A new bilinear four-noded quadrilateral element (called quadrilateral linear refined zigzag) for the analysis of composite laminated and sandwich plates/shells based on the refined zigzag theory is presented. The element has seven kinematic variables per node. Shear locking is avoided by introducing an assumed linear shear strain field. The performance of the element is studied in several examples where the reference solution is the 3D finite element analysis using 20-noded hexahedral elements. Copyright © 2013 John Wiley & Sons, Ltd.
The present paper deals with the enrichment of 3D low-order finite elements. The used concept is based on the idea that a 3D virtual fiber, after a spatial rotation, introduces an enhancement of the strain field tensor approximation. A consistent stiffness matrix is obtained, allowing a better approximation of the actual solution compared with that resulting from low-order finite elements. Implemented for two eight-node hexahedral elements, the performance of the space fiber rotation concept is assessed by running some classical beam, plate, and shell benchmarks, and the obtained results are compared especially with those given by linear eight-node and quadratic 20-node hexahedral elements. In particular, it is shown that the developed elements accuracy is significantly superior to that of the classical eight-node hexahedral element and close to that of the classical 20-node hexahedral element. Copyright © 2013 John Wiley & Sons, Ltd.
This work is a first attempt to address efficient stabilizations of high dimensional advection–diffusion models encountered in computational physics. When addressing multidimensional models, the use of mesh-based discretization fails because the exponential increase of the number of degrees of freedom related to a multidimensional mesh or grid, and alternative discretization strategies are needed. Separated representations involved in the so-called proper generalized decomposition method are an efficient alternative as proven in our former works; however, the issue related to efficient stabilizations of multidimensional advection–diffusion equations has never been addressed to our knowledge. Thus, this work is aimed at extending some well-experienced stabilization strategies widely used in the solution of 1D, 2D, or 3D advection–diffusion models to models defined in high-dimensional spaces, sometimes involving tens of coordinates.Copyright © 2013 John Wiley & Sons, Ltd.
In this paper a coupled two-scale shell model is presented. A variational formulation and associated linearization for the coupled global–local boundary value problem is derived. For small strain problems, various numerical solutions are computed within the so-called FE 2 method. The discretization of the shell is performed with quadrilaterals, whereas the local boundary value problems at the integration points of the shell are discretized using 8-noded or 27-noded brick elements or so-called solid shell elements. At the bottom and top surface of the representative volume element stress boundary conditions are applied, whereas at the lateral surfaces the in-plane displacements are prescribed. For the out-of-plane displacements link conditions are applied. The coupled nonlinear boundary value problems are simultaneously solved within a Newton iteration scheme. With an important test, the correct material matrix for the stress resultants assuming linear elasticity and a homogeneous continuum is verified.Copyright © 2013 John Wiley & Sons, Ltd.
An isogeometric solid-like shell formulation is proposed in which B-spline basis functions are used to construct the mid-surface of the shell. In combination with a linear Lagrange shape function in the thickness direction, this yields a complete three-dimensional representation of the shell. The proposed shell element is implemented in a standard finite element code using Bézier extraction. The formulation is verified using different benchmark tests.Copyright © 2013 John Wiley & Sons, Ltd.
Hamiltonian models of high-velocity impact dynamics, based on a hybrid particle-element kinematic scheme, offer an energy conserving description of general contact-impact, perforation, and fragmentation physics with applications in a number of important engineering fields. Published work on these models has considered only a uniform finite element mesh, requiring curved surfaces and many target and projectile geometries to be represented in an approximate fashion. In recent research, the authors have developed a new formulation suitable for application to any solid model described by an unstructured hexahedral mesh. The formulation incorporates a new algorithm, which constructs an ellipsoidal particle discretization of the mass distribution described by a general hex mesh and a new density interpolation suitable for use with general ellipsoidal arrays whose particles vary in mass, shape, and spatial orientation. Application of the method in the simulation of high-velocity impact problems shows good agreement with experiment, for both smoothly graded and deliberately distorted hexahedral meshes. Copyright © 2013 John Wiley & Sons, Ltd.
In many space missions, expandable or reusable launch systems are used. In this context, the reliable design of liquid rocket engines (LREs) is a key issue. In the present paper, we present a novel combination of numerical schemes. It is applied to model the extreme physical phenomena a typical LRE undergoes during its loading cycles. The numerical scheme includes a partitioned fluid–structure interaction (FSI) algorithm in combination with a unified viscoplastic damage model. This allows the complex description of the material response under cyclic thermomechanical loading taking place in LREs. In this regard, we focus on the response of the cooling channel wall that is made from copper alloys. For the coupled FSI analysis, the individual domains of the rocket thrust chamber are modeled by a 3D parametrized approach. The well-established single field solver codes, DLR TAU for the hot gas and ABAQUS FE software for the structural domain, are coupled via the inhouse developed simulation environment ifls. Ifls provides the necessary algorithms for a partitioned coupling approach such as individual code steering, data interpolation, time integration and iteration control. Finally, the results of an FSI analysis of a complete engine cycle are presented. They show the potential of the new numerical scheme for the lifetime prediction of LREs.Copyright © 2013 John Wiley & Sons, Ltd.
