Journal of South China University of Technology(Natural Science) >

2024 , Vol. 52 >Issue 12: 65 - 78

DOI: https://doi.org/10.12141/j.issn.1000-565X.230749

Mechanics

Method of Imposing Local Fixed Constraints Exactly in Isogeometric Analysis

  • WANG Yingjun ,
  • LI Jinghui
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  • School of Mechanical and Automotive Engineering，South China University of Technology，Guangzhou 510640，Guangdong，China

Received date: 2023-12-01

  Online published: 2024-08-22

Supported by

the National Natural Science Foundation of China(52075184);Guangdong Basic and Applied Basic Research Foundation(2024A1515011786)

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Abstract

Isogeometric analysis uses computer splines such as non-uniform rational B-splines as the basis functions. When the order of the basis function is 2 or greater, the control points do not coincide with the element nodes and the support domain of the basis function spans multiple elements, which makes it difficult to impose local fixed constraints precisely in isogeometric analysis. To solve this problem, this paper uses a step function to modify the displacement interpolation function of isogeometric analysis. The step function takes a value of 0 in the locally fixed constraint region and 1 in the other region, so that the displacement value in the fixed constraint region is forced to be 0, and the displacement interpolation function in other region is revert to the original form. In order to minimize the influence of step function on the analysis domain, the rising interval of the step function is set to be small. Meanwhile, the hierarchical spline is used to subdivide the elements in the rising interval locally, therefore, the Gaussian points of the subdivided elements fall into the rising interval of the step function as well as the step function has an effect on the stiffness matrix. In addition, the element subdivision also effectively improves the solution accuracy in the local constraint region where large strains are present. Finally, the method mentioned above is compared with analytical solution and the finite element method to verify its accuracy, flexibility and reliability, finding that the results of calculation coincide with the analytical solution. Finally, by considering the situations with different fixed constrains that vary in shape, area and location., the finite element method with coarse mesh and fine mesh are used to calculate the examples, finding that the displacement and stress obtained by the proposed method are closer to those obtained by the fine mesh finite element method, which illustrates that the solution accuracy can be achieved with fewer elements; and that the proposed method is of good accuracy, flexibility and reliability.

Key words： isogeometric analysis; fixed constraint; step function; hierarchical spline

Cite this article

WANG Yingjun , LI Jinghui . Method of Imposing Local Fixed Constraints Exactly in Isogeometric Analysis[J]. Journal of South China University of Technology(Natural Science), 2024 , 52(12) : 65 -78 . DOI: 10.12141/j.issn.1000-565X.230749

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