An isogeometric approach to the adaptive solution based on error estimates for FGMs

In this study, we discuss the development of the stress recovery method and error estimation in analyzing Functionally Graded Material (FGM) problems using the isogeometric method. The paper furnishes evidence elucidating why Gauss points demonstrate enhanced accuracy in tackling these issues. Additionally, the effectiveness of this error estimation approach is explored in guiding a network improvement algorithm, which relies on the adjustment of control points. In this approach, which uses Gaussian points, each component of the improved stress tensor is considered as an imaginary surface. This surface is created with the same B-spline basis functions used to approximate the primary variables in the isogeometric method. The results show that by comparing the exact and approximate energy error norm in six numerical examples and estimating the effectiveness index of more than 85%, the proposed method can be used as a suitable approach to improve the stress and error estimation of functionally graded material problems by isogeometric method.