| The objective of this study is to develop a more efficient algorithm for solving solid mechanics problems involving either a homogeneous material or a material with a microstructure. The approach is based on the technology of finite element multilevel methods.; This dissertation starts with a brief discussion about adaptivity, error estimate methods, and mesh refinement strategies. Then the development and application of a new algorithm, for solving solid mechanics problems with multilevel finite element method, is presented. Applying this method, computer program MLFEM is developed. Various example problems are solved to show the performance of the proposed method. After this, the multilevel algorithm is improved and modified to determine the displacement field of general composite materials by considering their microstructure. This displacement field is a combination of micro level and macro level solutions. Step-by-step hand calculations of a 1-dimensional model is shown. Computer program MSTRUCARB is developed based on this algorithm for solving 2-dimensional composite material models. Again, to show the capability of this method, a few numerical examples are presented. Finally, a new algorithm is introduced to improve the accuracy of the micro level solution of composite materials displacement field. |