A four-node corotational quadrilateral elastoplastic shell element is presented. The local coordinate system of the element is defined by the two bisectors of the diagonal vectors generated from the four corner nodes and their cross product. This local coordinate system rotates rigidly with the element but does not deform with the element. As a result, the element rigid-body rotations are excluded in calculating the local nodal variables from the global nodal variables. The two smallest components of each nodal orientation vector are defined as rotational variables, leading to the desired additive property for all nodal variables in a nonlinear incremental solution procedure. Different from other existing corotational finite-element formulations, the resulting element tangent stiffness matrix is symmetric owing to the commutativity of the local nodal variables in calculating the second derivative of strains with respect to these variables. For elastoplastic analyses, the Maxwell–Huber–Hencky–von Mises yield criterion is employed, together with the backward-Euler return-mapping method, for the evaluation of the elastoplastic stress state; the consistent tangent modulus matrix is derived. To eliminate locking problems, we use the assumed strain method. Several elastic patch tests and elastoplastic plate/shell problems undergoing large deformation are solved to demonstrate the computational efficiency and accuracy of the proposed formulation. Copyright © 2013 John Wiley & Sons, Ltd.
A formulation of a quadrilateral finite element with embedded strong discontinuity, suitable for the material failure numerical analysis of plane stress solids, is presented. The kinematics of standard finite element is enhanced by displacement jumps that vary linearly along the embedded discontinuity line. They are described by four kinematic parameters that are related to four element separation modes. The modes are designed for no stress transfer over the discontinuity line at its fully softened (opened) state. As for the material, the bulk of the element is assumed to be elastic, and the softening plasticity, in terms of discontinuity tractions and displacement jumps, is assumed along the discontinuity line. The bulk stresses are described by the optimal five-parameter interpolation. The combination of stress interpolation and enhanced kinematics yields simple form of the element stiffness matrix. To achieve efficient implementation, the stiffness matrix is statically condensed for both the enhanced kinematic parameters and the stress parameters. In a set of numerical examples, the performance of the derived element is illustrated. Obtained results are compared with some other representative embedded discontinuity quadrilateral elements (displacement-based and enhanced assumed strain based). It turns out that the element performs very well. Copyright © 2013 John Wiley & Sons, Ltd.
We propose a simple and efficient algorithm for FEM-based computational fracture of plates and shells with both brittle and ductile materials on the basis of edge rotation and load control. Rotation axes are the crack front nodes, and each crack front edge in surface discretizations affects the position of only one or two nodes. Modified positions of the entities maximize the modified mesh quality complying with the predicted crack path (which depends on the specific propagation theory in use). Compared with extended FEM or with classical tip remeshing, the proposed solution has algorithmic and generality advantages. The propagation algorithm is simpler than the aforementioned alternatives, and the approach is independent of the underlying element used for discretization. For history-dependent materials, there are still some transfer of relevant quantities between elements. However, diffusion of results is more limited than with tip or full remeshing. To illustrate the advantages of our approach, three prototype models are used: tip energy dissipation linear elastic fracture mechanics (LEFM), cohesive-zone approaches, and ductile fracture. Both the Sutton crack path criterion and the path estimated by the Eshelby tensor are employed. Traditional fracture benchmarks, including one with plastic hinges, and newly proposed verification tests are solved. These were found to be very good in terms of crack path and load ∕ deflection accuracy. Copyright © 2013 John Wiley & Sons, Ltd.
In this paper, we obtain explicit expressions to evaluate the derivatives of maximum-entropy (max-ent) basis function on the boundary of a convex domain. In the max-ent formulation, the basis functions are obtained by maximizing a concave functional subjected to linear constraints (reproducing conditions). In doing so, it is found that the Lagrange multipliers blow up when x ∈ ∂Ω, and the expressions for the derivatives of the max-ent basis functions in Ω are of an indeterminate form for points on ∂Ω. We appeal to l'Hôpital's rule to derive expressions to determine the derivatives of the basis functions. We consider the Shannon entropy functional and the relative entropy functional with different choices of the prior weight function. The first-order derivatives of all basis functions are bounded. In contrast, on an irregular grid with a certain nodal spacing, some of the second derivatives of the basis functions are unbounded on the boundary. Necessary and sufficient conditions on the priors to obtain bounded Lagrange multipliers are established. Optimal convergence rates for fourth-order problems are demonstrated for a Galerkin approach with a quadratically complete partition-of-unity enriched max-ent approximation.Copyright © 2013 John Wiley & Sons, Ltd.
This study developed an element-free Galerkin method (EFGM) to simulate notched anisotropic plates containing stress singularities at the notch tip. Two-dimensional theoretical complex displacement functions are first deduced into the moving least-squares interpolation. The interpolation functions and their derivatives are then determined to calculate the nodal stiffness using the Galerkin method. In the numerical validation, an interface layer of the EFGM is used to combine the mesh between the traditional finite elements and the proposed singular notch EFGM. The H-integral determined from finite element analyses with a very fine mesh is used to validate the numerical results of the proposed method. The comparisons indicate that the proposed method obtains more accurate results for the displacement, stress, and energy fields than those determined from the standard finite element method. Copyright © 2013 John Wiley & Sons, Ltd.