Weak-form Quadrature Element Analysis Of High-order Beams And Plates

The weak form quadrature element method (QEM) is a new method based on variational principles and the conventional differential quadrature method. Since its inception, it has found applications in structural analysis. The QEM has demostrated its superiority over the finite element method in handling complex geometry, complicated boundary conditions, inhomogeneous materials and strong nonlinearity. Implementation of the QEM consists of following essential procedures. Firstly, the variational description of a problem is established. Secondly, the physical domain is divided into a number of quadrature elements, each being mapped onto a standard computational domain. Thirdly, numerical integrations and the differential quadrature method are introduced to characterize the problem in terms of quantities at quadrature points. A set of algebraic equations result eventualy after introduction of the stationary condition. The weak form QEM inherits the high computational efficiency of the differential quadrature method and enjoys flexibility and wide applicability of weak formulation. Functionally Graded Materials (FGMs) are a new kind of material. FGM are composed of two different materials and there is continuous gradient of composition and structure between the two materials, without any explicit interfaces. Because of its excellent properties, FGMs have been playing more and more important roles in the areas of aerospace and mechanical engineering. It will hopefully find application in civil engineering in the future.High-order beam and plate theories have been adopted in analysis of FGM components which necessiates an efficient and accurate numerical method.The purpose of this thesis is to extend the weak form QEM to high-order beam and plate analysis, and study functionally graded beams and plates. The issue of neutral-axis for FGM components is addressed. Numerical examples are presented and comparison with results in the literature and those of the commecial software ANSYS is made to exhibit the efficacy , accuracy and superiority of the QEM. The present work exploits the advantages of the QEM and performs preliminary analysis of FGM components. The achievement will serve as the stepping-stone for its application in analysis and design of FGMs.