The Scaled Boundary Finite Element Method for Plate Structures

Abstract

The primary goal of this thesis is to develop a three-dimensional consistent numerical technique for solving plate structures with any geometry, thickness, boundary and loading conditions in a uniformly efficient and accurate manner based on scaled boundary finite element method. Meanwhile, the technique is free from shear locking and can be flexibly applied for the plate structures with advanced materials. The numerical technique is firstly developed for the isotropic plates. The formulation is derived from the three-dimensional governing equations. The in-plane dimensions of the plates are discretised with high-order spectral elements, which represent curved boundaries accurately. The solution along the thickness direction is obtained analytically and approximated by a Pade expansion for efficiency. A diagonal mass matrix is obtained, and standard explicit time-stepping schemes are directly applicable. Advantages of this numerical technique include that no ad hoc factors, such as the shear correction factor, are required, no shear locking problem and hourglass effect arise, and it can model the plate with distorted mesh accurately. Numerical examples for static, free vibration and explicit transient analysis are presented. High accuracy and computational efficiency are achieved as demonstrated in the numerical examples. The formulations for the plate structures with advanced materials, such as functionally graded materials and laminated composite materials are subsequently developed. For the functionally graded plates, the material properties are graded only in the in-plane direction by a simple power law and assumed to be temperature independent. For the laminated composite plates, a layer-wise approach is applied. The three-dimensional consistent behaviour allows the proposed numerical technique to describe both discrete layer transverse shear effects and discrete layer transverse normal effects accurately. No ill-conditioning occurs when the thickness of the plate becomes thin. The influence of material gradient index, fiber orientations, loading, boundary conditions and geometry of the plate on the deflections, stresses, natural frequencies and critical buckling load are computed numerically. Efficient and accurate results are obtained.