Development of Pyramidal Elements in Hybrid-type Penalty Method

Abstract

In the FEM, the displacement field is represented using a shape function, and the continuity of displacement between elements is secured using a nodal displacement. On the other hand, HPM assumes an independent displacement field for each element without using a shape function. Thus, the continuity of displacement between elements is approximately satisfied by using a penalty function. For this reason, it is not clear whether equivalent accuracy can be obtained by using the numerical integration used in FEM for pyramid elements. In this paper, we assume a linear, a quadratic and a bilinear function independently of the element shape as the displacement field of HPM. Then, this displacement field is applied to various elements including pyramid elements, and the accuracy of the displacement solution is verified from the viewpoint of numerical analysis. As a result, elements other than tetrahedral elements could not be solved in the displacement field of the linear function. In addition, the pyramid element proposed in this paper and its numerical integration method also obtained a highly accurate solution.