An advanced boundary element method for solving 2D and 3D static problems in Mindlin's strain-gradient theory of elasticity

An advanced boundary element method (BEM) for solving two- (2D) and three-dimensional (3D) problems in materials with microstructural effects is presented. The analysis is performed in the context of Mindlin's Form-II gradient elastic theory. The fundamental solution of the equilibrium partial differential equation is explicitly derived. The integral representation of the problem, consisting of two boundary integral equations, one for displacements and the other for its normal derivative, is developed. The global boundary of the analyzed domain is discretized into quadratic line and quadrilateral elements for 2D and 3D problems, respectively. Representative 2D and 3D numerical examples are presented to illustrate the method, demonstrate its accuracy and efficiency and assess the gradient effect on the response. The importance of satisfying the correct boundary conditions in gradient elastic problems is illustrated with the solution of simple 2D problems. Copyright (C) 2010 John Wiley & Sons, Ltd.