Construction method of isogeometric hybrid Kirchhoff-Love shell unit

Abstract

According to the construction method of the isogeometric hybrid Kirchhoff-Love shell unit, the Bessel dual basis function is constructed and used for independently interpolating film strain, it is ensured that the rigidity matrix of the thin shell structure still has small bandwidth and sparsity after degree-of-freedom condensation. And the defects of the existing isogeometric hybrid Kirchhoff-Love thin-shell unit are overcome, i.e., the sparsity of a rigidity matrix can be destroyed by degree-of-freedom condensation and the like. Meanwhile, the novel isogeometric hybrid KirchhoffLove thin shell unit can eliminate the thin film locking effect, and the advantages of an existing isogeometric hybrid shell unit are kept. The method has the advantages of being simple, efficient, high in precision and high in universality, and therefore the method is easy to apply and popularize in engineering structure analysis.

Description

technical field [0001] The invention relates to the field of computational mechanics, in particular to a construction method of equigeometric mixed Kirchhoff-Love shell elements. Background technique [0002] Isogeometric Analysis (Isogeometric Analysis) is a new type of finite element method, which introduces Non-Uniform Rational B-Splines (NURBS) to describe geometric shapes in Computer Aided Design (CAD) In the isoparametric finite element, the repeated data conversion process between computer-aided design (CAD) and computer-aided analysis (Computer Aided Engineering, CAE) software in the product design process is eliminated, and a lot of pre-processing time is saved. Accurate, high-order continuity and other characteristics, so it is especially suitable for the structural analysis of plates and shells with curved surface characteristics. [0003] There are a large number of thin-walled structures in products such as aerospace, automobiles, and ships, which are mainly du...

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Problems solved by technology

[0005] In the traditional mixed shell element based on the Hellinger-Reissner two-field variation, the independent unknowns are the displacement of the shell element and the strain / stress of the membrane. Interpolation can effectively alleviate the coupling effect between the bending strain and the film strain, thereby eliminating the film locking phenomenon, but compared with the traditional Kirchhoff-Love shell element, the hybrid shell element needs to introduce additional strain / stress degrees of freedom, thus increasing The dimensions of the stiffness matrix, although the additional strain / stress degrees of freedom can be converted into the displacement degrees of freedom through static condensation, will cause the stiffness matrix to lose its sparse, banded and other characteristics, reducing computational efficiency

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