Thin plate bending analysis and treatment of material discontinuities using the generalised RKP-FSM

Abstract

A finite strip method (FSM) utilising the generalised reproducing kernel particle method (RKPM) [Behzadan, Shodja, and Khezri (2011)] is developed for the bending analysis of thin plates. In this innovative approach, the spline functions in the conventional spline finite strip method (SFSM) are replaced with generalised RKPM 1-D shape functions in the longitudinal direction, while the transverse cubic functions which are used in the conventional formulations are retained. Since the generalised RKPM is one of the class of meshfree methods which deal efficiently with derivative-type essential boundary conditions, its introduction in the FSM is beneficial for solving boundary value problems such as the bending of thin plates in which a number of essential boundary conditions can include first derivatives of the displacement function. In this paper, the formulation for the generalised RKP-FSM is derived for the analysis of thin plates, and its accuracy and convergence are examined through a series of numerical studies. Moreover, by modifying the concept of the augmented corrected collocation method [Shodja, Khezri, Hashemian, and Behzadan (2010)] a new feature is added to the conventional SFSM and the generalised RKP-FSM which allows for the exact treatment of material discontinuities in bending analysis. Oscillatory behaviour of solutions near the interface of material discontinuities due to Gibb's phenomenon is successfully eliminated in both methods.