A VISCOUS-SPRING BOUNDARY ELEMENT USING MASS-PROPORTIONAL DAMPING

The viscous-spring boundary element is deduced using the damping matrix proportional to the lumped mass matrix to represent concentrated dampers. The damping matrix is diagonal, ensuring the computational efficiency of the original central difference method. Meanwhile, the damping matrix is independent of the thickness of the boundary element. Numerical stability in explicit algorithms using the proposed viscous-spring boundary element is analyzed. Results demonstrate that the numerical stability of viscous-spring elements based on mass-proportional damping is slightly superior to that using the stiffness-proportional damping. Taking the uniform half space problem and the dynamic response analysis of a gravity dam as examples, the results indicate that when the mass-proportional damping-based viscous-spring boundary element is used, the calculated dynamic responses are basically consistent with those of the stiffness-proportional damping-based viscous-spring boundary element.