Coupled stretching-bending boundary element analysis for unsymmetric magneto-electro-elastic laminates with multiple holes, cracks and inclusions

Abstract

Based upon the corresponding boundary element method (BEM) for the elastic composite laminates under coupled stretching-bending (CSB) deformation, the BEM for magneto-electro-elastic (MEE) laminates is developed in this study. By using the Stroh-like complex variable formalism, recently we derived Green's functions for the MEE laminates with or without holes/cracks/inclusions. Its associated fundamental solutions employed in BEM for the MEE laminated plates under CSB deformation are then derived accordingly, with which no meshes are required for the boundaries of holes/cracks/inclusions. At each corner of the plate, three nodes are usually suggested to cover all the nodal tractions (including corner force) at, behind and ahead of the corner. If the triple nodes are placed at the same position, the auxiliary equations would be necessary to replace the trivial equations for displacement-prescribed corner and are therefore constructed in this study. Since the proposed MEE-BEM is purposely organized in the same form as its corresponding elastic case, the associated techniques in dealing with singular integrals, complete solutions for boundary and internal nodes, dual coordinates for inclined holes/cracks/inclusions, and evaluation of stress intensity factors are now successfully extended from elastic to MEE laminates. Moreover, the subregion technique is employed to cover the problems with multiple holes, cracks, and inclusions.