A novel hybrid finite element analysis of inplane singular elastic field around inclusion corners in elastic media

Abstract

a b s t r a c tThis paper deals with the inplane singular elastic field problems of inclusion corners in elastic media by an ad hoc hybrid-stress finite element method. A one-dimensional finite element method-based eigenanalysis is first applied to determine the order of singularity and the angular dependence of the stress and displacement field, which reflects elastic behavior around an inclusion corner. These numerical eigensolutions are subsequently used to develop a super element that simulates the elastic behavior around the inclusion corner. The super element is finally incorporated with standard four-node hybrid-stress elements to constitute an ad hoc hybrid-stress finite element method for the analysis of local singular stress fields arising from inclusion corners. The singular stress field is expressed by generalized stress intensity factors defined at the inclusion corner. The ad hoc finite element method is used to investigate the problem of a single rectangular or diamond inclusion in isotropic materials under longitudinal tension. Comparison with available numerical results shows the present method is an efficient mesh reducer and yields accurate stress distribution in the near-field region. As applications, the present ad hoc finite element method is extended to discuss the inplane singular elastic field problems of a single rectangular or diamond inclusion in anisotropic materials and of two interacting rectangular inclusions in isotropic materials. In the numerical analysis, the generalized stress intensity factors at the inclusion corner are systematically calculated for various material type, stiffness ratio, shape and spacing position of one or two inclusions in a plate subjected to tension and shear loadings.

Effective elastic properties of solids with irregularly shaped inclusions

“…The singularity orders k n and the eigenvectors q (n) are numerically solved from the following characteristic equation by the onedimensional finite element technique given by Sze and Wang (2000) as well as Chen and Ping (2008…”

“…in which P e 1 þe 2 represents the assemblage of elements belonging to wedge domain 1 and 2; k is eigenvalue (also called as singularity order) and q e eigenvector, MatricesP e ;Q e ; and " R e are referred to references (Sze and Wang 2000;Chen and Ping 2008).…”

“…Following the Hellinger-Reissner principle and our work (Chen and Ping 2008), we define the following hybrid functional for a specified mixed boundary value problem in a domain around the inclusion corner consisting of two sub-domains X 1 and X 2 , as shown in Fig. 3:…”

“…The reason is due to the fact that, in the standard four-node hybrid-stress finite element analysis and the conventional finite element analysis, relatively refined meshes are required to obtain the same as the accuracy of numerical solutions by the proposed method. Furthermore, the ad hoc hybridstress finite element approach is especially suitable for solving the elastic problems containing single or multiple singular points, for example, inclusion problems (Zhang and Katusbe 1995;Chen and Ping 2008).…”

Mixed Volume and Boundary Integral Equation Method with Elliptical Inclusions and a Circular/Elliptical Void

“…In addition, the VIEM is not sensitive to the geometry or concentration of the inclusions. Moreover, in contrast to the finite element method (FEM), where the full domain needs to be discretized, the VIEM requires discretization of the inclusions only [13,14].…”