Xây dựng tiêu chuẩn góc bé nhất trong đánh giá sai số và tốc độ hội tụ của phần tử tam giác trong phân tích chất lượng lưới phần tử hữu hạn

Abstract

With the increasing use of finite element analysis programs, the development of a reliable and robust modeling procedure is necessary for engineers who do not possess extensive numerical expertise. An adaptive mesh refinement finite element method, also called a refinement method, is the subject of extensive investigation with the objective of obtaining solutions with pre-specified accuracy with minimum cost of model preparation and computation. In a refinement procedure, a finite element mesh is sequentially upgraded in such a way that the discretization error in the final solution is reduced to a desired level. The computational effectiveness of a refinement method depends on several factors including the type of refinement scheme, error estimator used, equation solver used, and computer programming technique. At present, some commercial finite element programs have incorporated a refinement procedure that provides promised accuracy of final results. However, computational effectiveness of those programs did not reach yet an optimum point. The goal of this study is to further investigate and to develop a more efficient adaptive mesh p-refinement procedure based on a criteria of the minimum angle for the triangular element in the quality finite element mesh for two-dimensional elastostatic mechanics problems.