(1 同济大学建筑工程系，上海 200092； 2 同济大学建筑设计研究院，上海 200092)
［摘要］以薄板的大挠度弯曲微分方程组为基础，以平面内可自由滑动、平面外无位移的局部测量范围内膜材为边界条件，推导出不同材性膜材的位移与张力对应比例关系。结合鹿岛建设株式会社的试验，得到双向等张力情况下膜张力-位移相关公式，该公式适用于各向同性与正交异性的膜材。ANSYS有限元验证表明，该公式具有很高的精度，可以满足工程需要。
［关键词］薄板；大挠度弯曲微分方程组；膜；张力-位移；有限元
Formulation and verification of membrane pressure-deflection formula based on similarity transformation theory
Deng Changgen1, Liu Bing2(1 Department of Building Engineering, Tongji University，Shanghai 200092，China;2 Architecture Design and Research Institute of Tongji University，Shanghai 200092，China)
Abstract:Based on the differential equations of large deflection bending of thin plates,
with the boundary condition that the local measuring membrane can slip in the plane without any out-of-plane deflection, the deflection and pressure corresponding proportion of different membrane are derived. Then combined with the experiment of Japan Kajima Building Company, the formula of membrane with equal tension in both ways is summarized, and the formula is suitable for both isotropic and orthotropic membrane. It is verified through ANSYS FEM analysis that the formula has great accuracy, so it can be applied in the practical project.
Keywords:thin plate; differential equations of large deflection bending; membrane; pressuredeflection; FEM
作者简介：邓长根，教授，博导，Email:dengcg@mail.tongji.edu.cn。
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