A Boundary Element Formulation for Generalized Viscoelastic Solids in Time Domain

  • M. Schanz
  • L. Gaul
  • W. Wenzel
  • B. Zastrau
Conference paper


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 on 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. Herein viscoelastic behaviour of materials in time domain is implemented in a boundary element formulation. The constitutive equations are generalized by taking time derivatives of fractional order. Instead of generating a viscoelastic fundamental solution in time domain used by the first two authors before, the present approach uses an analytical integration of the boundary integral equation in a time step. Viscoelastic constitutive properties are introduced after taking Laplace transform of an elastic-viscoelastic correspondence principle. The transient response is obtained through the inverse transformation in each time step and the elastic as well as a viscoelastic wave propagation in 3-d continuum are studied numerically.


Boundary Element Method Fractional Derivative Boundary Integral Equation Foundation Slab Linear Shape Function 
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© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • M. Schanz
  • L. Gaul
  • W. Wenzel
  • B. Zastrau

There are no affiliations available

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