Application of RKP‐FSM in the buckling and free vibration analysis of thin plates with abrupt thickness changes and internal supports

Abstract

SummaryA description is given of the development and use of the Reproducing Kernel Particle Finite Strip Method for the buckling and flexural vibration analysis of plates with intermediate supports and step thickness changes. The generalized 1‐D shape functions of the Reproducing Kernel Particle Method replace the spline functions in the conventional spline finite strip method in the longitudinal direction. The structure of the generalized Reproducing Kernel Particle Method makes it a suitable tool for dealing with derivative‐type essential boundary conditions, and its introduction in the finite strip method is beneficial for solving buckling and vibration problems for thin plates in which a number of the essential boundary conditions can include the first derivatives of the displacement function. Moreover, the modified corrected collocation method is further developed for the buckling and free vibration analysis of plates with abrupt thickness changes. This provides a versatile and powerful analysis capability which facilitates the analysis of problems including plate structures with abrupt thickness changes of its component plates. The application of the proposed technique for the treatment of discontinuities and the enforcement of the internal support conditions are illustrated with a series of numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.