Research on nonuniform rational basis spline-based isogeometric analysis method and finite element method in two dimensions

Abstract

Isogeometric analysis is a new numerical method that has been developed in recent years based on the finite element method. The method avoids the geometric errors of the finite element method by unifying the models used for modeling and analysis, and has a Cn continuous nature. This paper studies the representation method of the nonuniform rational basis spline (NURBS) geometry used in isogeometric analysis; the stiffness matrix is derived according to basic finite element theory, boundary and constraint conditions are imposed, and the static analysis results are finally obtained by solving the linear equations. We use a two-dimensional plate with holes as an example to establish a model to enable comparison of the calculation results obtained from isogeometric analysis and finite element analysis from the perspectives of both calculation accuracy and calculation efficiency. The numerical example results show that, when compared with traditional finite element analysis, the isogeometric analysis method based on NURBS shows obvious advantages in both performing calculations and obtaining a solution. Isogeometric analysis can obtain accurate solutions with fewer system degrees of freedom and offers good flexibility and practicability.