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Buckling analysis of functionally graded thin plate with in-plane material inhomogeneity. (English) Zbl 1403.74031
Summary: Buckling analysis of functionally graded material (FGM) thin plates with in-plane material inhomogeneity is investigated based on radial basis functions associated with collocation method. No background mesh is required in the discretization and solution which makes it a truly meshfree method. Two independent problems raised in the buckling analysis are studied according to the procedure. First, radial basis collocation method (RBCM) is employed to yield the non-uniform pre-buckling stresses by solving a 2D plane stress problem. Afterwards, based on Kirchhoff assumption and employing the predetermined non-uniform pre-buckling stresses, Hermite radial basis function collocation method (HRBCM) is proposed to study the buckling loads of FGM thin plates with in-plane material inhomogeneity. Compared to an over-determined system resulting from the conventional RBCM, HRBCM introducing more degrees of freedom on the boundary nodes can lead to a determined system for the eigenvalue problem. Convergence and comparisons studies with analytical solutions demonstrate that the proposed method possesses high accuracy and exponential convergence. Numerical examples illustrate that the material inhomogeneity has considerable effects on the buckling loads and mode shapes of thin plates. As a result, material inhomogeneity can be exploited to optimize the in-plane stress distribution and prevent the buckling of thin plates.

MSC:
74G60 Bifurcation and buckling
74K20 Plates
74S25 Spectral and related methods applied to problems in solid mechanics
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