A NEW RESIDUAL FINITE-ELEMENT FORMULATION FOR ELASTODYNAMIC PROBLEMS

Abstract

In the research undertaken a finite element formulation has been developed for an elastodynamic problem using a least squares approach. The special requirements of the problem demanded a study of suitability of various elements. The emergence of the final element is a result of both theoretical and numerical study of three different elements. The approximation function is assumed on the basis of the order of the governing differential equations. Then the square of the error resulting from the approximate solution is minimized over the entire domain as well as the boundaries in the same functional. The element equation emerging from the formulation does not yield a singular stiffness matrix, since the boundary conditions are already taken into account in the element equation. The formulation presented in this thesis is only for the normal propagation of phi-wave. A finite element code has been developed based on the new formulation.