张力膜结构初始形态分析的曲面四边形单元  

FORM FINDING ANALYSIS OF TENSILE MEMBRANE STRUCTURES BY CURVED QUADRILATERAL ELEMENT

作　　者：纵智育[1] 辛克贵[1] 王珊[2] 

机构地区：[1]清华大学土木工程系教育部结构与振动重点实验室,北京100084 [2]北方工业大学建筑学院,北京100043

出　　处：《工程力学》2006年第3期32-36,26,共6页Engineering Mechanics

基　　金：北京市教育委员会科技发展计划项目(01KJ-027)

摘　　要：张力膜结构的初始形状不能随意选择,它必须符合平衡条件和建筑使用要求。根据几何非线性有限元理论,提出张力膜结构初始形态分析的8结点曲面四边形等参单元。通过建立曲线坐标,在应变的线性部分引入法向位移及单元曲率和扭率的影响,推导了张力膜结构的单元刚度矩阵和结点力列阵。采用完全的Newton-Raphson迭代法求解非线性方程组。数值算例表明该单元是一种高效、稳定和可靠的单元。The initial forms of tensile membrane structures can not be selected arbitrarily. They must satisfy static equilibrium and architectural need. Based on geometrical nonlinear finite element theory, a curved quadrilateral isoperimetric element with 8 nodes for presented. The components caused by the element initial form analysis of tensile membrane structures is curvatures are added to the equilibrium equations by establishing curvilinear coordinates. The expressions of the element stiffness matrix and the nodal force array are derived. Newton - Raphson iteration method is adopted to solve nonlinear equations. Numerical examples indicate that this method is efficient, reliable, and stable.

关 键 词：张力膜结构 初始形态分析 曲面四边形等参元 几何非线性有限元法 极小曲面 

分 类 号：TU318[建筑科学—结构工程]