Three-dimensional BEM for transient dynamic analysis of piezoelectric and anisotropic elastic solids

A boundary element approach based on the Green's functions in integral representation and the convolution quadrature method is presented. Proposed approach is designed for analyzing 3D initial boundary-value problems of the dynamics of general anisotropic elastic and piezoelectric linear homogeneous solids with mixed boundary conditions. Numerical modelling of transient dynamics of elastic anisotropic and piezoelectric three-dimensional solids is carried out to demonstrate the potential of the developed boundary element software. Obtained solutions are compared with the corresponding ELM results and results of the dynamic experiment. A numerical technique based on the exact Laplace-domain boundary integral equations for the direct approach of 3D linear theories of anisotropic elasticity and piezoelectricity is employed. The BEM scheme is constructed using the collocation method and the convolution quadrature method in the form of a stepping method for numerical inversion of integral Laplace transform. Results of the stepped BE-modelling of the problems when a transient force is acting on 3D piezoelectric and anisotropic elastic homogeneous solids are presented.