A Multiscale Homogenization Procedure for Analysis of Processes Involving Heat Deposition Using Constrained Parameter Optimization

摘要

We present aspects of a general procedure to be used in conjunction with constrained parameter optimization for the analysis of processes involving heat deposition such as welding processes and those involving rapid prototyping by means of powder deposition. Our emphasis in this report is on the construction of generating functions and subdomain elliptic solvers useful for the practical application of constrained parameter optimization for the calculation of thermal histories. The procedure for constructing generating functions and elliptic solvers is based on the concept of multiscale homogenization. We discuss those elements of the theoretical foundation of the general methodology based on constrained parameter optimization as these elements relate to the application of generating functions and subdomain solvers. In addition, we present a prototype weld analysis, which serves to demonstrate many of the details associated with the application of this methodology.