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本文首先采用余能原理推导曲梁的转角位移方程式,求出曲梁的单元刚度矩阵解析表达式。然后根据结构的几何特征推导梁单元的杆端位移坐标转换矩阵,并引用所给正交曲线-直线交叉染系的等效结点荷载列阵,进而提出了一个求解此类结构的精确的有限元计算模型。文末采用本文编制的程序作了实例计算,数值分析结果表明:当使曲梁退化为直梁时,所求得的内力和位移值与相同条件下正交直染系的计算结果接近一致。
This paper first uses the principle of residual energy to derive the angular displacement equation of curved beam, and obtains the analytical expression of the element stiffness matrix of curved beam. Then, according to the geometrical characteristics of the structure, the rod-end displacement coordinate transformation matrix of the beam element is deduced, and the equivalent node load matrix of the orthogonal cross-history curve-line cross-staining system is quoted, and then an exact finite structure for solving such structures is proposed. Meta-computing model. At the end of the paper, an example calculation was made using the procedure developed in this paper. The numerical analysis results show that when the curved beam is degenerated into a straight beam, the calculated internal forces and displacement values are close to the results of the orthogonal straight dyeing system under the same conditions.