Application of the Complex Variable Finite Element Method, ZFEM, to Structural Mechanics Sensitivity Analysis

摘要

The complex variable finite element method, herein called ZFEM, provides sensitivity information as a byproduct of the analysis in addition to the traditional finite element output. ZFEM is based on the Complex Taylor Series Method (CTSE). In this case, the parameter of interest in the model is perturbed a small amount along the imaginary axis. This requires the finite element method be fully complex and support complex nodal coordinates, loading, and material properties. Two- and Three- Dimensional example problems verify the high accuracy of the numerical derivatives.