【摘要】 提出适合张拉结构几何非线性分析的两节点曲线单元有限元方法．假定索元的初始形状呈二次抛物线，根据单索的平衡条件、几何和物理关系建立了索元的位移函数；由拉格朗日应变的定义建立了可以考虑任意次高阶位移影响的索元轴向应变的精确表达式，并基于拉格明日描述方法和虚功原理得到了索元的非线性平衡方程与切线刚度矩阵．采用荷载增量法与Newton－Raphson法相结合的混合法进行了实例计算，结果表明：本文方法的精度明显优于两节点直线索单元，适合于大跨度索阿、索穹顶等张拉结构的几何非线性分析．更多还原

【Abstract】 Various numerical methods including mainly the finite element methods with two--nodestraight-line and polynode curved cable element have been presented to analyze the nonlinearity ofthe tension structures which airs playing a great role in structures. As far as the polynode curvedelement methods are concerned, the precision of which is well but its freedoms are higher, andthe coordinates of inner nodes in the element is usually difficult to determine. The straight-lineelement model leads to bad precision, resulting from neglecting the effect of the cable’s deflectionunder its own weight, therefore, it is necessary and significant to research the nonlinear mechanicalmodel for the analysis of tension structures.A nonlinear finite element method with two-node curved element for the analysis of tensionstructures is presented in this paper. Assuming the cable’s initial shape to be parabolic curve, basedon the equilibrium co0ndition, geometrical and physical equation of the cables, the displacementfunction of the element is established. In terms of the definition of Lagrangian strain, the preciseexpression of the axial strain of the element is obtained, with which the effects of the displacementwith the terms of high-order can be considered. By means of the virtual displacement principle,the authors have derived the nonlinear finite element formulation, and have used this model tocompute cable structures. Comparing .with the straight--line and curved cable element methods,the authors have found that the proposed model leads to good precision and can meet the need ofengineering.更多还原