both in terms of element shape and in terms of size field efficiency. Copyright © 2011 John Wiley & Sons, Ltd.

We present explicit and parametric forms of transformation matrices for three well-known and widely used symmetry groups: S₂, C_2v and C_4v. Group representation theory is the most powerful method for exploiting symmetry. We propose an efficient algorithm for systematic generation of reducible representations that can be combined linearly to obtain the projection operators. The exact column spaces of these projection operators are calculated and integrated through special orderings, leading to exact explicit and parametric forms of transformation matrices. The transformation matrices could be used directly for block diagonalization of single-variable scalar field problems. Another algorithm is proposed to extend the application of the method to nonscalar and multivariable field problems. Finally, the generality and efficiency of the proposed method in relation to computation times and the accuracy of results are illustrated through examples from spectral decomposition, free vibration, buckling of FEMs and boundary element analysis of a symmetric field. Copyright © 2011 John Wiley & Sons, Ltd.

A rigorous method for stabilizing projection-based linear reduced-order models without significantly affecting their accuracy is proposed. Unlike alternative approaches, this method is computationally efficient. It requires primarily the solution of a small-scale convex optimization problem. Furthermore, it is nonintrusive in the sense that it operates directly on readily available reduced-order operators. These can be precomputed using any data compression technique including balanced truncation, balanced proper orthogonal decomposition, proper orthogonal decomposition, or moment matching. The proposed method is illustrated with three applications: the stabilization of the reduction of the Computational Fluid Dynamics-based model of a linearized unsteady supersonic flow, the reduction of a Computational Structural Dynamics system, and the stabilization of the reduction of a coupled Computational Fluid Dynamics–Computational Structural Dynamics model of a linearized aeroelastic system in the transonic flow regime.Copyright © 2012 John Wiley & Sons, Ltd.

A comprehensive study is performed on the use of higher-order terms of the crack tip asymptotic fields as enriching functions for the eXtended FEM (XFEM) for both cohesive and traction-free cracks. For traction-free cracks, the Williams asymptotic field is used to obtain highly accurate stress intensity factors (SIFs), directly from the enriched degrees of freedom without any post-processing. The low accuracy of the results of the original research on this subject by Liu et al. [Int. J. Numer. Meth. Engng., 2004; 59:1103–1118] is remedied here by appropriate modifications of the enrichment scheme. The modifications are simple and can be easily included into an XFEM computer code. For cohesive cracks, the relevant asymptotic field is used, and two widely used criteria including the SIFs criterion and the stress criterion are examined for the crack growth simulation. Both linear and nonlinear cohesive laws are used. For the stress criterion, averaging is avoided due to the highly accurate crack tip approximation because of the higher-order enrichment. Then, a modified stress criterion is proposed, which is shown to be applicable to a wider class of problems. Several numerical examples, including straight and curved cracks, stationary and growing cracks, single and multiple cracks, and traction-free and cohesive cracks, are studied to investigate in detail the robustness and efficiency of the proposed enrichment scheme. Copyright © 2012 John Wiley & Sons, Ltd.

Analogously to the classical return-mapping algorithm, so-called variational constitutive updates are numerical methods allowing to compute the unknown state variables such as the plastic strains and the stresses for material models showing an irreversible mechanical response. In sharp contrast to standard approaches in computational inelasticity, the state variables follow naturally and jointly from energy minimization in case of variational constitutive updates. This leads to significant advantages from a numerical, mathematical as well as from a physical point of view. However, while the classical return-mapping algorithm has been being developed for several decades, and thus, it has already reached a certain maturity, variational constitutive updates have drawn attention only relatively recently. This is particularly manifested in the numerical performance of such algorithms. Within the present paper, the numerical efficiency of variational constitutive updates is critically analyzed. It will be shown that a naive approximation of the flow rule causes a singular Hessian within the respective Newton–Raphson scheme. However, by developing a novel parameterization of the flow rule, an efficient algorithm is derived. Its performance is carefully compared to that of the classical return-mapping scheme. This comparison clearly shows that the novel variationally consistent implementation is, at least, as efficient as the classical return-mapping algorithm. Copyright © 2011 John Wiley & Sons, Ltd.

This paper presents a perfectly matched layer (PML) technique for the numerical simulation of three-dimensional linear elastodynamic problems, where the geometry is invariant in the longitudinal direction. Examples include transportation infrastructure, dams, lifelines, and alluvial valleys.

For longitudinally invariant geometries, a computationally efficient two-and-a-half-dimensional (2.5D) approach can be applied, where the Fourier transform from the longitudinal coordinate to the wavenumber domain allows for the representation of the three-dimensional radiated wave field on a two-dimensional mesh. In this 2.5D framework, the equilibrium equations of a PML continuum are formulated in a weak form for an isotropic elastodynamic medium and discretized using a Galerkin approach.

The 2.5D PML methodology is validated by computing the Green's displacements of a homogeneous halfspace, demonstrating that the 2.5D PML absorbs all propagating waves for different angles of incidence. Furthermore, the dynamic stiffness of a rigid strip foundation and the efficiency of a vibration isolating screen are computed. The examples demonstrate that the PML methodology is computationally efficient, especially when only the response of the structure or the near field response is of interest.Copyright © 2011 John Wiley & Sons, Ltd.

The nodally integrated continuum element (NICE) formulation is an assumed-strain finite element technique derived from a weighted residual statement that weakly enforces both the balance equation and the kinematic equation. The original NICE formulation has a number of desirable attributes (e.g., resistance to volumetric locking), but, similar to classical finite elements, it is sensitive to a geometrical distortion of the finite element mesh. The present work analyzes the NICE technique from this viewpoint, the source of the sensitivity to the shape of the element is identified, and an improvement of the NICE formulation is proposed. We illustrate the performance of the revised NICE formulation on extremely distorted meshes. The tetrahedral meshes contain zero-volume or negative-volume elements, including slivers, and the new NICE formulation is shown to have the condition number of the stiffness matrix under control even in the presence of slivers. Furthermore, insensitivity to distortions is demonstrated for quadratic and cubic hexahedral elements. The proposed improvement confers robustness to all element shapes treated by the NICE formulation. The approximation properties of the original NICE formulation are preserved, in particular the improved version is also locking free, and at the same time, the need for stabilization also carries over. Copyright © 2011 John Wiley & Sons, Ltd.

This work is concerned with the construction of stochastic models for random elasticity matrices, allowing either for the generation of elasticity tensors exhibiting some material symmetry properties almost surely (integrating the statistical dependence between the random stiffness components) or for the modeling of random media that requires the mean of a stochastic anisotropy measure to be controlled apart from the level of statistical fluctuations. To this aim, we first introduced a decomposition of the stochastic elasticity tensor on a deterministic tensor basis and considered the probabilistic modeling of the random components, having recourse to the MaxEnt principle. Strategies for random generation and estimation were further reviewed, and the approach was exemplified in the case of a material that was transversely isotropic almost surely. In a second stage, we made use of such derivations to propose a generalized model for random elasticity matrices that took into account, almost separately, constraints on both the level of stochastic anisotropy and the level of statistical fluctuations. An example was finally provided and showed the efficiency of the approach. Copyright © 2011 John Wiley & Sons, Ltd.

