عنوان مقاله [English]
Finite-element method is a famous and robust numerical method like other numerical methods. Due to the use of pre-defined and standard form of shape functions, this method will face a difficult situation and without any accuracy for exact modeling of the areas. The process of the finite-element network generation, with the appropriate number and type of elements, is one of the future challenges to this approach; its aim is to reduce the computational costs in order to discretize and solve the predominant equations of the problem. The derivatives of answer usually need the refinement operations to achieve acceptable accuracy in network-based methods. For this purpose, the methods of the enrichment-displacement refinement, refinement of enhancing element order and refinement of increasing the number of elements, and the combination methods can be used. The refinement in numerical methods is an efficient tool to reduce the computational costs and increase the accuracy of the results obtained. If the parts of the area of solving problem that needs more accuracy be clear, it can greatly reduce the computational complexity with an appropriate process. In this paper, energy norm of error method and refinement of enrichment-displacement, using the optimization algorithm of charged system search, are presented to improve the accuracy of the two-dimensional linear elasticity. Problems simultaneously use two methods of enrichment and displacement techniques. At first, replacing the points would reduce the predominant error of the problem. Moreover, in the event of failure to reach an allowable error, in the next step, elements that have a higher error than permissible one using enrichment method of new nodes enter the domain of problem, and new meshing is offered. Enrichment-displacement method continues to obtain the desired accuracy. The proposed method with achieving a suitable layout for finite-element network, in addition to solving the problem of some nodes occurring in conventional enrichment methods, improves the accuracy of answers as well. Furthermore, the approximate answers will be provided with the lower number of degrees of freedom than the compared methods. A comparison of result for the present method by other researchers show the efficiency and acceptable accuracy of the method.