10 - Special purpose elements

Abstract

This chapter focuses on several special purpose elements and methods that are especialy designed for specific circumstances. These elements are used for very specific purposes to either simplify meshing and calculation, or to obtain better accuracy, which usual elements cannot obtain. These include crack tip elements, infinite elements, finite strip elements and strip elements. In fracture mechanics, much interest for analysts is on the tip of the crack, as it is a singularity point where the stress field becomes mathematically infinite. When modeled with the conventional, polynomial-based finite elements (FEs) discussed in previous chapters, the FE approximations are usually quite bad unless a very dense mesh consisting of numerous small elements is modelled around the crack tip. Using elements with gradually increased artificial damping elements attached on the regular FE mesh is a very efficient way to model vibration problems with infinite boundaries. Another effective method of dealing with infinite domains is to use the finite element method (FEM) coupled with the boundary element method (BEM). The FEM is used in the interior portions of the problem domain where the problem is very complex, and the BEM is used for the exterior portion that can extend to infinity. The use of finite strip elements instead of the conventional FEs can be a very effective method for solving structural problems involving regular geometry and simple boundary conditions.