There are many recent advances in mesh deformation methods for computational fluid dynamics simulation in deforming geometries. We present a method of constructing dynamic mesh around deforming objects by solving the bi-elliptic equation, an extension of the biharmonic equation. We show that introducing a stiffness coefficient field a(x) in the bi-elliptic equation can enable mesh deformation for very large boundary movements. An indicator of the mesh quality is constructed as an objective function of a numerical optimization procedure to find the best stiffness coefficient field a(x). The optimization is efficiently solved using steepest descent along adjoint-based, integrated Sobolev gradients. A multiscenario optimization procedure is performed to calculate the optimal stiffness coefficient field a^蜧(x) for a priori unpredictable boundary movements. Copyright © 2011 John Wiley & Sons, Ltd.

In this paper, enhanced four-node shell elements with six DOFs/node based on the Hu–Washizu (HW) functional are developed for Green strain. The drilling rotation is included through the drilling rotation constraint equation. The key features of the approach are as follows.

1. The shell HW functional is derived from the shell potential energy functional, which is an alternative to the derivation from the three-dimensional HW functional. This method is more versatile as it enables the derivation of the so-called partial HW functionals, with different treatment of the bending/twisting part and the transverse shear part of strain energy.
2. For the membrane part of HW shell elements, a seven-parameter stress, a nine-parameter strain and a two-parameter enhanced assumed displacement gradient enhancement are selected as optimal. The assumed representations of stress and strain are defined in skew coordinates in the natural basis at the element's center. This improves accuracy and has positive theoretical consequences.
3. The drilling rotation constraint equation is treated by the perturbed Lagrange method. The faulty term resulting from the equal-order approximations of displacements and the drilling rotation is eliminated, and one spurious mode is stabilized using the gamma method. The proposed formulation is insensitive to the element's distortions and yields a large radius of convergence in the examples involving in-plane bending.

The performance of 4 four-node shell HW elements, having different bending/twisting and transverse shear parts, is analyzed on several numerical examples. Such aspects are considered as: accuracy, radius of convergence, required number of iterations of the Newton method or the arc-length method and time of computations. The element with 29 parameters (HW29) is selected as the best performer. Copyright © 2011 John Wiley & Sons, Ltd.

In single point incremental forming (SPIF), the sheet is incrementally deformed by a small spherical tool following a lengthy tool path. The simulation by the finite element method of SPIF requires extremely long computing times that limit the application to simple academic cases. The main challenge is to perform thousands of load increments modelling the lengthy tool path with elements that are small enough to model the small contact area. Because of the localised deformation in the process, a strong nonlinearity is observed in the vicinity of the tool. The rest of the sheet experiences an elastic deformation that introduces only a weak nonlinearity because of the change of shape. The standard use of the implicit time integration scheme is inefficient because it applies an iterative update (Newton–Raphson) strategy for the entire system of equations. The iterative update is recommended for the strong nonlinearity that is active in a small domain but is not required for the large part with only weak nonlinearities. It is proposed in this paper to split the finite element mesh into two domains. The first domain models the plastically deforming zone that experiences the strong nonlinearity. It applies a full nonlinear update for the internal force vector and the stiffness matrix every iteration. The second domain models the large elastically deforming zone of the sheet. It applies a pseudolinear update strategy based on a linearization at the beginning of each increment. Within the increment, it reuses the stiffness matrix and linearly updates the internal force vector. The partly linearized update strategy is cheaper than the full nonlinear update strategy, resulting in a reduction of the overall computing. Furthermore, in this paper, adaptive refinement is combined with the two domain method. It results in accelerating the standard SPIF implicit simulation of 3200 shell elements by a factor of 3.6.Copyright © 2011 John Wiley & Sons, Ltd.

In the context of Hamiltonian ODEs, a necessary condition for an integrator to be symplectic or conjugate-symplectic is that it nearly preserves the exact Hamiltonian. This paper introduces a numerical test of this necessity for rigid body methods. It turns out that several rigid body integrators proposed in literature fail this test. Hence, these integrators should be used with caution for long-time simulation. Copyright © 2011 John Wiley & Sons, Ltd.

Models encountered in computational mechanics could involve many time scales. When these time scales cannot be separated, one must solve the evolution model in the entire time interval by using the finest time step that the model implies. In some cases, the solution procedure becomes cumbersome because of the extremely large number of time steps needed for integrating the evolution model in the whole time interval. In this paper, we considered an alternative approach that lies in separating the time axis (one-dimensional in nature) in a multidimensional time space. Then, for circumventing the resulting curse of dimensionality, the proper generalized decomposition was applied allowing a fast solution with significant computing time savings with respect to a standard incremental integration. Copyright © 2011 John Wiley & Sons, Ltd.

This paper presents stabilized mixed finite element formulations for tetrahedral elements at large deformations using volume and area bubble functions. To this end, the corresponding weak formulations are derived for the standard two-field method, the method of incompatible modes and the enhanced strain method. Then, the weak formulations will be linearized. Furthermore, the matrix formulations for the weak formulations and its linearizations are summarized. The numerical results for incompressible rubber-like materials using a Neo-Hookean material law show the locking-free performance and the drastic damping of the stresses for the new stabilized tetrahedral elements in finite deformation problems. This paper is an extension of the works published by the authors regarding small deformation problems for linear elasticity and plasticity. Copyright © 2011 John Wiley & Sons, Ltd.

Prosperetti's seminal Physalis method for fluid flows with suspended particles is extended to electric fields to directly resolve finite-sized particles and to investigate accurately the mutual fluid–particle, particle–particle, and particle–boundary interactions. The present paper shows the straightforward extension of the two dimensions [Liu, Q., 2011, J. Comput. Phys. 230:8256–8274] to three dimensions as one of the important advantages. The method can be used for uncharged/charged dielectrics, uncharged/charged conductors, conductors with specified voltage, and general weak and strong discontinuous interface conditions. These general interface conditions can be in terms of field variable, its gradients, and surface integration, which has not been addressed by other numerical methods. In addition, for the first time, we rigourously derive the force and torque on the finite-sized particles resulting from the interactions between harmonics. The method, for the first time, directly resolves the particles with accurate local charge distribution, force, and torque on the particles, making many applications in engineering, mechanics, physics, chemistry, and biology possible, such as heterogeneous materials, microfluidics, electrophotography, electric double-layer capacitors, and microstructures of nanodispersions. In the present paper, the accuracy of the coefficients in the general analytical solutions is extensively investigated. The method is numerically verified to be accurate even for very strong jump in the weak and strong discontinuous interface conditions, which have not yet been investigated in any other numerical methods. The efficiency of the method is demonstrated with up to 100,000 3D particles, which suggests that the method can be used for many important engineering applications of broad interest. Copyright © 2011 John Wiley & Sons, Ltd.

Finite element simulations of rubbers and biological soft tissue usually assume that the material being deformed is slightly compressible. It is shown here that, in shearing deformations, the corresponding normal stress distribution can exhibit extreme sensitivity to changes in Poisson's ratio. These changes can even lead to a reversal of the usual Poynting effect. Therefore, the usual practice of arbitrarily choosing a value of Poisson's ratio when numerically modelling rubbers and soft tissue will, almost certainly, lead to a significant difference between the simulated and actual normal stresses in a sheared block because of the difference between the assumed and actual value of Poisson's ratio. The worrying conclusion is that simulations based on arbitrarily specifying Poisson's ratio close to 1∕2 cannot accurately predict the normal stress distribution even for the simplest of shearing deformations. It is shown analytically that this sensitivity is caused by the small volume changes, which inevitably accompany all deformations of rubber-like materials. To minimise these effects, great care should be exercised to accurately determine Poisson's ratio before simulations begin. Copyright © 2011 John Wiley & Sons, Ltd.

