Open Access

ARTICLE

Reusing the Evaluations of Basis Functions in the Integration for Isogeometric Analysis

Zijun Wu¹, Shuting Wang², Wenjun Shao^{3, *}, Lianqing Yu¹

1 Hubei Key Laboratory of Digital Textile Equipment, Wuhan Textile University, Wuhan, 430200, China.
2 National CAD Support Software Engineering Research Center, Huazhong University of Science and Technology, Wuhan, 430074, China.
3 School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China.

* Corresponding Author: Wenjun Shao. Email: .

(This article belongs to the Special Issue: Recent Developments of Isogeometric Analysis and its Applications in Structural Optimization)

Computer Modeling in Engineering & Sciences 2020, 122(2), 459-485. https://doi.org/10.32604/cmes.2020.08697

Received 27 September 2019; Accepted 13 November 2019; Issue published 01 February 2020

Abstract

We propose a new approach to reuse the basis function evaluations in the numerical integration of isogeometric analysis. The concept of reusability of the basis functions is introduced according to their symmetrical, translational and proportional features on both the coarse and refined levels. Based on these features and the parametric domain regularity of each basis, we classify the bases on the original level and then reuse them on the refined level, which can reduce the time for basis calculations at integration nodes. By using the sum factorization method and the mean value theorem for the integrals, a new integration method with high integral efficiency is proposed. We validate the proposed method by some structural analysis problems in domains with different dimensionality. Comparing the numerical result accuracy and the time cost of the proposed integration method with the full Gauss integration quadrature, it turns out to be very promising.

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