EXPLICIT FINITE ELEMENT ARTIFICIAL BOUNDARY SCHEME FOR WAVE EQUATION ON UNBOUNDED DOMAIN

摘要

Dynamic soil-structure interaction is a wave propagation problem on unbounded domain. An explicit finite element artificial boundary scheme that couples the standard dynamic finite element method and a high-order accurate artificial boundary condition (ABC) is proposed to solve the unbounded wave problem. The out-of-plane wave equation is considered in this paper. An exact dynamic-stiffness ABC that is global in space and time is constructed. A temporal localization method that consists of the rational function approximation and the auxiliary variable realization is developed. This method is applied to the dynamic-stiffness ABC to result in a high-order accurate ABC that is local in time but global in space. By discretizing the high-order accurate ABC along artificial boundary and coupling the result with the standard lumped-mass finite element equation of near field,a coupled dynamic equation is obtained,which is a symmetric system of purely second-order ordinary differential equations in time with the diagonal mass and non-diagonal damping matrices. A new explicit time integration algorithm in structural dynamics is used to solve this equation. Numerical examples demonstrate the effectiveness of the proposed explicit finite element artificial boundary scheme.