The paper is focused on a piezoelectric 3D hexahedral finite element formulation on the basis of the space fiber rotation concept. The proposed electromechanical finite element has eight nodes and is animated by the virtual rotation of an elementary spatial fiber that creates an additional mechanical displacement enhancing the classical one generally considered to formulate the standard solid elements. The mechanical strain tensor and the electric field vector are expressed in a curvilinear coordinate system to handle the transverse isotropy behavior of piezoelectric materials. Numerical examples demonstrate that the proposed electromechanical element is less sensitive to mesh distortion than the standard piezoelectric solid elements. Besides, it is shown that the developed element response is better than those of the standard first-order piezoelectric elements. Copyright © 2011 John Wiley & Sons, Ltd.

The solution of problems in computational fluid dynamics (CFD) represents a classical field for the application of advanced numerical methods. Many different approaches were developed over the years to address CFD applications. Good examples are finite volumes, finite differences (FD), and finite elements (FE) but also newer approaches such as the lattice-Boltzmann (LB), smooth particle hydrodynamics or the particle finite element method. FD and LB methods on regular grids are known to be superior in terms of raw computing speed, but using such regular discretization represents an important limitation in dealing with complex geometries. Here, we concentrate on unstructured approaches which are less common in the GPU world. We employ a nonstandard FE approach which leverages an optimized edge-based data structure allowing a highly parallel implementation. Such technique is applied to the ‘convection-diffusion’ problem, which is often considered as a first step towards CFD because of similarities to the nonconservative form of the Navier–Stokes equations. In this regard, an existing highly optimized parallel OpenMP solver is ported to graphics hardware based on the OpenCL platform. The optimizations performed are discussed in detail. A number of benchmarks prove that the GPU-accelerated OpenCL code consistently outperforms the OpenMP version. Copyright © 2011 John Wiley & Sons, Ltd.

This paper aims to propose a meshless Galerkin level set method for shape and topology optimization of continuum structures. To take advantage of the implicit free boundary representation scheme, the design boundary is represented as the zero level set of a scalar level set function, to flexibly handle complex shape fidelity and topology changes by maintaining concise and smooth interface. Compactly supported radial basis functions (CSRBFs) are used to parameterize the level set function and construct the shape functions for meshfree approximations based on a set of unstructured field nodes. The meshless Galerkin method with global weak form is used to implement the discretization of the state equations. This provides a pathway to unify the two different numerical stages in most conventional level set methods: (1) the propagation of discrete level set function on a set of Eulerian grid and (2) the approximation of discrete equations on a set of Lagrangian mesh. The original more difficult shape and topology optimization based on the level set equation is transformed into a relatively easier size optimization, to which many efficient optimization algorithms can be applied. The proposed level set method can describe the moving boundaries without remeshing for discontinuities. The motion of the free boundary is just a question of advancing the discrete level set function in time by solving the size optimization. Several benchmark examples are used to demonstrate the effectiveness of the proposed method. The numerical results show that the proposed method can simplify numerical process and avoid numerical difficulties involved in most conventional level set methods. It is straightforward to apply the proposed method to more advanced shape and topology optimization problems. Copyright © 2011 John Wiley & Sons, Ltd.

The common-plane (CP) algorithm is widely used in the discrete element method to model contact forces between interacting particles or blocks of rock. A new simple contact algorithm, similar to the CP algorithm, is proposed to model discontinuities such as joints, faults and material interfaces in an explicit finite difference code. The CP is defined as a plane separating interacting faces of grid cells, instead of blocks or particles used in the original CP method. The new method does not require iterations even for very stiff contacts. It is very robust and easy to implement, both in 2D and 3D parallel codes. Copyright © 2011 John Wiley & Sons, Ltd.

This paper presents a one-dimensional lumped parameter model (LPM) that accurately represents the impedance function between two nodes arbitrarily selected in general linear structural systems having proportional damping. Through a procedure based on the modal analysis, the impedance function can be transformed into an equivalent LPM consisting of units arranged in series, with each unit consisting of a spring, a dashpot, and a so-called gyro mass element arranged in parallel. The gyro mass element generates a reaction force proportional to the relative acceleration of the nodes between where it is placed. Three application examples show that the LPMs accurately simulate the impedance functions in a mass–spring structure, a truss frame structure, and a cantilever plate. For a more efficient representation, a large number of units associated with high-order modes in the high-frequency region can be removed from the proposed gyro mass LPM (GLPM) as an approximation of the impedance functions in a target frequency region. The accuracy of the approximated GLPMs is improved by incorporating an additional unit associated with residual stiffness. This approximation greatly reduces the number of degrees of freedom of the GLPMs so that a marked decrease in the computational domain size and time can be expected for solving dynamic problems. Copyright © 2011 John Wiley & Sons, Ltd.

This brief article outlines a new and rather simple method for obtaining the finite element matrices for a perfectly matched layer used for elastic wave propagation in the context of a frequency-domain formulation. For this purpose, we introduce a fairly mild simplification, which allows applying the stretching functions directly to the mass and stiffness matrices obtained via conventional methods (i.e., elastic elements), a novel strategy that allows circumventing the use of integration via Gaussian quadrature. In essence, the technique proposed herein is equivalent to a direct application of the method of weighted residuals in stretched space, followed by a conversion of the linear dimensions into position-dependent complex-values. Most importantly, numerical tests demonstrate that the technique does work as intended, and in fact, splendidly so. Copyright © 2011 John Wiley & Sons, Ltd.

A method for topology optimization of continuum structures based on nodal density variables and density field mapping technique is investigated. The original discrete-valued topology optimization problem is stated as an optimization problem with continuous design variables by introducing a material density field into the design domain. With the use of the Shepard family of interpolants, this density field is mapped onto the design space defined by a finite number of nodal density variables. The employed interpolation scheme has an explicit form and satisfies range-restricted properties that makes it applicable for physically meaningful density interpolation. Its ability to resolve more complex spatial distribution of the material density within an individual element, as compared with the conventional elementwise design variable approach, actually provides certain regularization to the topology optimization problem. Numerical examples demonstrate the validity and applicability of the proposed formulation and numerical techniques. Copyright © 2011 John Wiley & Sons, Ltd.

In this paper, we present a family of mixed finite elements, which are suitable for the discretization of slim domains. The displacement space is chosen as Nédélec's space of tangential continuous elements, whereas the stress is approximated by normal–normal continuous symmetric tensor-valued finite elements. We show stability of the system on a slim domain discretized by a tensor product mesh, where the constant of stability does not depend on the aspect ratio of the discretization. We give interpolation operators for the finite element spaces, and thereby obtain optimal order a priori error estimates for the approximate solution. All estimates are independent of the aspect ratio of the finite elements. Copyright © 2011 John Wiley & Sons, Ltd.

Traditional algebraic multigrid (AMG) preconditioners are not well suited for crack problems modeled by extended finite element methods (XFEM). This is mainly because of the unique XFEM formulations, which embed discontinuous fields in the linear system by addition of special degrees of freedom. These degrees of freedom are not properly handled by the AMG coarsening process and lead to slow convergence. In this paper, we proposed a simple domain decomposition approach that retains the AMG advantages on well-behaved domains by avoiding the coarsening of enriched degrees of freedom. The idea was to employ a multiplicative Schwarz preconditioner where the physical domain was partitioned into “healthy” (or unfractured) and “cracked” subdomains. First, the “healthy” subdomain containing only standard degrees of freedom, was solved approximately by one AMG V-cycle, followed by concurrent direct solves of “cracked” subdomains. This strategy alleviated the need to redesign special AMG coarsening strategies that can handle XFEM discretizations. Numerical examples on various crack problems clearly illustrated the superior performance of this approach over a brute force AMG preconditioner applied to the linear system. Copyright © 2011 John Wiley & Sons, Ltd.

