Adaptive FEM-BEM Coupling for Elasto-Plastic Analysis

The finite element method (FEM) and the boundary element method (BEM) are powerful computational techniques for obtaining approximate solutions to the partial differential equations that arise in scientific and engineering applications. Each method has its own range of applications where it is most efficient and neither enjoys the distinction of being "the best" for all applications. Thus, it is conceptually and computationally very attractive to subdivide the computational domain into sub-domains in which the most appropriate solution technique is applied. This approach has been addressed in many publications, mainly in the context of FEM-BEM coupling. There are many situations where coupling the FEM and BEM may prove advantageous, e.g. local nonlinearity, shape optimization, change of dimensionality and presence of infinite domains/singularities. However, in the commonly used coupling approaches, the finite element and the boundary element zones of discretization are defined a priori (manually localized in advance) and do not change during the computation. This requires preliminary expert knowledge about the problem at hand and may limit the general applicability of the coupling method. Furthermore, the computational cost can be higher than necessary depending on the definition of the finite element and boundary element zones of discretization. The proposed research aims at developing efficient coupled finite element-boundary element method (FEM-BEM) for elasto-plastic analysis. The nonlinearity, e.g., plastic material behavior, is treated by the finite element method while large parts of the finite/infinite linear elastic body are treated using the boundary element method. The FEM sub-domain discretization is progressively adapted and automatically generated to include zones where plasticity occurs, according to the state of computation. The substantial decrease in the size of FEM meshes, plainly leads to reduction of required system resources and gain in efficiency. The possible outcomes of this research will help in finding more efficient and economical tools for solving wide range of practical problems. The efficient FEM-BEM coupling method will be utilized to solve practical applications involving elasto-plastic analysis. Examples include, but not limited to, the detailed analysis of stresses around pressure holes in an infinite/semi-infinite medium. The same is true for many problems in solid mechanics.