DYNAMICS OF VISCOELASTIC SOLIDS TREATED BY BOUNDARY-ELEMENT APPROACHES IN TIME-DOMAIN

The boundary element method (BEM) provides a powerful tool for the calculation of elastodynamic response in frequency and time domain. Field equations of motion and boundary conditions are cast into boundary integral equations (BIE), which are discretized only at the boundary. The boundary data often are of primary interest because they govern the transfer dynamics of members and the energy radiation into a surrounding medium. Formulations of BEM currently include conventional viscoelastic constitutive equations in the frequency domain. In the present paper viscoelastic behaviour is implemented in a time domain approach as well. The constitutive equations are generalized by taking fractional order time derivatives into account. Previous work of the authors on this subject was based on the generation of a viscoelastic fundamental solution in time domain. The present approach uses an analytical integration of the boundary integral equation in a time step. Viscoelastic constitutive properties are introduced after Laplace transformation by means of an elastic-viscoelastic correspondence principle. The transient response is obtained by inverse transformation in each time step. The elastic as well as a viscoelastic wave propagation in an 3-d continuum are studied numerically. In an elastic continuum the response leads to instability if small time steps below critical values are chosen. Replacement of derivatives in the fundamental solution by finite differences according to a suggestion by Figueiredo et al. in acoustics increases the stability range and reduces numerical damping.