This paper presents a novel numerical procedure for computing limit and shakedown loads of structures using a node-based smoothed FEM in combination with a primal–dual algorithm. An associated primal–dual form based on the von Mises yield criterion is adopted. The primal-dual algorithm together with a Newton-like iteration are then used to solve this associated primal–dual form to determine simultaneously both approximate upper and quasi-lower bounds of the plastic collapse limit and the shakedown limit. The present formulation uses only linear approximations and its implementation into finite element programs is quite simple. Several numerical examples are given to show the reliability, accuracy, and generality of the present formulation compared with other available methods. Copyright © 2011 John Wiley & Sons, Ltd.

The mechanical properties of soft biological tissues vary depending on how the internal structure is organized. Classical examples of tissues are ligaments, tendons, skin, arteries, and annulus fibrous. The main element of such tissues is the fibers which are responsible for the tissue resistance and the main mechanical characteristic is their viscoelastic anisotropic behavior. The objective of this paper is to extend an existing model for isotropic viscoelastic materials in order to include anisotropy provided by fiber reinforcement. The incorporation of the fiber allows the mechanical behavior of these tissues to be simulated. The model is based on a variational framework in which its mechanical behavior is described by a free energy incremental potential whose local minimization provides the constraints for the internal variable updates for each load increment. The main advantage of this variational approach is the ability to represent different material models depending on the choice of suitable potential functions. Finally, the model is implemented in a finite-element code in order to perform numerical tests to show the ability of the proposed model to represent fiber-reinforced materials. The material parameters used in the tests were obtained through parameter identification using experimental data available in the literature. Copyright © 2011 John Wiley & Sons, Ltd.

This paper presents a new methodology for identifying defects under the presence of both sensor and defect uncertainties. This methodology introduces a representation of the beliefs of both the locations of defects and the sensors each by a probability density function and updates them using the extended Kalman filter. Because the beliefs are recursively maintained while the sensor is moving and the associated observation data are updated, the proposed approach considers not only the current observation data but also the prior knowledge, the past observation data and beliefs, which include both sensor and defect uncertainties. The concept of differential entropy has been introduced and is utilized as a performance measure to evaluate the result of defect identification and handle the identification of multiple defects. The verification and evaluation of the proposed methodology performance were conducted via parametric numerical studies. The results have shown the successful identification of defects with reduced uncertainty when the number of measurements increases, even under the presence of large sensor uncertainties. Furthermore, the proposed methodology was applied to the more realistic problem of identifying multiple defects located on a specimen and has demonstrated its applicability to practical defect identification problems. Copyright © 2011 John Wiley & Sons, Ltd.

A precorrected fast Fourier transform (pFFT) accelerated boundary element method (BEM) for large-scale transient elastodynamic analysis is developed and described in this paper. The frequency-domain approach is used. To overcome the ‘wrap-around’ problem associated with the discrete Fourier transform, the exponential window method (EWM) is employed and incorporated in the frequency-domain BEM. An improved implementation scheme of the pFFT method based on polynomial interpolation technique is developed and applied to accelerate the elastodynamic BEM. This new scheme reduces the memory required to save the convolution matrix by a factor of 8. To further improve the efficiency of the code, a newly developed linear system solver based on the induced dimension reduction method is employed. Its performance is investigated and compared with that of the well-known GMRES. The accuracy and computational efficiency of the method are evaluated and demonstrated by three examples: a classical benchmark, a plate subject to an impact loading and a porous cube with nearly half million DOFs subject to a step traction loading. Both analytical and experimental results are employed to validate the method. It has been found that the EWM can effectively resolve the wrap-around problem and accurate time responses for an arbitrarily chosen time period can be obtained. Copyright © 2011 John Wiley & Sons, Ltd.

A new enriched weight function for meshless methods is proposed for the numerical treatment of multiple arbitrary cracks in two dimensions. The main novelty consists in modifying the weight function with an intrinsic enrichment which is discontinuous over the finite length of the crack, represented by a segment, but continuous all around the crack tips. An analytical function is used to introduce discontinuities that are incorporated in the kernel in a simple, multiplicative manner.

The resulting method allows a more straightforward implementation and simulation of the presence of multiple cracks, crack branching and crack propagation in a meshless framework without using any of the existing algorithms such as visibility, transparency, and diffraction and without using additional unknowns and additional equations for the evolution of the level-sets, as in extrinsic partition of unity-based methods.

Stress intensity factors calculated using the J-integral demonstrate excellent agreement with analytical solutions for classical fracture mechanics benchmarks. Copyright © 2011 John Wiley & Sons, Ltd.

This paper is concerned with stochastic boundary value problems (SBVPs) whose formulation involves inequality constraints. A class of stochastic variational inequalities (SVIs) is defined, which is well adapted to characterize the solution of specified inequality-constrained SBVPs. A methodology for solving such SVIs is proposed, which involves their discretization by projection onto polynomial chaos and collocation of the inequality constraints, followed by the solution of a finite-dimensional constrained optimization problem. Simulation studies in contact and elastoplasticity are provided to demonstrate the proposed framework. Copyright © 2011 John Wiley & Sons, Ltd.

A new Lagrangian particle method called the consistent particle method (CPM), which solves the Navier–Stokes equations in a semi-implicit time stepping scheme, is proposed in this paper. Instead of using kernel function as in some particle methods, partial differential operators are approximated in a way consistent with Taylor series expansion. A boundary particle recognition method is applied to help define the changing liquid domain. The incompressibility condition of free surface particles is enforced by an adjustment scheme. With these improvements, the CPM is shown to be robust and accurate in long time simulation of free surface flow particularly for smooth pressure solution. Two types of free surface flow problems are presented to verify the CPM, that is, two-dimensional dam break and liquid sloshing in a rectangular tank. In the dam break example, the CPM solutions of pressure and wave elevation are in good agreement with published experimental results. In addition, an experimental study of water sloshing in tank on a shake table was conducted to verify the CPM solutions. Copyright © 2011 John Wiley & Sons, Ltd.

This paper discusses higher-order extended finite element methods (XFEMs) obtained from the combination of the standard XFEM with higher-order FEMs. Here, the focus is on the embedding of the latter into the partition of unity method, which is the basis of the XFEM. A priori error estimates are discussed, and numerical verification is given for three benchmark problems. Moreover, methodological aspects, which are necessary for hp-adaptivity in XFEM and allow for exponential convergence rates, are summarized. In particular, the handling of hanging nodes via constrained approximation and an hp-adaptive strategy are presented. Copyright © 2011 John Wiley & Sons, Ltd.

