A boundary value method for the singular behavior of bimaterial systems under inplane loading

Abstract

Based on the governing equations of linear elasticity, this paper develops a novel boundary value method to study the singular behavior of elastic stress fields at the corners of bimaterial wedges and junctions by using the eigenfunction expansion technique. The resulted one-dimensional differential system, which consists of the reduced equilibrium equations and boundary conditions, just relates to an angular coordinate in the polar coordinate system. Implementing discretization of this differential system by the finite cloud method, we readily derive the so-called generalized eigenproblem in the singular eigenvalue. The performance of the methodology is subsequently verified through the well-known crack and interface crack problems, demonstrating high accuracy and quick convergence characteristics. In addition, a selected set of practically useful models is numerically analyzed to examine the angular variations of the displacement and stress fields, and the influences of wedge-side boundary conditions to singular behavior are also studied.

Asymptotic fields near an interface corner in orthotropic bi-materials

“…Liu et al (1999) investigated the general problem of the spatial axisymmetric interface corner, by using the series expansion technique of separation of the variables in terms of power series, and obtained an eigenequation for the order of the stress singularity and the related displacement and singular stress fields near the interface corner. Recently, based on the governing equations of linear elasticity, Wang (2005) developed a novel boundary value method for computing the orders of the stress singularity and the associated singular stress fields at both the interface edge and the interface corner in isotropic bi-materials. Chen (1998) investigated the stress singularities at anisotropic multi-material interface edges and interface corners, based on the displacement and singular stress fields near the tip of an interface crack in anisotropic composites developed by Ting (1986) using the Stroh formulism.…”

A meshless approach to solving partial differential equations using the finite cloud method for the purposes of computer aided design

“…The The original authors of the FCM have since adapted the method to form a com bined BEM and FCM approach in stress and strain problems [25]. This combined approach was then modified with a novel BEM and a bimaterial system discretized and solved using the one dimensional FCM [26]. A combined approach has also been used to solve beam deflection and electrostat ics in MEMS structures.…”

“…Previously published uses for the FCM have focused on solving materially homogeneous problems, in particular for the Poisson equation [14,15,29]. As thus far seen, apart from a one dimensional quasi-inhomogeneous BEM /FCM solution [26], discussed in section 3.2, the method has not been adapted for materially inhomogeneous problems, which is the basis of this chapter. We will first begin by discussing the method used to treat materially inhomogeneous problems, and then will apply this method to heat transfer problems in stationary and transient states.…”