Boundary Element Formulation for the Standard Viscoelastic Solids in Time Domain

Viscoelastic analysis is one of the most important subjects in engineering structures. Several attempts have been so far made for the integral equation approach to viscoelastic problems. There is no available much literature for the application of a direct boundary element method to the time dependent problems of this kind using a step-wise time integration scheme. In this paper, we propose a direct boundary integral formulation. This formulation needs only Kelvin’s fundamental solution of the isotropic elastostatics with material constants prescribed as explicit functions of time. From basic assumptions of the viscoelastic constitutive equations and weight residual techniques, a simple but effective Boundary Element formulation is implemented for the standard viscoelastic solid model. Imposing the spatial approximations and adopting convenient kinematical relations for the strain velocities, so, a system of time differential equations is derived. Important aspect of the derived formulation is absence of domain discretizations that simplify treatment of the problems involving the infinite domains. Successive application of this solution scheme can determine the whole behavior of viscoelastic problems. A numerical example is provided to validate the formulation which compared to analytical solution.

کلیدواژه ها:

“Viscoelastic Solids” ، “Boundary Element Method” ، “Boltzmann Rheological Model”.