Meshless method for static bending and free bending vibration analysis of&nbsp; stiffened circular plates on elastic foundation

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Journal of Vibration and Shock ›› 2022, Vol. 41 ›› Issue (7) : 11-22.

Meshless method for static bending and free bending vibration analysis of stiffened circular plates on elastic foundation

PENG Linxin1,2,3, SHEN Yajing1, QIN Xia1, YANG Jiansheng1

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Abstract

Based on the first-order shear deformation theory, a meshless method for bending analyses of stiffened circular plates in static and free vibrational state on elastic foundation is proposed. Winkler foundation is used to model the elastic foundation. The stiffened circular plate is modelled as a composite structure that consists of a flat circular plate and many stiffeners. A series of points are used to discretize the flat circular plate and stiffeners to obtain the mesh-free model. The moving least-squares approximation is used to construct the shape functions and to derive the displacement fields of the flat circular plate and stiffeners, respectively. The total potential energy and kinetic energy of the stiffened circular plate is obtained according to the compatibility condition between the flat circular plate and the stiffeners. The equations governing the bending behaviors of the stiffened circular plate in static and free vibrational state are derived according to the principle of Minimum Potential Energy and the Hamilton's Principle, respectively. The boundary conditions are enforced by the full transformation method. The convergence of the proposed method and the domain of influence that affects the calculated results are studied. Several numerical examples are calculated by the proposed method and compared with the results available in the literature or given by the finite element software ABAQUS. The results show that the proposed method frees the researchers from determining a nodal line on the plate along every stiffener, which is very beneﬁcial for carrying out optimization studies on stiffeners’ locations.

Key words

elastic foundation / stiffened circular plate / linear bending / free vibration / meshless method

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PENG Linxin1,2,3, SHEN Yajing1, QIN Xia1, YANG Jiansheng1. Meshless method for static bending and free bending vibration analysis of stiffened circular plates on elastic foundation[J]. Journal of Vibration and Shock, 2022, 41(7): 11-22

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