複合材料板件結構之最佳化設計

Abstract

本文利用一階剪變形及多層的位移場理論之有限單元法來探討複合材料板件結構的力學行為，內容主要探討積層板╱三明治板在受力下的應力值，首層破壞力及最佳化設計的問題。在最佳化設計方面，建立一含束制條件的全域性最佳設計方法來設計複合材料板件結構，設計的目的是提高板件結構的勁度 (stiffness)，自然頻率及容積阻尼比，在不同的長厚比，長寬比及層數組 (number of layergoups) 下，求取最佳的纖維角度及厚度。 另外將含束制條件的全域性最佳設計方法和branch and dboundmethod，使用二階段的最佳化過程來研究積層板和三明治板的輕量化設計，其設計的目的是增加板件的強度而降低其重量。最佳設計過程中是將三明治板的面板層厚和纖維方向以及夾心材的厚度做為設計變數，在不同的邊界條件，長厚比，長寬比及層數組下，求取最佳纖維方向及層數。 最後，對複合材料積層板和三明治板進行一系列的破壞試驗，並比較實驗與理論值的差異性。由本研究知道，採用所提多層理論的有限單元法來進行分析，可精確預估板件結構的破壞強度。

Two types of finite element, namely, a shear deformable finite element and a finite element constructed on the basis of the layerwise linear displacement theory are developed for the design and analysis of thick laminated composite plates and sandwich plates. In the formulation of the layerwise finite element, the plate thickness is divided into a number of mathematical layer groups and displacements are assumed to vary linearly in each layer group which contains eight or nine nodal points. Two methods are used to solve a variety of problems on deflection, stress distribution, first natural frequency and first-ply failure load. Utilizing the proposed finite element methods, the optimal layups for the plates with maximum stiffhesses, maximum vibration frequencies or minimum weight, respectively, are designed via a constrained global optimization method. The previously proposed constrained global optimization method is incorporated into the branch and bound method to formulate a two level optimization technique for conducting the minimum weight design of thick laminated composite plates and sandwich plates with continuous (core thickness) and discrete (number of layer) design variables subject to strength constraint. A number of examples of the design of symmetrically laminated plates with various material properties, side-to thickness ratios, aspect ratios, several failure criteria and different numbers of layers are given to illustrate the applications of the present method. Besides, experimental and theoretical methods are presented to study the first-ply failure strength of laminated composite/sandwich plates under different loading conditions. The first-ply failure loads are determined using the acoustic emission AMS3(AE) system. The proposed finite element methods together with Tsai-Wu failure criterion are used to predict the first-ply failure strength of the plates. The experimental results are then used to verify the accuracy of the proposed analytical methods.