The Application of Dynamic Relaxation to the Finite Element Method of Structural Analysis

摘要

The report is a study in depth of the method of Dynamic Relaxation, a matrix iterative method for the solution of simultaneous linear equations, and used principally in problems of structural analysis under static stress conditions. Whereas earlier investigators have restricted themselves almost exclusively to the finite difference formulation in space of both the equations of motion and the constitutive relationships, the present study formulates an alternative approach using finite elements in space. The mathematical basis for the finite element approach in space is developed, and followed by an analysis of convergence based upon a transformation into a standard eigenvalue problem for the error vector, intimately associated with the conditioning of the equations. Optimum convergence is studied and comparisons made with other iterative methods. Dynamic Relaxation is demonstrated by applying it to plane stress problems of statically loaded plates having discontinuities in the form of circular, elliptical and filleted square holes. (Author)