Adaptive mesh refinement in finite element analysis

Abstract

Among the acceptable numerical methods, Finite Element Analysis stands as the most acceptable one for problems characterised by partial differential equations. However, inaccuracy in Finite Element Analysis is unavoidable since a continuum with infinite degrees of freedom is modelled into finite degrees of freedom. In addition to the mesh generation task being tedious and error prone, the accuracy and cost of the analysis depend directly on size, shape and number of dements in the mesh. The procedure of refining the mesh automatically based on the error estimate and distribution of the error is known as "adaptive" mesh refinement. A simplified method called "Divide and Conquer" rule based on "Fuzzy Logic" is used to refine the mesh by using <i>h, p </i>and <i>hp </i>versions. Automatic mesh generator developed in this paper based on Fuzzy logic is able to develop well shaped elements. The program for automatic mesh generation and subsequent mesh refinement is developed in ‘‘C” language and the analysis is carried out using ‘‘ANSYS’’¹ package. Automatic mesh generation is&nbsp; applied to problems such as dam, square plate with a hole, thick spherical pressure vessel and a corbel and error less than 5% is achieved in most of the cases.