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本文推导出了任意截面形状的楔形杆的单元刚度矩阵和单元几何刚度矩阵。文中截面面积和惯性矩沿杆轴的变化性质由杆件的截面尺寸精确表达,屈曲位移模式近似地用已知杆端位移产生的弹性变位曲线描述,单元刚度矩阵和单元几何刚度矩阵采用结构力学和能量原理相结合的方法推导,形式简单,精度良好,可以方便地用于实际工程。文中附有计算实例。
In this paper, the element stiffness matrix and element geometric stiffness matrix of wedge-shaped rods with arbitrary cross-section shapes are deduced. The cross-sectional area and the moment of inertia along the shaft axis are precisely expressed by the cross-sectional dimensions of the rod. The buckling displacement pattern is described approximately by the elastic displacement curve resulting from the known rod end displacement. The element stiffness matrix and the element geometric stiffness matrix adopt the structure. The combination of mechanics and energy principles leads to a simple form, good accuracy, and can be conveniently used in practical projects. Examples are given in the text.