Proceeding of ACE 2006 Advances in Civil Engineering 7th International Conference, İstanbul, Turkey, 11 - 13 October 2006, pp.1-11
The complexity of engineering problems hinders analytical approaches and leads to the use of numerical methods, one of which is Finite Element Method (FEM). FEM has come to an undeniable point as an attractive numerical analysis method in the scope of Engineering Design. A lot of studies that FEM has been successfully employed have been conducted. In general low order finite elements are used for the reliable simulation of structural mechanics. Unfortunately, the pure displacement based elements tend to locking effects which cause significant calculation errors. In order to avoid these problems of low order elements, several element techniques, e.g. the assumed natural strain approach and the enhanced assumed strain concept, have been developed. In the present study higher order finite elements as an alternative approach are investigated. The p-finite element method avoids locking naturally within a pure displacement based element formulation. Higher order finite elements based on Lagrange (p=1,…,5), Serendipity (p=2,3,4) and Hierarchic Legendre (p=2,3,4) shape functions are compared to the classical h-method using low order elements and fine meshes. The analyses are performed by a research oriented finite element program developed in MATLAB. Several examples are showing the application to linear structural mechanics, the correctness of the program and the properties of the investigated p-finite element methods. It is observed that the program gets satisfactory results in both displacement and stress field with ANSYS and analytical way. P-method provides more qualified results than h-method in both coarse and fine mesh.
Keywords: Lagrange element, Serendipity element, Hierarchic Legendre element, High order element, Elastostatic plane problem, hp-FEM.