Generalised RKP-FSM and its application in analysis of thin plates with abrupt rigidity changes and generally laminated composite plates

摘要

A finite strip method (FSM) utilising the meshfree generalised reproducing kernel particle method (RKPM) is developed for the numerical analysis of plates and of laminated plate assemblies. 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 polynomial functions which are used in conventional formulations are retained. The structure of the generalised RKPM 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 bending, 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. In this thesis, the formulation for the generalised RKP-FSM is derived for flexure, buckling, and free vibration analyses, and its accuracy and convergence are elucidated through a series of numerical studies. Moreover, by modifying the concept of the augmented corrected collocation method, a new feature is added to the conventional SFSM and the generalised RKP-FSM which allows for the exact treatment of rigidity discontinuities in plate analysis. This provides a versatile and powerful computational capability which facilities the analysis of problems including plate structures with abrupt thickness changes of its component plates. This thesis also presents a novel numerical procedure based on the state space approach for the static analysis of thick and laminated composite plates using the proposed RKP-FSM. A semi-analytical technique is presented for the static analysis of thick and generally laminated composite plates by combining the RKP-FSM with the state space method. The present formulation is based on the application of the RKP-FSM in the plane of the problem to approximate the in-plane variations of displacement and stress components while the state space method is adopted for the prediction of stress and displacement components in the thickness direction.