Abstract
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 FEM 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.
Highlights
Three-dimensional transient problems of linear anisotropic elasticity and piezoelectricity can be successfully treated by the direct Boundary Element Method (BEM)
Such BEM formulations hardly reported in the literature due to the lack of the exact closed-form expressions of dynamic fundamental solutions and high complexity of their integral representations [1, 2]
In this study we present a Laplace domain direct BEM formulation based on exact singular boundary integral equation (BIE) and on integral expressions of corresponding dynamic fundamental solutions
Summary
Three-dimensional transient problems of linear anisotropic elasticity and piezoelectricity can be successfully treated by the direct Boundary Element Method (BEM). Such BEM formulations hardly reported in the literature due to the lack of the exact closed-form expressions of dynamic fundamental solutions (often referred to as Green’s functions) and high complexity of their integral representations [1, 2]. The Dual Reciprocity BEM (DRBEM) formulations which require only static fundamental solutions were proposed [3,4,5] to avoid this complication. In this study we present a Laplace domain direct BEM formulation based on exact singular boundary integral equation (BIE) and on integral expressions of corresponding dynamic fundamental solutions. Where n is the unit outward normal vector to the boundary and σi j is the Cauchy stress tensor
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