| 张力膜结构初始形态分析的曲面四边形单元 |
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| 引用本文： | 纵智育,辛克贵,王珊.张力膜结构初始形态分析的曲面四边形单元[J].工程力学,2006,23(3):32-36,26. |
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| 作者姓名： | 纵智育 辛克贵 王珊 |
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| 作者单位： | 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 |
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| 基金项目： | 北京市教委科技发展计划项目 |
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| 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。
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| 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 |
| 文章编号： | 1000-4750（2006）03-0032-05 |
| 收稿时间： | 2004-03-26 |
| 修稿时间： | 2004-03-262004-05-21 |
FORM FINDING ANALYSIS OF TENSILE MEMBRANE STRUCTURES BY CURVED QUADRILATERAL ELEMENT |
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| ZONG Zhi-yu,XIN Ke-gui,WANG Shan.FORM FINDING ANALYSIS OF TENSILE MEMBRANE STRUCTURES BY CURVED QUADRILATERAL ELEMENT[J].Engineering Mechanics,2006,23(3):32-36,26. |
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| Authors: | ZONG Zhi-yu XIN Ke-gui WANG Shan |
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| Affiliation: | 1. Department of Civil Engineering, Tsinghua University, Key Laboratory of Structural Engineering and Vibration of Education Ministry, Beijing 100084 China; 2. School of Architecture, North China University of Technology, Beijing 100043, China |
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| Abstract: | 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. |
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| Keywords: | tensile membrane structures initial form analysis curved quadrilateral isoperimetric element geometrical nonlinear finite element minimal surface |
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