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中文摘要：
以梁单元平衡微分方程为基础，推导了考虑剪切变形影响的空间梁单元位移插值函数，用于模拟结构中无轴力的杆件．利用Maclaurin级数统一了空间梁柱单元在拉、压两种情况下的不同位移插值函数，与稳定函数表示的位移插值函数等价，用于模拟结构中有轴力的杆件．推导了包含轴向变形、剪切变形、双向弯曲、扭转及其耦合效应的二阶单元切线刚度矩阵．从计算精度与总体刚度矩阵的正定性两方面考虑确定了位移插值函数中级数的展开项数．对承受不同轴压力的悬臂梁梁端位移进行计算，表明所提出的单元模型可以很好地体现二阶效应的影响．利用不同单元模型对单层柱面网壳进行对比分析，表明所提出的梁系结构二阶分析单元模型具有较高的计算精度与效率，可以很好地反映单层柱面网壳的几何非线性．
英文摘要：
On the basis of equilibrium differential equation of beam, the displacement interpolating functions with shear effect of spatial beam elements used to simulate the structure members without axial forces are deduced. The different displacement interpolating functions in compression and tension spatial beam-column elements are unified by the method of Maclaurin series expansion, and the unified expressions used to simulate structure members with axial forces are equivalent to those expressed by stability functions. The second-order element tangent stiffness matrix which includes axial deformation, shear deformation, compound bending, torsion and their coupling effects is deduced. The number of expansion terms of the series in interpolating functions is determined from aspects of the calculating accuracy and positive definiteness of general stiffness matrixes of the structure. Numerical analysis results of cantilevers under different axial loads show that the element model proposed in this paper can perfectly incarnate the second-order effects. Numerical analysis results of single-layer reticulated shells indicate the effectiveness and accurateness of the element model proposed in this paper, can perfectly describe the geometrical nonlinearity of single-layer reticulated shells as well.
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