Method and apparatus for shape-based energy analysis of solids

Abstract

A computer-readable medium stores instructions including storing a model of a physical structure and defining a mesh for the model. The mesh includes finite elements, each defined by a respective set of edges. The instructions include, for each finite element, identifying a governing differential equation and a set of complementary functions that exactly satisfy the governing differential equation. The instructions include determining an applied physical stimulus for the physical structure. The instructions include generating an energy optimization model that minimizes a difference between internal energy and external energy of the finite elements in response to the applied physical stimulus. The model includes a matrix of respective scalar multipliers for the complementary functions for each finite element. The instructions include transforming the matrix and calculating a physical parameter of interest. The instructions include, in response to the physical parameter not satisfying a design parameter, updating the model of the physical structure.