Open Access

ARTICLE

A New Isogeometric Finite Element Method for Analyzing Structures

Pan Su¹, Jiaxing Chen², Ronggang Yang², Jiawei Xiang^2,*

1 College of Power Engineering, Naval University of Engineering, Wuhan, 430033, China
2 College of Mechanical and Electrical Engineering, Wenzhou University, Wenzhou, 325035, China

* Corresponding Author: Jiawei Xiang. Email:

(This article belongs to the Special Issue: Scientific Computing and Its Application to Engineering Problems)

Computer Modeling in Engineering & Sciences 2024, 141(2), 1883-1905. https://doi.org/10.32604/cmes.2024.055942

Received 10 July 2024; Accepted 04 September 2024; Issue published 27 September 2024

Abstract

High-performance finite element research has always been a major focus of finite element method studies. This article introduces isogeometric analysis into the finite element method and proposes a new isogeometric finite element method. Firstly, the physical field is approximated by uniform B-spline interpolation, while geometry is represented by non-uniform rational B-spline interpolation. By introducing a transformation matrix, elements of types C⁰ and C¹ are constructed in the isogeometric finite element method. Subsequently, the corresponding calculation formats for one-dimensional bars, beams, and two-dimensional linear elasticity in the isogeometric finite element method are derived through variational principles and parameter mapping. The proposed method combines element construction techniques of the finite element method with geometric construction techniques of isogeometric analysis, eliminating the need for mesh generation and maintaining flexibility in element construction. Two elements with interpolation characteristics are constructed in the method so that boundary conditions and connections between elements can be processed like the finite element method. Finally, the test results of several examples show that: (1) Under the same degree and element node numbers, the constructed elements are almost consistent with the results obtained by traditional finite element method; (2) For bar problems with large local field variations and beam problems with variable cross-sections, high-degree and multi-nodes elements constructed can achieve high computational accuracy with fewer degrees of freedom than finite element method; (3) The computational efficiency of isogeometric finite element method is higher than finite element method under similar degrees of freedom, while as degrees of freedom increase, the computational efficiency between the two is similar.

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Keywords

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