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Buckling analysis of skew and circular stiffened plates using the Galerkin meshless method

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Abstract

Based on the first-order shear deformation theory, a Galerkin meshless method for buckling analysis of skew and circular stiffened plates is proposed. A series of points is used to discretize the stiffened plate to establish the mesh-free model, in which the flat plate and stiffeners are combined by implementing the displacement compatibility conditions between them. The moving least-squares approximation (MLS) is employed to construct the shape functions and the displacement fields. The geometric stiffness matrix of the stiffened plate is derived based on the prestress distribution of the stiffened plate subjected to a partial edge loading. The equations governing the buckling behaviour of the structure are derived according to the principle of minimum potential energy. The stiffeners in the formulation can be set at any location on the flat plate, and the remeshing of the flat plate is naturally avoided when the stiffener location changes. Several numerical examples are calculated by the proposed method and compared with FEM results. The results show that the proposed method is accurate and efficient, and frees researchers from determining a nodal line on the plate along every stiffener.

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Acknowledgements

The work described in this paper has been supported by grants awarded by the National Natural Science Foundation of China (Nos. 12162004 and 11562001), the National Key R&D Program of China (No. 2019YFC1511103), and the Guangxi Major Science and Technology Project (No. AA18118029).

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Authors and Affiliations

  1. College of Civil Engineering and Architecture, Guangxi University, Nanning, People’s Republic of China

    Xia Qin, Jiacheng Xiang, Xingchuan He, Yajing Shen, Wei Chen & L. X. Peng

  2. Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education, Guangxi University, Nanning, People’s Republic of China

    L. X. Peng

  3. Guangxi Key Laboratory of Disaster Prevention and Structural Safety, Guangxi University, Nanning, People’s Republic of China

    L. X. Peng

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  1. Xia Qin
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Qin, X., Xiang, J., He, X. et al. Buckling analysis of skew and circular stiffened plates using the Galerkin meshless method. Acta Mech 233, 1789–1817 (2022). https://doi.org/10.1007/s00707-022-03191-w

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