薄膜皺折之有限元素分析

Abstract

本研究主要目的為以共旋轉有限元素法及殼元素(shell elememt) 探討薄膜結 構受面內(in plane)位移負荷作用，產生皺折後的幾何形狀。 本 研 究 擬 採 用 平 面 三 角 殼 元 素 分 析 薄 膜 結 構 ， 並 採 用 牛 頓 - 拉福森 (Newton-Raphson)法和弧長控制(arc length control)法的增量迭代法來解受位移 負荷之結構的非線性平衡方程式。 皺折為側方向的變形，由於平面薄膜結構受到平面上的剪位移作用並沒有產 生側方向變形的機制，本研究擬利用結構切線剛度的行列式值偵測結構平路徑 的分歧點，計算挫屈模態，再以挫屈模態當擾動位移，使平面薄膜結構由主要 平衡路徑進入次要平衡路徑。 本研究擬分析在邊界受剪位移作用的平面薄膜結構的皺折，並將分析結果與 文獻上的實驗結果及數值結果比較。

The formation of wrinkling deformation for thin membrane subjected to in plane displacement loading is simulated by using the co-rotational finite element formulation and thin shell element. The flat three-node triangular shell element will be employed for the analysis. An incremental-iterative method based on the Newton-Raphson method and constant arc length method will be used for solving nonlinear equilibrium equations with displacement loading. In order to initiate the out-of-plane buckled deformation for planar membranes subjected to purely in-plane displacement loading at the bifurcation point, a perturbation displacement proportional to the first buckling mode is added to the equilibrium configuration, and then equilibrium iteration is carried out until a new equilibrium state is achieved. Wrinkling of a planar membrane under uniform shear displacement loading along the edge of a membrane will be analyzed here. The present results will be compared with experimental data and numerical results in the literature.