Finite element analysis of a compressible dynamic viscoelastic sphere using FFT

Abstract

An extension to a compressible dynamic viscoelastic hollow sphere problem with both finite and infinite outer radius is performed. The governing viscoelastic equations of motion are transformed into the Laplace domain via the elastic–viscoelastic correspondence principle. Real and imaginary parts of the nodal displacements are obtained by solving a non-symmetric matrix equation in the complex Laplace domain. Inversion into the time domain is performed using the discrete inverse Fourier transform. Use is made of an infinite element in the infinite sphere problem. Numerical solutions are compared to both the exact Laplace and time domain solutions wherever possible.