We show how we can exploit our recently proposed algorithms for the solution of contact problem of elasticity to the 2D analysis of the interfacial debonding of samples that consist of several fibres embedded in a homogeneous matrix, aligned in the longitudal direction. The performance of the algorithm is demonstrated on analysis of deformations of samples of the fibrous composite material.

Partial differential equations arise in formulations of problems involving functions of several variables such as the propagation of sound or heat, electrostatics, electrodynamics, fluid flow, and elasticity, etc. The present paper deals with a general introduction and classification of partial differential equations and the numerical methods available in the literature for the solution of part...

In this paper, the existence of a solution in the form of a minimizer or microstructure is established for the boundary value problems of nonlinear elasticity with certain nonconvex stored energy functions such as those of St. Venant-Kirchhoff type materials. Necessary and sufficient conditions for minimizing sequences of the potential energy to converge to a minimizer or to microstructure are ...

A solution for a class of two-dimensional elasticity problems concerning an isotropic body with an arc crack in its interior is obtained in terms of an integral taken around the exterior boundary of the body. A numerical procedure for solving this integral equation is outlined and numerical results for a test problem are given.

The vector-valued Allen-Cahn equations are combined with elasticity where a linear stress-strain relationship is assumed. A short physical derivation of the generalised model is given and global existence and uniqueness of the solution are shown under suitable growth conditions on the nonlinearity.

The The main objective of this research paper is to present 3-D elasticity solution for free vibration analysis of elastically supported continuously graded carbon nanotube-reinforced (CGCNTR) annular plates. The volume fractions of oriented, straight single-walled carbon nanotubes (SWCNTs) are assumed to be graded in the thickness direction. An equivalent continuum model based on the Eshelby-M...

The aim of this work is to present a nonstandard linear finite element method for a planar elasticity problem. The error for the solution computed with this method is estimated with respect to H 1 ×H 1-norm and second-order convergence is shown.  2001 IMACS. Published by Elsevier Science B.V. All rights reserved.

A ctitious domain method based on boundary Lagrange multipliers is proposed for linear elasticity problems in two dimensional domains. The solution of arising saddle-point problem is obtained iteratively using MINRES method with a positive deenite block diagonal preconditioner which is based on a fast direct solver for diiusion problems. Numerical experiments demonstrate the behavior of conside...

21  Abstract—This paper describes a numerical solution for plane elasticity problem. It includes algorithms for discretization by mixed finite element methods. The discrete scheme allows the utilization of Brezzi-Douglas-Fortin-Marini (BDFM2) for the stress tensor and piecewise linear elements for the displacement. The numerical results are compared with some previously published works or with...

h this paper, we use a generalized Fourier series to approximate the solution of a boundary value problem describing the torsion of an elliptic micropolar beam. We provide an example demonstrating the effect of material microstructure. @ 2004 Elsevier Ltd. All rights reserved. Keywords-Linear micropolar elasticity, Generalized Fourier series, Torsion, Material microstructure.