A new Petrov–Galerkin (PG) method involving two parameters, namely α₁ and α₂, is presented, which yields the following schemes on rectangular meshes: (i) a compact stencil obtained by the linear interpolation of the Galerkin FEM and the classical central finite difference method (FDM), should the parameters be equal, that is, α₁ = α₂ = α; and (ii) the nonstandard compact stencil presented in (Int. J. Numer. Meth. Engng 2011; 86:18–46) for the Helmholtz equation if the parameters are distinct, that is, α₁ ≠ α₂. The nonstandard compact stencil is obtained by taking the linear interpolation of the diffusive terms (specified by α₁) and the mass terms (specified by α₂) that appear in the stencils obtained by the standard Galerkin FEM and the classical central FDM, respectively. On square meshes, these two schemes were shown to provide solutions to the Helmholtz equation that have a dispersion accuracy of fourth and sixth order, respectively (Int. J. Numer. Meth. Engng 2011; 86:18–46). The objective of this paper is to study the performance of this PG method for the Helmholtz equation using nonuniform meshes and the treatment of natural boundary conditions. Copyright © 2011 John Wiley & Sons, Ltd.

It is well known that use of standard penalty methods can decrease the critical time step of time domain dynamic finite element analyses. The bipenalty method utilises both stiffness and mass penalties to impose constraints that have a minimal effect on the eigenfrequencies of the finite element system. One way of achieving this goal is to find a ratio of stiffness and mass penalty parameters—the critical penalty ratio (CPR)—that does not affect the maximum eigenfrequency (and therefore, for conditionally stable solution schemes, the critical time step) of a system. In this contribution, we develop a new method of calculating the CPR associated with a finite element formulation by examining the eigenvalue problem in detail. Advantages of the method compared with previous solutions include increased simplicity and generality and the ability to consider multiple constraints. The method is demonstrated by deriving CPRs for a few finite element formulations, which are then verified using simple numerical examples. The superiority of the bipenalty method over standard mass penalty methods is also demonstrated. Copyright © 2011 John Wiley & Sons, Ltd.

Steel fiber reinforced concrete (SFRC) allows overcoming brittleness and weakness under tension, the main drawbacks of plain concrete. The influence of the fibers on the behavior of SFRC depends on their shape, length, slenderness, and also on their orientation and distribution into the plain concrete. The goal of this paper is to develop an ad hoc numerical strategy to account for the contribution of the fibers in the simulation of the mechanical response of SFRC. In the model presented, the individual fibers immersed in the concrete bulk are accounted for in their actual location and orientation. The selected approach is based on the ideas introduced in the immersed boundary (IB) methods. These methods were developed to account for 1D (or 2D) solids immersed in 2D (or 3D) fluids. Here, the concrete bulk is playing the role of the fluid and the cloud of steel fibers is acting as the immerse boundary (that is, a 1D structure in a 2D or 3D continuous). Thus, the philosophy of the IB methodology is used to couple the behavior of the two systems, the concrete bulk and fiber cloud, precluding the need of matching finite element meshes. Note that, considering the different size scales and the intricate geometry of the fiber cloud, the conformal matching of the meshes would be a restriction resulting in a practically unaffordable mesh.

In the proposed approach, the meshes of the concrete bulk and fiber cloud are independent, and the models are coupled imposing displacement compatibility and equilibrium of the two systems. In the applications presented here, the concrete bulk is modeled using a standard nonlinear damage model. The constitutive model for the fibers is designed to account for the complex interaction between fibers and concrete. The fiber models are based on the previous investigations describing the concrete-fiber interaction and its dependence on the factors identified to be relevant: shape of the fiber (straight or hooked) and angle between the fiber and crack plane. Copyright © 2011 John Wiley & Sons, Ltd.

The present paper investigates the performance of a shifted factorized sparse approximate inverse as a parallel preconditioner for the iterative solution to the linear systems arising in the finite element discretization of non-linear groundwater flow models. The shift strategy is based on an inexpensive preconditioner update exploiting the structure of the coefficient matrix. The proposed algorithm is experimented with in the parallel simulation of a large-scale real multi-aquifer system characterized by a stochastic distribution of the hydraulic conductivity. The numerical results show that the shifted factorized sparse approximate inverse algorithm may yield an overall computational gain up to 300% with respect to the non-shifted scheme with an excellent parallel efficiency. Copyright © 2011 John Wiley & Sons, Ltd.

We develop both stable and stabilized methods for imposing Dirichlet constraints on embedded, three-dimensional surfaces in finite elements. The stable method makes use of the vital vertex algorithm to develop a stable space for the Lagrange multipliers together with a novel discontinuous set of basis functions for the multiplier field. The stabilized method, on the other hand, follows a Nitsche type variational approach for three-dimensional surfaces. Algorithmic and implementational details of both methods are provided. Several three-dimensional benchmark problems are studied to compare and contrast the accuracy of the two approaches. The results indicate that both methods yield optimal rates of convergence in various quantities of interest, with the primary differences being in the surface flux. The utility of the domain integral for extracting accurate surface fluxes is demonstrated for both techniques. Copyright © 2011 John Wiley & Sons, Ltd.

This paper considers the inverse problem in electrical impedance tomography with non-informative prior information on the required conductivity function. The problem is approached with a Newton-type iterative algorithm where the solution of the linearized approximation is estimated using Bayesian inference. The novelty of this work focuses on maximum a posteriori estimation assuming a model that incorporates the linearization error as a random variable. From an analytical expression of this term, we employ Monte Carlo simulation in order to characterize its probability distribution function. This simulation entails sampling an improper prior distribution for which we propose a stable scheme on the basis of QR decomposition. The simulation statistics show that the error on the linearized model is not Gaussian, however, to maintain computational tractability, we derive the posterior probability density function of the solution by imposing a Gaussian kernel approximation to the error density. Numerical results obtained through this approach indicate the superiority of the new model and its respective maximum a posteriori estimator against the conventional one that neglects the impact of the linearization error. Copyright © 2011 John Wiley & Sons, Ltd.

In order to study the interaction of sloshing and structural vibrations of baffled tanks, a reduced order model based on modal analysis of structure model and boundary element method for fluids motion is developed. For this purpose, the governing equations of elastic structure and incompressible flow are used to derive simple models to simulate both fields. Using the modal analysis technique, the structural motions are applied to the fluid model and on the other hand by using boundary element method, the fluid loads are applied to the structural model. Based on this formulation, a code is developed which is applicable to an arbitrary elastic tank with arbitrary arrangement of baffles. The obtained results are validated with literature data and then the effects of baffle flexibility on the sloshing frequencies and structural vibration frequencies are investigated. Copyright © 2011 John Wiley & Sons, Ltd.

In the present work, an isogeometric contact analysis scheme using mortar method is proposed. Because the isogeometric analysis is employed for contact analysis, the geometric exactness of the contact region is maintained without any loss of geometric data because of geometry approximation. Thus, the proposed method can overcome underlying shortcomings that result from the geometric approximation of contact surfaces in the conventional finite element (FE)-based contact analysis. For an isogeometric contact analysis, the schemes for treating the contact conditions and detecting the real contact surfaces are essentially required. In the proposed method, the mortar method is adopted as a nonconforming contact treatment scheme because it is expected to be in good harmony with the useful characteristics of nonuniform rational B-spline A new matching algorithm is proposed to combine the mortar method with the isogeometric analysis to guarantee consistent contact surface information with the nonuniform rational B-spline curve. The present scheme is verified by patch test and the well-known problems which have theoretical solutions such as interference fit and the Hertzian contact problem. It is shown that the problems with curved contact surfaces which are difficult to treat by conventional approaches can be easily dealt with. Copyright © 2011 John Wiley & Sons, Ltd.

