Stability analysis of the thin plates with arbitrary shapes subjected to non-uniform stress fields using boundary element and radial integration methods.

*(English)*Zbl 1403.74201Summary: In this paper, a boundary element method is applied to buckling analysis of thin plates with arbitrary shapes under various load types. The governing differential equation is converted into equivalent integral equation using the static fundamental solutions of the biharmonic equation. The arising domain integrals due to in-plane stresses are evaluated applying the radial integration method. The in-plane stresses are implemented through Gaussian integration points along radial direction in the convex domains. For the concave domains, an idea has been introduced to compute radial integration along new direction from an auxiliary point to the field point. This method can be easily applied to buckling analysis of thin plates with arbitrarily distributed and concentrated edge loading. Six sample problems are presented to illustrate the effectiveness and accuracy of the proposed method.

##### MSC:

74S15 | Boundary element methods applied to problems in solid mechanics |

65N38 | Boundary element methods for boundary value problems involving PDEs |

74H55 | Stability of dynamical problems in solid mechanics |

74K20 | Plates |

74G60 | Bifurcation and buckling |

##### Keywords:

boundary element method; radial integration method; buckling analysis under arbitrary loading; thin plates
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\textit{L. Najarzadeh} et al., Eng. Anal. Bound. Elem. 87, 111--121 (2018; Zbl 1403.74201)

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##### References:

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