Finite Element Analysis of Dynamic Behavior of Viscoelastic Materials by Use of FFT.

Abstract

A new type of finite element method is presented for analyzing dynamic behavior of viscoelastic materials. In this method, the finite element formulation can be accomplished in simple form based on the correspondence principle between elasticity and viscoelasticity. Namely, the finite element equations for a viscoelastic problem are found by applying the Laplace transform to those for the corresponding elastic problem and then replacing elastic constants by viscoelastic functions. Laplace transforms of the nodal displacements can be obtained by solving the matrix equation described in the Laplace plane (complex s domain). Laplace inverse transformation is subsequently performed with the FFT (fast Fourier transform) algorithm to obtain solutions in the time domain. The present method is successfully applied to analyze some typical problems, and the numerical results show the adequacy of the method.