A method for two-dimensional and three-dimensional crack propagation that combines the advantages of explicit and implicit crack descriptions is presented. An implicit description in the frame of the level set method is advantageous for the simulation within the extended finite element method (XFEM). The XFEM has proven its potential in fracture mechanics as it provides accurate solutions without any remeshing during the crack simulation. On the other hand, an explicit representation of the crack, for example, by means of a polyhedron, enables a simple update of the crack during the propagation. A key aspect in the proposed method is the introduction of three level set functions that are computed exactly from the explicit representation. These functions imply a coordinate system at the crack front and serve as a basis for the enrichment. Furthermore, a simple model for the crack propagation is presented. One of the biggest achievements of the proposed method is that two-dimensional and three-dimensional crack simulations are treated in a consistent manner. That is, the extension from two to three dimensions is truly straightforward. Copyright © 2011 John Wiley & Sons, Ltd.

A previous technique for recovering equilibrated stresses from compatible finite element models of structural mechanics problems is extended to cover those cases where the partitioned loads applied to star patches are not initially balanced, regarding rotational equilibrium. The residual moments are removed by adding a suitable corrective stress field to the compatible one before deriving the fictitious body forces. Corrective stress fields are determined by solving another set of local problems based on subdomains that each contain elements forming a neighbourhood of a loaded kernel element. The conditions for the existence of a solution of these problems are studied for simplicial elements. The parameters that control the extended technique are assessed from numerical tests on a variety of two-dimensional linear elastic problems based on constant strain elements for the compatible solutions. These tests are presented in the context of computing bounds on quantities of interest such as total strain energy and local reactions and displacements. Copyright © 2011 John Wiley & Sons, Ltd.

It is recognized that the convergence of FFT-based iterative schemes used for computing the effective properties of elastic composite materials drastically depends on the contrast between the phases. Particularly, the rate of convergence of the strain-based iterative scheme strongly decreases when the composites contain very stiff inclusions and the method diverges in the case of rigid inclusions. Reversely, the stress-based iterative scheme converges rapidly in the case of composites with very stiff or rigid inclusions but leads to low convergence rates when soft inclusions are considered and to divergence for composites containing voids. It follows that the computation of effective properties is costly when the heterogeneous medium contains simultaneously soft and stiff phases. Particularly, the problem of composites containing voids and rigid inclusions cannot be solved by the strain or the stress-based approaches. In this paper, we propose a new polarization-based iterative scheme for computing the macroscopic properties of elastic composites with an arbitrary contrast which is nearly as simple as the basic schemes (strain and stress-based) but which has the ability to compute the overall properties of multiphase composites with arbitrary elastic moduli, as illustrated through several examples. Copyright © 2011 John Wiley & Sons, Ltd.

A hybrid multiscale framework is presented, which processes the material scales in a concurrent manner, borrowing features from hierarchical multiscale methods. The framework is used for the analysis of non-linear heterogeneous materials and is capable of tackling strain localization and failure phenomena. Domain decomposition techniques, such as the finite element tearing and interconnecting method, are used to partition the material in a number of non-overlapping domains and adaptive refinement is performed at those domains that are affected by damage processes. This refinement is performed in terms of material scale and finite element size. It is verified that the results are independent of the chosen domain decomposition. Moreover, the multiscale analyses are validated with reference solutions obtained with a full fine-scale solution procedure. Copyright © 2011 John Wiley & Sons, Ltd.

This paper deals with the formulation and numerical implementation of a fully coupled continuum model for deformation–diffusion in linearized elastic solids. The mathematical model takes into account the effect of the deformation on the diffusion process, and the affect of the transport of an inert chemical species on the deformation of the solid. We then present a robust computational framework for solving the proposed mathematical model, which consists of coupled non-linear partial differential equations. It should be noted that many popular numerical formulations may produce unphysical negative values for the concentration, particularly, when the diffusion process is anisotropic. The violation of the non-negative constraint by these numerical formulations is not mere numerical noise. In the proposed computational framework, we employ a novel numerical formulation that will ensure that the concentration of the diffusant be always snon-negative, which is one of the main contributions of this paper. Representative numerical examples are presented to show the robustness, convergence, and performance of the proposed computational framework. Another contribution of this paper is to systematically study the affect of transport of the diffusant on the deformation of the solid and vice versa, and their implication in modeling degradation/healing of materials. We show that the coupled response is both qualitatively and quantitatively different from the uncoupled response. Copyright © 2011 John Wiley & Sons, Ltd.

In this paper, the dual boundary element method is combined with a multiregion formulation to simulate plate assembly undergoing large deflection. The incremental load approach is used to treat the geometrical nonlinearity, and radial basis functions are used to approximate the derivatives of the large deflection terms. The dual reciprocity method is used to transfer all the domain integrals to the boundary. Once the solution at the boundary is obtained for the assembly, a J −integral for large deflection is implemented to extract the fracture parameters. Copyright © 2011 John Wiley & Sons, Ltd.

Computational issues concerning the calculation of acoustic responses of a complex finite element (FE) model for various noise and vibration inputs have become prevalent. Such a model requires a significant amount of computation time because of repeated inversions of dynamic stiffness matrices. Thus, even state-of-the-art computer hardware and software often face limitations where a model order reduction (MOR) scheme can help. The established MOR schemes such as Ritz vector or quasi-static Ritz vector methods are efficient for general engineering systems, but these MOR methods become inaccurate for frequency response analyses in some acoustic systems with frequency-dependent mass and stiffness matrices and force vectors (hereinafter frequency-dependent acoustic systems). To cope with the inaccurate prediction by these methods for frequency-dependent acoustic systems, this research presents and applies the multifrequency quasi-static Ritz vector method. Unlike the Ritz vector or quasi-static Ritz vector methods, the present multifrequency quasi-static Ritz vector method employs direct Krylov subspace bases without an orthonormal procedure at multiple center frequencies. In comparison with the existing MOR scheme, a significant gain in computational efficiency is achieved, as well as enhanced accuracy. A comparison of these methods based on criteria such as efficiency, accuracy, and reliability was also conducted.Copyright © 2011 John Wiley & Sons, Ltd.

The finite cell method (FCM) combines the fictitious domain approach with the p-version of the finite element method and adaptive integration. For problems of linear elasticity, it offers high convergence rates and simple mesh generation, irrespective of the geometric complexity involved. This article presents the integration of the FCM into the framework of nonlinear finite element technology. However, the penalty parameter of the fictitious domain is restricted to a few orders of magnitude in order to maintain local uniqueness of the deformation map. As a consequence of the weak penalization, nonlinear strain measures provoke excessive stress oscillations in the cells cut by geometric boundaries, leading to a low algebraic rate of convergence. Therefore, the FCM approach is complemented by a local overlay of linear hierarchical basis functions in the sense of the hp-d method, which synergetically uses the h-adaptivity of the integration scheme. Numerical experiments show that the hp-d overlay effectively reduces oscillations and permits stronger penalization of the fictitious domain by stabilizing the deformation map. The hp-d-adaptive FCM is thus able to restore high convergence rates for the geometrically nonlinear case, while preserving the easy meshing property of the original FCM. Accuracy and performance of the present scheme are demonstrated by several benchmark problems in one, two, and three dimensions and the nonlinear simulation of a complex foam sample. Copyright © 2011 John Wiley & Sons, Ltd.

