FEM for one- and two-dimensional viscoelastic materials with spherical and rotating domains using FFT

A compressible dynamic viscoelastic hollow sphere problem and a two-dimensional rotating disc problem are discussed. Materials that are almost incompressible are also analysed for both the quasi-static and dynamic sphere. 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. Numerical solutions are compared to both the exact Laplace and time domain solutions wherever possible.