The analog equation method: A boundary-only integral equation method for nonlinear static and dynamic problems in general bodies

Abstract

In this paper the Analog Equation Method (AEM) a boundary-only method is presented for solving nonlinear static and dynamic problems in continuum mechanics. General bodies are considered, that is bodies whose properties may be position or direction dependent and their response is nonlinear. The no linearity may result from both nonlinear constitutive relations (material no linearity) and large deflections (geometrical no linearity). The quintessence of the method is the replacement of the coupled nonlinear partial differential equations with variable coefficients governing the response of the body by an equivalent set of linear uncoupled equations under fictitious sources. The fictitious sources are established using a BEM-based technique and the solution of the original problem is obtained from the integral representation of the solution of the substitute problem. A variety of static and dynamic problems are solved using the AEM are presented to illustrate the method and demonstrate its efficiency and accuracy.