A solution approach to non-linear multi-field problems. - Tomaz Sustar (2002)
In this work a solution approach for non-linear multi-filed problems is presented. The approach is based on co-operative usage of several advanced techniques inside a single environment instead of combining several different systems. The objective of this work is to demonstrate the applicability of advanced computational techniques to complex numerical problems and to present advantages of a co-operative solution environment in the development of finite elements. The solution environment, implemented in Mathematica, consists of a symbolic code generator - AceGen, a package of prearranged modules for the automatic creation of the interfaces between the generated code and specific finite element environment - Computational Templates and a model finite element environment called Finite Element Driver. Within the scope of this work the ANSI C version of Finite Element Driver - CDriver was developed and used for numerical evaluation throughout the work. The CDriver is fully integrated with Mathematica and it provides high numerical efficiency to the environment. The solution approach is demonstrated on magneto-thermo-mechanical problem of inductive heat treatment. First the high abstract formulation level, which is required for efficient symbolic description, was introduced. Following the general formulation the models of individual magnetic, thermal and displacement fields were derived. After the individual fields model were verified the magneto-thermal and magneto- thermo-mechanical problems were formulated and derived. Both non-linear multi- filed models were verified using analytical solutions and numerical convergence tests. Different multi-filed solution strategies were applied to numerical examples and their performance issues were studied using the magneto-thermo-mechanical model. Finally the large scale numerical example of inductive heat treatment was solved.