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

Here, based on the first-order shear theory and the moving least square method, a meshless method was proposed to analyze static and free vibration of stiffened circular plates on elastic foundation. Winkler foundation model was used for elastic foundation. Circular plate and rib were considered separately for a ribbed circular plate, and parameter conversion equations of both two were established with displacement coordination conditions. The plate and rib were discretized using a series of points, and shape functions established using the moving least square method were used to describe their displacement fields, respectively. Then, static bending and free bending vibration governing equations of elastic foundation were derived using the minimum potential energy principle and Hamilton principle, respectively. Finally, the complete transformation method was used to deal with boundary conditions. Taking a series of stiffened circular plates on elastic foundation with different subgrade coefficients, loads, boundaries and rib arrangements as examples, the convergence and stability of the proposed method were studied, the calculation results were compared with those obtained using finite element method and those published in literature. The results showed that the proposed method can effectively analyze static and free vibration problems of stiffened circular plates' linear bending on elastic foundation; the grid reconstruction can be avoided when rib positions are changed. © 2022, Editorial Office of Journal of Vibration and Shock. All right reserved.