充气膜结构有限元找形的体积微分法

A New Approach of Volume Differential Method with Finite Elementin Form-finding Analysis of Pneumatic Membrane Structures

为确定充气膜结构找形分析时,在内压已知情况下膜面张力的大小,根据多元函数泰勒展开公式推导了该类结构充气膨胀的体积微分方程,并由基于U.L.格式的非线性有限单元法,建立了以节点位移和膜面初始张力为未知量的平衡方程,编制了在给定内部气压及膨胀体积情况下的找形分析程序。对球面及圆柱面充气膜结构进行了找形计算,得到的数值结果与由球面及圆柱面的矢高、内压、初始张力相互关系得到的理论解进行比较并得到了验证。计算结果表明,提出的基于有限元的体积微分法可有效的用于充气膜结构的找形分析。

In order to determine the initial stress of pneumatic membrane structures in form-finding analysis in the condition that the internal pressure is given, the Taylor Expansion of a multi-variable function is used to establish the volume differential equation. With the nonlinear finite element method based on Updated Lagranglan formulations, this paper presents a new approach to calculate the nodal displacements and initial stress in pneumatic membrane structures form-finding analysis. A numerical procedure has been developed and two air supported membrane structures are selected as the analytical models. By comparing the numerical results with the corresponding theoretical results, the validity of the presented approach is shown.