The aim of the present work is to develop a new finite element model for the finite strain analysis of plate structures constituted of shape memory alloy (SMA) material. A three-dimensional constitutive model for shape memory alloys able to reproduce the special thermomechanical behavior of SMA characterized by pseudoelasticity and shape memory effects is adopted. The finite strain constitutive model is thermodynamically consistent and is completely formulated in the reference configuration. A two-dimensional plate theory is proposed based on a tensor element shape function formulation. The displacement field is expressed in terms of increasing powers of the transverse coordinate. The equilibrium statement is formulated on the basis of the virtual displacement principle in a total Lagrangian format. The proposed displacement formulation is particularly suitable for the simple derivation of high-order finite elements. Numerical applications are performed to assess the efficiency and locking performance of the proposed plate finite element. Some additional numerical examples are carried out to study the accuracy and robustness of the proposed computational technique and its capability of describing the structural response of SMA devices. Copyright © 2011 John Wiley & Sons, Ltd.

Multi-scale modeling frequently relies on microstructural representative volume elements (RVEs) on which macroscopic deformation is imposed through kinematical boundary conditions. A particular choice of these boundary conditions may influence the obtained effective properties. For strain localization and damage analyses, the RVE is pushed beyond the limits of its representative character, and the applied boundary conditions have a significant impact on the onset and the type of macroscopic material instability to be predicted.

In this article, we propose a new type of boundary conditions for microstructural volume elements, called percolation-path-aligned boundary conditions. Intrinsically, these boundary conditions capture the constraining effect of the material surrounding the RVE upon developing localization bands. The alignment with evolving localization bands allows the highly strained band to cross the RVE and fully develop with minimal interference of the applied boundary conditions. For an illustration of the performance of the newly proposed boundary conditions, macroscopic deformation has been imposed on a voided elasto-plastic RVE using different types of boundary conditions. It is observed that the new RVE boundary conditions provide a good estimate for the effective stiffness, are not susceptible to spurious localization, and permit the development of a full strain localization band up to failure. Copyright © 2011 John Wiley & Sons, Ltd.

A simple explicit–implicit finite element tearing and interconnecting (FETI) algorithm (AFETI-EI algorithm) is presented for partitioned transient analysis of linear structural systems. The present algorithm employs two decompositions. First, the total system is partitioned via spatial or domain decomposition to obtain the governing equations of motions for each partitioned domain. Second, for each partitioned subsystem, the governing equations are modally decomposed into the rigid-body and deformational equations. The resulting rigid-body equations are integrated by an explicit integrator, for its stability is not affected by step-size restriction on account of zero-frequency contents (ω  =  0). The modally decomposed partitioned deformation equations of motion are integrated by an unconditionally stable implicit integration algorithm. It is shown that the present AFETI-EI algorithm exhibits unconditional stability and that the resulting interface problem possesses the same solution matrix profile as the basic FETI static problems. The present simple dynamic algorithm, as expected, falls short of the performance of the FETI-DP but offers a similar performance of implicit two-level FETI-D algorithm with a much cheaper coarse solver; hence, its simplicity may offer relatively easy means for conducting parallel analysis of both static and dynamic problems by employing the same basic scalable FETI solver, especially for research-mode numerical experiments. Copyright © 2011 John Wiley & Sons, Ltd.

Finite elements providing a C¹ continuous interpolation are useful in the numerical solution of problems where the underlying partial differential equation is of fourth order, such as beam and plate bending and deformation of strain-gradient-dependent materials. Although a few C¹ elements have been presented in the literature, their development has largely been heuristic, rather than the result of a rational design to a predetermined set of desirable element properties. Therefore, a general procedure for developing C¹ elements with particular desired properties is still lacking.

This paper presents a methodology by which C¹ elements, such as the TUBA 3 element proposed by Argyris et al., can be constructed. In this method (which, to the best of our knowledge, is the first one of its kind), a class of finite elements is first constructed by requiring a polynomial interpolation and prescribing the geometry, the location of the nodes and the possible types of nodal DOFs. A set of necessary conditions is then imposed to obtain appropriate interpolations. Generic procedures are presented, which determine whether a given potential member of the element class meets the necessary conditions. The behaviour of the resulting elements is checked numerically using a benchmark problem in strain-gradient elasticity. Copyright © 2011 John Wiley & Sons, Ltd.

This paper describes a novel upper-bound formulation of limit analysis. This formulation is an innovative variant of an existing two-field mixed formulation based on the augmented Lagrangian method also developed by the authors. A natural approach is used to describe the deformation of each finite element. Furthermore, and in contrast to the previous formulation, two independent field approximations are now both used to define the velocity field, defined globally and at element level. It is shown that this feature allows a governing system of uncoupled linear equations to be obtained. Some numerical examples in plane strain conditions are presented in order to illustrate the current model performance. In conclusion, the potential and advantages of this new approach are discussed. Copyright © 2011 John Wiley & Sons, Ltd.

A finite element analysis of implant positioning inside a bone requires the creation of many meshes that model various implant orientations. This process can be very labour intensive and is difficult to automate. In order to facilitate this type of modelling, we present a large sliding contact algorithm that does not require the creation of a conforming discretization for the bone. The cavity inside the bone, necessary to accommodate the implant, is modelled with a Heaviside function calculated on the level set field, which is defined in terms of material coordinates of the bone. The algorithm is based on the minimization of the energy functional with a constraint term, formulated as in classical contact mechanics; however, instead of the distance function, we use the above-mentioned level set function. The presented numerical 2D and 3D examples validate the algorithm against the solutions obtained with commercial finite element software. Copyright © 2011 John Wiley & Sons, Ltd.

In the last decade, metamaterials have been gaining attention and have been investigated because of their unique characteristics, which conventional materials do not have, such as negative refraction indexes. However, it is sometimes difficult to design metamaterials on the basis of experience and theoretical considerations because the relationship between their electromagnetic characteristics and structure is often vague. A mathematical structural design methodology targeting metamaterials may therefore be useful for expanding the engineering applications of metamaterials in industry. In this paper, a new level set-based topology optimization method is proposed for designing composite right- and left-handed transmission lines, each of which consists of a waveguide and periodically located dielectric resonators. Such transmission lines function as a fundamental metamaterial. In the proposed method, the shape and topology of the dielectric resonators are represented by the level set function, and topology optimization problems are formulated on the basis of the level set-based representation. Copyright © 2011 John Wiley & Sons, Ltd.

This paper presents a new model order reduction strategy for flexible multibody simulation, namely the Subsystem Global Modal Parameterization. The proposed method is based on a system-level reduction technique, named Global Modal Parameterization, but offers significant improvements for systems with many independent DOFs. The approach splits up the motion of a mechanism or part of a mechanism into a relative motion, in which the members move relatively with respect to each other, and a global motion of the system, in which the relative position of the members does not change. The relative motion is described by a local Global Modal Parameterization model expressed in a mechanism-attached frame, and the global motion is described by the motion of the mechanism-attached frame. In order to improve simulation efficiency, mass invariants are used, which are also introduced in this paper. Two numerical examples are presented, which show the good accuracy and the major simulation efficiency improvements this new approach offers. Copyright © 2011 John Wiley & Sons, Ltd.

