Boundary Element Analysis of Unsymmetric Laminates with Corners

  • 張 瀚文

Student thesis: Doctoral Thesis

Abstract

For the boundary element analysis of the elastic bodies in the practical engineering problems researchers in this field have explored into the many aspects of this numerical method when it is engaged with different applications and different kinds of materials In their studies some critical concerns had been paid attention to such as the need of an adequate fundamental solution the singular integrals and the corner discontinuities All of these problems can be regarded as the “classical” topics in these days and many applications had indeed been well treated in the literature However most of these studies were confined to the two dimensional problems plate bending problems or three dimensional problems utilizing isotropic or metallic materials In the industry in order to meet some structural designs such as the criteria of the light weight or the strengthening of the materials in the directions of applying force today engineers are more willing to take advantages of the designable characteristics of the composite materials or laminates With this understanding over the past few decades some researches had been conducted for the types of laminates such as specially orthotropic materials symmetric or antisymmetric laminates Nevertheless if an unsymmetric laminate is considered the mechanical behaviors of the plates will become more complex in such a way that the coupling between the in-plane and out-of-plane bending problems will be unavoidable and this problem was seldom received a thorough solution via the use of boundary elements In this dissertation to cover the complex mechanical behaviors of the composite laminates in response to all the possibility of symmetric anti-symmetric or unsymmetric stacking sequences and the corner discontinuities of a laminated plate the coupled stretching-bending analysis of the general composite laminates via boundary elements has been developed with the help of the associated boundary integral equation and the fundamental solution obtained via the Green’s function written in the form of Stroh-like complex variable formalism To effectively treat the singular problem and the corner discontinuities which may result in dependent equations in the system of equations established via the discretization of the boundary integral equation various methodologies were investigated to see their adequacies for the present application And the explicit solutions of the weakly and strongly singular integrals and the four auxiliary equations employed to replace the dependent equations are proposed in this study to solve the nodal displacements and tractions accurately and promptly Besides similar to the needs in the traditional boundary element analysis the post-processing for the calculations of the complete components of the strains and stress resultants at or near the boundary nodes was also implemented and carried out in the present study In order to obtain these results we can make useful the already known nodal displacements through the method of finite difference and all the other correct results of strains and stress resultants calculated via the derivatives of boundary integral equation at the points not so close to the boundary and the use of the constitutive equation of laminates Finally by utilizing the moving least square method with these results we can further approximate the solution in the vicinity of boundary nodes with good accuracy In this process we don’t need to tackle again the singular problems which involve hyper-singular and strongly singular integrals Hence based on all the works required at different stages the full-domain solution can be obtained for the coupling analysis of composite laminated plates via boundary elements with accuracy and efficiency
Date of Award2017 Jan 23
Original languageEnglish
SupervisorChyanbin Hwu (Supervisor)

Cite this

Boundary Element Analysis of Unsymmetric Laminates with Corners
瀚文, 張. (Author). 2017 Jan 23

Student thesis: Doctoral Thesis