Error estimation based on stress recovery by adaptivity in nonlinear problems of elasto-plasticity behavior by isogeometric method

In this research, the efficiency of error estimation based on two methods of recovering the equilibrium stress of patches and superconvergent points in guiding the adaptive solution of nonlinear problems by isogeometric method has been investigated. Also, by analyzing elasto-plastic problems based on material properties, and adaptive solution by temperature gradient method, the stress improvement process has been investigated. The method of the adaptive solution of this research is based on the movement of control points and it is used in stress recovery, taking into account the difference between the exact stress level and the stress level obtained from the isogeometric analysis for each element, as a criterion to determine the amount of error in it. The element is obtained. For this purpose, the modeling of two problems in the non-linear range, which has an exact solution, has been considered. The results have shown that the total norm difference of exact and approximate error in both stress recovery methods used is more than 33% and in the direction of improving the network of control points. Also, the method by equilibrium patches is more effective than the method based on superconvergent points, which can be used as a suitable solution to improve the stress field.