FE simulation in production engineering - comparison between conventional FEM and adaptive FEM

Finite Element Method (FEM) is the most widely used numerical simulation method for solving problems of engineering and physics in macroscopic scale. Using FEM, the continuous domain of the problem will be divided into a nite number of smaller areas. In order to increase the accuracy of results, the size of elements will be reduced to have a ner mesh. The whole mesh refinement is not an optimal use of computational resources. Furthermore, if we have singularities in our problem, we get convergence error close to them. Here, Adaptive Finite Element Method (AFEM) steps in. Its performance is greater than conventional FEM and is known to practitioners for optimal convergence rate [3].The aim of this study is to compare performance of these methods, measurement of relative error vs degrees of freedom, with computational efficiency point of view. This investigation is done using \MSC Marc 2015.0.0" FEM solver engine and results are compared with analytical solution as a reference. Results show less relative error at fewer number of degrees of freedom in case of stress analysis for adaptive FE analysis in comparison with conventional FE analysis in all of our problems. Combination of the best refinement criterion and the optimal set of refinement parameters lead to fantastic achievements. As an example, we get 3 times more accuracy in results at just about 4% number of DOF as in the conventional FE analysis (Fig. 3.30).