ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
Copyright © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Recently Published Articles
- On perturbation method in mechanical, thermal and thermo-mechanical loadings of plates: cylindrical bending of FG plates
F. Fallah, A. Nosier, M. Sharifi and F. Ghezelbash
Article first published online: 4 MAR 2015 | DOI: 10.1002/zamm.201400136
The performance of perturbation method in nonlinear analyses of plates subjected to mechanical, thermal, and thermo-mechanical loadings is investigated. To this end, cylindrical bending of FG plates with clamped and simply-supported edges is considered. The governing equations of Mindlin's first-order shear deformation theory with von Kármán's geometric nonlinearity are solved using one- and two-parameter perturbation methods and the results are compared with the results of an analytical solution. The material properties are assumed to vary continuously through the thickness of the plate according to a power-law distribution of the volume fraction of the constituents. It is shown that the accuracy of any-order expansion in perturbation method depends not only on the perturbation parameter, but also on the location chosen for the perturbation parameter and, in general, the solution becomes more accurate when the perturbation parameter is specified at the location where its corresponding response quantity is a maximum. Under thermal loading the possibility of using different parameters as the perturbation parameter for various boundary conditions is investigated. It is observed that, instead of a one-parameter perturbation method, a two-parameter perturbation method must be used in the thermal analysis of FG plates. Also, buckling and post-buckling behavior of FG plates in cylindrical bending is investigated. It is shown that under thermal loading, a bifurcation-type buckling occurs in clamped FG plates. In addition, a snap-through buckling may occur in simply-supported FG plates under thermo-mechanical loading.
- Dielectric signatures and interpretive analysis for changes of state in composite materials
Rassel Raihan, Kenneth Reifsnider, Dan Cacuci and Qianlong Liu
Article first published online: 4 MAR 2015 | DOI: 10.1002/zamm.201400226
A myriad of nondestructive interrogation methods have been developed to assess the initial and progressive integrity of composite materials, with varying degrees of success. Some frontiers, however, have stubbornly resisted this progress; the present paper addresses three of these by discussing our recent progress in the development and application of through-thickness dielectric methods for a wide range of heterogeneous materials. The first topic is the creation of a characterization method and interpretive analysis that can correctly reveal the process of distributed damage initiation and accumulation with non-dilute concentrations in heterogeneous structural composite materials, in contrast to more standard methods that focus on identifying individual flaws. The second topic is development of inverse and adjoint methods to enable the design of heterogeneous materials for specific dielectric responses. And the third topic is the development of a “current state method” for such materials that can provide measurements to predict the subsequent strength and life of individual specimens, in a manner that is somewhat analogous to a single crack analysis in homogeneous materials. The foundation for our discussion of those topics is through-thickness characterization of the low-frequency spectral dielectric response of composite materials to harmonic EMF signals. Successes and remaining challenges are discussed and opportunities for implementation identified.
- Non-periodic homogenization of infinitesimal strain plasticity equations
Martin Heida and Ben Schweizer
Article first published online: 4 MAR 2015 | DOI: 10.1002/zamm.201400112
We consider the Prandtl-Reuss model of plasticity with kinematic hardening, aiming at a homogenization result. For a sequence of coefficient fields and corresponding solutions , we ask whether we can characterize weak limits u when as . We assume neither periodicity nor stochasticity for the coefficients, but we demand an abstract averaging property of the homogeneous system on reference volumes. Our conclusion is an effective equation on general domains with general right hand sides. The effective equation uses a causal evolution operator Σ that maps strains to stresses; more precisely, in each spatial point x, given the evolution of the strain in the point x, the operator Σ provides the evolution of the stress in x.
- A singularly perturbed Neumann problem for the Poisson equation in a periodically perforated domain. A functional analytic approach
Massimo Lanza de Cristoforis and Paolo Musolino
Article first published online: 4 MAR 2015 | DOI: 10.1002/zamm.201400035
We consider a Neumann problem for the Poisson equation in the periodically perforated Euclidean space. Each periodic perforation has a size proportional to a positive parameter ε. For each positive and small ε, we denote by a suitably normalized solution. Then we are interested to analyze the behavior of when ε is close to the degenerate value , where the holes collapse to points. In particular we prove that if , then can be expanded into a convergent series expansion of powers of ε and that if then can be expanded into a convergent double series expansion of powers of ε and . Our approach is based on potential theory and functional analysis and is alternative to those of asymptotic analysis.
- Numerical solution of stochastic partial differential equations using a collocation method
Article first published online: 23 FEB 2015 | DOI: 10.1002/zamm.201400080
In this article we apply spectral collocation method to find a numerical solution of stochastic partial differential equations (SPDEs). Spectral collocation method is known to be impressively efficient for PDEs. We investigate this method for numerical solution of SPDEs and we obtain its rate of convergence. At first, the results are expressed for equations with globally Lipschitz coefficient, then we extend it to cases with locally Lipschitz coefficient. The analysis is supported by numerical results for some important SPDEs such as stochastic Kuramoto-Sivashinksy equation.