含孔洞複合材料層板之邊界元素法分析

Abstract

本文使用Wu and Hsiao(2015)所提之邊界積分方程式，分析含孔洞之有限複合材料層板受力矩的力學反應，尤其是孔洞的應力放大現象。Wu and Hsiao(2015)所提之邊界積分方程式是以曲率為幾何參數，對於自由板的問題可得相當準確的數值結果，但對於一般邊界條件則不完全適用，因此本文另改以轉角為幾何參數，提出一個新的邊界積分方程式以補原積分方程式之不足。該邊界積分方程式是以柯西積分式為核心並使用古典層板理論和類似異向彈性力學中的史磋法理論作為推導的基礎。本文算例有自由板或懸臂板受彎矩作用的問題，考慮的層板則有正交性、單層異向性、雙層異向性三種。運用邊界積分方程式所得的數值均與有限元素法結果比對，以評估兩種數值方法的優缺點及適用的狀況。

This thesis uses the boundary integral equations proposed in Wu and Hsiao(2015) to analyze finite laminated plates with holes subjected to moments. Although the integral equations, which contain curvatures as geometric parameters, work well for free plates, they do not all apply to all boundary conditions. A new boundary integral formulation with rotations as parameters is proposed to remedy the issue. The formulation is based on a Stroh-Like formalism developed for the lamination theory with Cauchy integral formula. The numerical examples are a free plate or cantilever plate subjected to bending moments. The plates considered include homogeneous orthotropic, homogeneous anisotropic and two-layered anisotropic plates. The numerical results from boundary integral formulation are compared with those using finite element method to assess the advantages and disadvantages of two numerical methods.