Location of Optimal Stress Points in Isogeometric Analysis

Abstract

Abstract Isogeomteric Analysis is a newly developed method with some features that can be considered as ‎a potential substitute to other numerical methods such as finite elements and meshless approaches. ‎The NURBS technique, that allows precise geometrical modeling, plays an important role in this ‎method. However, similar to other numerical methods, existence of errors in the approximation of ‎the unknown function is inevitable. This paper is devoted to finding points with higher accuracy in ‎stress recovery by the isogeometric analysis. It can be shown that these points are coincident with ‎the Gauss quadrature points. By making use of these superconvergent points together with the ‎NURBS technique and the least square method, a surface is constructed for each component of ‎the stress tensor that represents the improved stresses. For this purpose, three examples with ‎available analytical results has been solved. The comparison of the obtained improved stresses ‎with the exact solution is used for the sake of verification of the proposed method. It is concluded ‎that the superconvergent points location in the isogeometric analysis are the same as the minimum ‎required Gauss points for the integration of a square element.‎

Keywords

• isogeometric analysis
• superconvergent points
• improved stress
• error estimation‎
• the nurbs technique