Three-dimensional elastic analysis of a bi-material system with a single domain boundary element method

Abstract

The three dimensional fundamental solution of bi-materials is introduced to the boundary element method (BEM) for elastic analysis of a bi-material system instead of solving a multi-domain problem. Using the explicit form of the Green’s function for bi-materials, the boundary integral equations (BIE) are set up for a finite bi-layered material system with a plane interface. The Green’s function for a bi-material system combines the Kelvin’s solution and disturbed fields by image source. Because it exactly satisfies the jointed continuity conditions at the interface (x3=0), no internal mesh is required along the interface and a single domain BEM can be established. The potential numerical errors of the multi-domain BEM using the Kelvin’s solution due to the mesh quality at the interface can be avoided. This single domain BEM for bi-material saves the effort of domain discretization, predicts the singularity on the interface analytically, and enables an efficient, straightforward analysis similar to the homogeneous solids. It is particularly suitable to simulate thin film/substrate systems, overlay/base structures, and other similar layered materials. The numerical simulations verify the effectiveness and convergence of the method, and the case studies of wind turbine blades and solar panels demonstrate the industrial applications of this method.