三維組合薄壁斷面有限元素非線性分析

Abstract

樑－柱結構元件的非線性的空間行為分析為一極為困難之課題，為了分析 日益複雜之薄殼結構，期能利用矩形薄壁斷面來組成任意形狀之薄壁結構 ，如 Ｉ 形，Ｔ 形及箱形等斷面。由於一般文獻於推導幾何非線性的薄 壁結構時，均是考慮特定的斷面形狀來推導結構勁度矩陣，本文期能利用 Bathe 的等參樑元素及Total Lagrangian Formulation來推導勁度矩陣， 並利用座標轉換及樑－柱於變形後，斷面上仍是平面保持平面的特性，將 組成任意斷面之樑元素對某一個參考點，作位移自由度濃縮的作用，來考 慮結構於線性及材料非線性及幾何非線性的空間樑－柱問題。 The analysys of nonlinear three-dimension thin-walled beam column member was a typical diffcult problem. In order to analyze complicated thin-walled beam column member ,in this study, any section of thin-walled member for example I-section , T-section ,box-section can be constituted by rectangular section.Because the thin-walled geometric nonlinear stiffness was derived from specific section by most researchers. This study apply Bathe's isoparametric beam element and Total Lagrange Formulation to form the geometric nonlinear stiffness. This study condenses the degrees of freedom to a reference point by utilizing coordinate transformation and the section plan remains plan after deformation occurs , then to solve the linear , material nonlinear and geometric nonlinear spatial thin-walled problem.