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) 對膜結構皺折後的幾何形狀作初步探討。 本研究採用文獻[19]的平面三角殼元素分析膜結構，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，本研究利用偵測結構平路徑的分歧點，計算挫屈模態，利用挫屈模態當擾動位移，使平面膜結構進入次要平衡路徑，以產生皺折。 本研究分析在邊界受剪位移作用的平面膜結構的皺折，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 is simulated by using the co-rotational finite element formulation and shell element. The shell element employed here is the flat three-node triangular shell element proposed by Bathe and Ho’s [19]. An incremental-iterative method based on the Newton-Raphson method and constant arc length method is 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 the membrane is analyzed here. The present results are compared with experimental data and numerical results in the literature. Good agreement between the present numerical results and experimental data is observed.