Abstract
This chapter presents the overview of finite element method (FEM) and boundary element method (BEM), focusing on narrow applications for two-dimensional elasticity problems. FEM techniques have been created for discrete and continuous problems, including static and dynamic behavior with both linear and nonlinear response. The method can be applied to one-, two-, or three-dimensional problems using a large variety of standard element types. The method discretizes the domain under study by dividing the region into subdomains called elements. The power and utility of the finite element method lies in the use of computer codes that implement the numerical method for the problems of general shape and loading. BEM method has recently emerged as one that provides good computational abilities and has some particular advantages when compared to FEM. Similar to the finite element method, BEM can analyze many different problems in engineering science, including those in thermal sciences and fluid mechanics. Although the method is not limited to elastic stress analysis, this presentation discusses this particular case. The formulation of BEM is based on an integral statement of elasticity, and this can be cast into a relation involving unknowns only over the boundary of the domain under study.
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