Investigating the efficiency of error estimation based on strees recovery in the adaptive solution of functionally graded materials by isogeometric method

In today's era, it is necessary to analyze functionally graded materials. Since the finite element method in the analysis of these materials has limitations and the error is an inseparable part of any numerical analysis, therefore, finding a solution to estimate the error in calculations is important. In the finite element method, modifying or enriching the network to reduce the error is associated with such things as the overlapping of elements during displacement, the formation of elements with zero areas, and the increase of cost in calculations. In this research, the isogeometric method has been used for the first time in the analysis of problems with functionally graded materials in the adaptive solution using the method of moving control points as adaptive correction based on error estimation, with the approach of improving the stress field. By comparing the exact and approximate error norm in the solved examples, the effectivity index is more than 75%, which shows the effectiveness of the proposed error estimator. In addition, improving the network of control points is effective in reducing the error rate by more than 60% and can be used to increase the accuracy of the results.