Plane Strain Finite Elements with Wachspress-Type Functions
For the numerical analysis of two-dimensional elasticity problems triangular and quadrilateral finite elements are popular for a long time. Considering the generation of meshes for domains with complicated boundaries, it easier to produce a high quality mesh with triangles than constructing a good mesh with quadrilateral finite elements. For triangles, shape functions can easily be obtained using barycentric coordinates. For quadrilateral elements traditional shape functions are constructed in a mapped bi-unit square. In this paper we consider the use of Wachspress-type rational functions for polygonal elements with four or more corner nodes. A special feature of the Wachspress rational functions is that they are linear on the finite element boundary between two neighboring corner nodes. The performance of the elements will be illustrated in a series of test examples.
Southeastern Atlantic Regional Conference on Differential Equations (SEARCDE)
"Plane Strain Finite Elements with Wachspress-Type Functions."
Mathematical Sciences Faculty Presentations.