An Efficient Adaptive Finite Element Analysis of Heterogeneous Materials Based on Centroid Material

One problem with the adaptive finite element analysis is that it needs more iterations, compared with the uniformly refined mesh method, to reach the desired accuracy of the solutions, although its convergence rate is higher than that of non adaptive computing. In order to improve the efficiency of the analysis and reduce the time for computing in each iteration, we develop a simple centroid material method instead of the integral on each element in forming the element stiffness matrix. There is no time needed for the integral on each element in linear finite element method, because the centroid material is used to approximate the material of the element, and then the finite element model is simplified as one consists of elements with homogeneous material. The efficiency of the method in both computing and implementation is shown as compared with the Gauss quadrature.