A boundary element method solution for anisotropic nonhomogeneous elasticity

A new BEM approach is presented for the plane elastostatic problem for nonhomogeneous anisotropic bodies. In this case the response of the body is described by two coupled linear second order partial differential equations in terms of displacement with variable coefficient. The incapability of establishing the fundamental solution of the governing equations is overcome by uncoupling them using the concept of analog equation, which converts them to two Poisson’s equations, whose fundamental solution is known and the necessary boundary integral equations are readily obtained. This formulation introduces two additional unknown field functions, which physically represent the two components of a fictitious source. Subsequently, they are determined by approximating them globally with radial basis functions series. The displacements and the stresses are evaluated from the integral representation of the solution of the substitutes equations. The presented method maintains the pure boundary character of the BEM. The obtained numerical results demonstrate the effectiveness and accuracy of the method.