عنوان مقاله [English]
Nowadays, numerical methods are known to be effective solutions to scientific problems. The most popular numerical methods include finite difference method, finite volume method, finite point method, and the finite element method. The standard finite element method may go through difficulty with highly-curved boundaries, and it lacks enough accuracy. In this method, another challenge is to generate finite element mesh by proper numbers, types, and orders of elements. Aimed at decreasing the computational costs of discretization and increasing the solution accuracy, a suitable solution is of great importance in this method. This paper presents a method to improve the meshes and accuracy of solutions regarding elasticity problems. In this paper, two techniques of h-refinement and h-enrichment are used by interpolation cover functions. Initially, regions exceeding the value of allowable error are detected. Mesh improvement is done through h-refinement for the elements existing in those regions. The total error of the domain is, thus, reduced and limited to the allowable range. To increase the accuracy of solutions to an excellent level,
the results of mesh refinement are reassessed in the next step, and the nodes exceeding the value of allowable error are determined. The method proposed here improves the region by interpolation cover functions and yields solutions of appropriate accuracy. The advantages of the proposed method include standard norm and its error determination, adaptive mesh generation, its validation for many 2D elasticity problems with extreme complexity within their domains, and automatic performance in both steps of h-refinement and determining the order of cover enrichment functions. This method can considerably reduce the computational attempts and properly enhance the accuracy of analytical results. This paper attempts to use fewer elements at the beginning and, then, introduces an individual generated indicator to determine the order of cover enrichment functions. In fact, it aims to suggest a method for automatic refinement in 2D problems. A comparison of solutions achieved by the proposed
method with those of other approaches as well as the exact solutions for linear elasticity examples implies acceptable efficiency and accuracy of the proposed method.