A novel approach based on a combination of isogeometric analysis (IGA) and extended FEM is presented for fracture analysis of structures. The extended isogeometric analysis is capable of an efficient analysis of general crack problems using nonuniform rational B-splines as basis functions for both the solution field approximation and the geometric description, and it can reproduce crack tip singular fields and discontinuity across a crack. IGA has attracted a lot of interest for solving different types of engineering problems and is now further extended for the analysis of crack stability and propagation in two-dimensional isotropic media. Concepts of the extended FEM are used in IGA to avoid the necessity of remeshing in crack propagation problems and to increase the solution accuracy around the crack tip. Crack discontinuity is represented by the Heaviside function and isotropic analytical displacement fields near a crack tip are reproduced by means of the crack tip enrichment functions. Also, the Lagrange multiplier method is used to impose essential boundary conditions. Moreover, the subtriangles technique is utilized for improving the accuracy of integration by the Gauss quadrature rule. Several two-dimensional static and quasi-static crack propagation problems are solved to demonstrate the efficiency of the proposed method and the results of mixed-mode stress intensity factors are compared with analytical and extended FEM results. Copyright © 2011 John Wiley & Sons, Ltd.

This paper presents a comparative study for the weakly compressible (WCSPH) and incompressible (ISPH) smoothed particle hydrodynamics methods by providing numerical solutions for fluid flows over an airfoil and a square obstacle. Improved WCSPH and ISPH techniques are used to solve these two bluff body flow problems. It is shown that both approaches can handle complex geometries using the multiple boundary tangents (MBT) method, and eliminate particle clustering-induced instabilities with the implementation of a particle fracture repair procedure as well as the corrected SPH discretization scheme. WCSPH and ISPH simulation results are compared and validated with those of a finite element method (FEM). The quantitative comparisons of WCSPH, ISPH and FEM results in terms of Strouhal number for the square obstacle test case, and the pressure envelope, surface traction forces, and velocity gradients on the airfoil boundaries as well as the lift and drag values for the airfoil geometry indicate that the WCSPH method with the suggested implementation produces numerical results as accurate and reliable as those of the ISPH and FEM methods. Copyright © 2011 John Wiley & Sons, Ltd.

Recently, numerous modified versions of immune algorithms (IAs) have been adopted in both theoretical and practical applications. However, few have been proposed for solving structural topology optimization problems. In addition, the design connectivity handling and one-node connected hinge prevention, which are vital in the application of population-based methods with binary representation for structural topology optimization, have not been applied to IAs in the literature. A stress-enhanced clonal selection algorithm (SECSA) incorporating an IA with a dominance-based constraint-handling technique and a new stress-enhanced hypermutation operator is proposed to rectify those deficiencies. To demonstrate the high viability of the presented method, comparisons between the presented SECSA and genetic algorithm-based methods were made on minimum compliance and minimum weight benchmark structural topology design problems in two-dimensional, three-dimensional, and multiloading cases. In each case, SECSA was shown to be competitive in terms of convergence speed and solution quality. The main goal of this study is not only to further explore the capabilities of IAs, but also to show that an IA with appropriate enhancements can lead to the development of attractive computational tools for global search in structural topology optimization. Copyright © 2011 John Wiley & Sons, Ltd.

In this study, an immersed boundary (IB) method based on a direct forcing is coupled with a high-order weighted-essentially non-oscillatory (WENO) scheme to simulate fluid–solid interaction (FSI) problems with complex geometries. The IB is a general simulation method for FSI, whereas the WENO is an efficient scheme for fluid flow simulations and shock waves, and both of them work on regular cartesian grids. The effectiveness and the accuracy of the coupled scheme are first analyzed on well-documented supersonic test problems for a wide range of Mach numbers. The results are in good agreement with both analytical and experimental data. A comprehensive analysis of the interaction of the moving shock through an array of cylinder matrix is then conducted by varying the number of cylinders in the matrix block while keeping the same opening passage. The relaxation length between two adjacent columns of cylinders is kept identical to study uniquely the effect of surface-to-volume ratio of the obstacle matrix. It is shown that the configuration with higher surface-to-volume ratio produces more post-shock flow instabilities downstream of the matrix block. The complex shock/shock and shock/vortex interactions are well resolved by the present computation. It is being observed that after the passage of the shock through the cylinder matrix, eddies of different length scales are generated, but the later stage of shock/vortex and shocklet/vortexlet interactions are different for the two cases. The analysis of the PSD of the total kinetic energy globally conforms to Richardson's inviscid cascade. An intermittent peaked PDF of downstream instantaneous vorticity field is obtained in the limit of Re →  ∞ . The baroclinic production of vorticity is found to be feeble as previously founded by Sun and Takayama (J. Fluid Mech. 2003; 478:237–256). Copyright © 2011 John Wiley & Sons, Ltd.

A new generalized FEM is introduced for solving problems with discontinuous gradient fields. The method relies on enrichment functions associated with generalized degrees of freedom at the nodes generated from the intersection of the phase interface with element edges. The proposed approach has several advantages over conventional generalized FEM formulations, such as a lower computational cost, easier implementation, and straightforward handling of Dirichlet boundary conditions. A detailed convergence study of the proposed method and a comparison with the standard FEM are presented for heat transfer problems. The method achieves the optimal rate of convergence using meshes that do not conform to the interfaces present in the domain while achieving a level of accuracy comparable to that of the standard FEM with conforming meshes. Various application problems are presented, including the conjugate heat transfer problem encountered in microvascular materials. Copyright © 2011 John Wiley & Sons, Ltd.

Meshfree methods (MMs) such as the element free Galerkin (EFG)method have gained popularity because of some advantages over other numerical methods such as the finite element method (FEM). A group of problems that have attracted a great deal of attention from the EFG method community includes the treatment of large deformations and dealing with strong discontinuities such as cracks. One efficient solution to model cracks is adding special enrichment functions to the standard shape functions such as extended FEM, within the FEM context, and the cracking particles method, based on EFG method.

It is well known that explicit time integration in dynamic applications is conditionally stable. Furthermore, in enriched methods, the critical time step may tend to very small values leading to computationally expensive simulations. In this work, we study the stability of enriched MMs and propose two mass-lumping strategies. Then we show that the critical time step for enriched MMs based on lumped mass matrices is of the same order as the critical time step of MMs without enrichment. Moreover, we show that, in contrast to extended FEM, even with a consistent mass matrix, the critical time step does not vanish even when the crack directly crosses a node. Copyright © 2011 John Wiley & Sons, Ltd.

Peridynamics is a theory of continuum mechanics expressed in forms of integral equations rather than partial differential equations. In this paper, a peridynamics code is implemented using a graphics processing unit for highly parallel computation, and numerical studies are conducted to investigate the responses of brittle and ductile material models. Stress–strain behavior with different grid sizes and horizons is studied for a brittle material model. A comparison of stresses and strains between finite element analysis (FEA) and peridynamic solutions is performed for a ductile material. By applying the proposed procedure to bridge the material model defined for peridynamic bonds and the corresponding macroscale material model for FEA, peridynamics and FEA show good agreements as regards the stresses and strains. Copyright © 2011 John Wiley & Sons, Ltd.

A Gurson-based constitutive model is presented, which includes non-linear mixed isotropic–kinematic hardening and creep, and allows the analysis of problems involving arbitrarily large plastic strains. This model was developed with the main objective of allowing, on the basis of a single set of material parameters, the numerical simulation of all the main features of cold metal forming processes, which usually imply severe loading–unloading cycles with very large plastic strains, difficult to be correctly reproduced numerically. A suitable integration scheme of the rate equations is described and implemented into a finite element code. The results obtained are compared with some reference experimental ones; an application of the model for the simulation of wire drawing processes is also presented. Copyright © 2011 John Wiley & Sons, Ltd.