ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
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Recently Published Articles
- Magnetohydrodynamic unsteady separated stagnation-point flow of a viscous fluid over a moving plate
Article first published online: 11 AUG 2015 | DOI: 10.1002/zamm.201400218
An analysis has been made for the unsteady separated stagnation-point (USSP) flow of an incompressible viscous and electrically conducting fluid over a moving surface in the presence of a transverse magnetic field. The unsteadiness in the flow field is caused by the velocity and the magnetic field, both varying continuously with time t. The effects of Hartmann number M and unsteadiness parameter β on the flow characteristics are explored numerically. Following the method of similarity transformation, we show that there exists a definite range of for a given M, in which the solution to the governing nonlinear ordinary differential equation divulges two different kinds of solutions: one is the attached flow solution (AFS) and the other is the reverse flow solution (RFS). We also show that below a certain negative value of β dependent on M, only the RFS occurs and is continued up to a certain critical value of β. Beyond this critical value no solution exists. Here, emphasis is given on the point as how long would be the existence of RFS flow for a given value of M. An interesting finding emerges from this analysis is that, after a certain value of M dependent on , only the AFS exists and the solution becomes unique. Indeed, the magnetic field itself delays the boundary layer separation and finally stabilizes the flow since the reverse flow can be prevented by applying the suitable amount of magnetic field. Further, for a given positive value of β and for any value of M, the governing differential equation yields only the attached flow solution.
- Modeling of passive and active external confinement of RC columns with elastic material
Theodoros C. Rousakis and Ioannis S. Tourtouras
Article first published online: 6 AUG 2015 | DOI: 10.1002/zamm.201500014
One of the most attractive applications of composite materials is their use as confining devices for concrete columns, which may result in remarkable increases of strength and ductility. The current investigation focuses on the modeling of reinforced concrete columns passively or actively confined by composites, under axial load. Furthermore, the research highlights the effectiveness and modeling of ultra high extension capacity fiber ropes implemented as external confining reinforcement so as to upgrade ductility and strength of concrete columns. It concerns columns of square cross-section with plain or steel reinforced concrete. The novel confining technique uses composite rope made of polypropylene fibers as passive or pretensioned reinforcement while it presents linear elastic behavior up to failure and is applied by hand. It may enable confined columns to dissipate enormous amounts of earthquake induced energy through concrete deformation. The proposed constitutive model is compared against available experimental results involving circular or square columns with passive or active FRP confinement.
- Metamodeling and robust minimization approach for the identification of elastic properties of composites by vibration method
Janis Auzins, Andris Chate, Rolands Rikards and Eduards Skukis
Article first published online: 6 AUG 2015 | DOI: 10.1002/zamm.201500008
This paper describes a method for determination of elastic parameters (elastic moduli and Poisson's ratio) of orthotropic composite plate-type structural elements using the results of natural frequency measurements. The identification of parameter values is provided by minimization of weighted squared difference (discrepancy) between physically measured frequencies and natural frequencies calculated by Finite Element Method. The metamodels for the frequency dependence on the elastic parameters and other geometrical and physical parameters of test specimens, including parameters with uncertainty (“noisy constants”) are built using experimental designs optimized according to the Mean Squared Error space filling criterion and third-order polynomial approximations. The minimum of weighted squared difference between measured and calculated frequencies is found using the multistart random search method. The expressions for standard deviations of identified parameters depending on deviations of “noisy constants” are derived using linearized metamodels. The expressions for identification errors allow the statement of the identification task as a robust minimization problem by simultaneous minimization of the discrepancy function and standard deviations of the identified values by varying the values of unknown elastic parameters and weighting coefficients for different frequencies. The partial scaling of natural frequencies is used for the reduction of the uncertainty impact on the identification error. This allows reducing the identification error of elastic moduli about two times and Poisson's ratio about 20 times in comparison with the results obtained by using dimensioned frequencies.
- Optimal control of the thickness of a rigid inclusion in equilibrium problems for inhomogeneous two-dimensional bodies with a crack
N. P. Lazarev
Article first published online: 6 AUG 2015 | DOI: 10.1002/zamm.201500128
The equilibrium problems for two-dimensional elastic body with a rigid delaminated inclusion are considered. In this case, there is a crack between the rigid inclusion and the elastic body. Non-penetration conditions on the crack faces are given in the form of inequalities. We analyze the dependence of solutions and derivatives of the energy functionals on the thickness of rigid inclusion. The existence of the solution to the optimal control problem is proved. For that problem the cost functional is defined by derivatives of the energy functional with respect to a crack perturbation parameter while the thickness parameter of rigid inclusion is chosen as the control function.
- Modeling the effects of material properties on the pull-in instability of nonlocal functionally graded nano-actuators
Hamid M. Sedighi, Farhang Daneshmand and Mohamadreza Abadyan
Article first published online: 20 JUL 2015 | DOI: 10.1002/zamm.201400160
Dynamic pull-in behavior of nonlocal functionally graded nano-actuators by considering Casimir attraction is investigated in this paper. It is assumed that the nano-bridge is initially at rest and the fundamental frequency of nano-structure as a function of system parameters is obtained asymptotically by Iteration Perturbation Method (IPM). The effects of actuation voltage, nonlocal parameter, properties of FGM materials and intermolecular force on the dynamic pull-in behavior are studied. It is exhibited that two terms in series expansions are adequate to achieve the acceptable approximations for fundamental frequency as well as the analytic solution. Comparison between the obtained results based on the asymptotic analysis and the reported experimental and numerical results in the literature, verify the effectiveness of the asymptotic analysis.