变曲率曲线梁的单元刚度矩阵分析

发布时间：2018-04-20 20:17

本文选题：单元刚度矩阵 + 变曲率曲线梁　；参考：《西南交通大学学报》2017年03期

【摘要】：针对单元刚度矩阵多为隐函数,不便于直接应用的问题,在极坐标系下,假定变曲率曲线梁剪心和形心重合,根据卡氏第二定理,推导了一种显式变曲率曲线梁单元悬臂端柔度矩阵的解析解公式.该公式先将其柔度矩阵退化到经典的形式;再通过求逆运算得到变曲率曲线梁单元悬臂端刚度矩阵;最后根据静力平衡条件与结点位移的任意性获得曲线梁的单元刚度矩阵.以两端固定曲线梁为例,利用MATLAB编程与ANSYS有限元计算结果进行了对比,结果表明:竖向位移和扭转角相差都在5%以内,两者的误差较小,验证了单元刚度矩阵对变曲率曲线梁计算的有效性;矩阵中的元素可用带参数的显函数表达,且所有参数都可直接引用,说明了它的正确性.
[Abstract]:In view of the problem that the element stiffness matrix is mostly implicit, it is not convenient for direct application. Under the polar coordinate system, the shear center of the curvilinear curved beam is assumed to coincide with the centroid. A formula for the analytical solution of the flexibility matrix of the cantilever end of the explicit curvilinear beam element is derived, based on the Carson's second theorem. The formula first degenerates its flexibility matrix to the classical form. The stiffness matrix of the cantilever end of the variable curvature curve element is obtained by the inverse calculation. Finally, the element stiffness matrix of the curved beam is obtained according to the static equilibrium condition and the arbitrariness of the node displacements. The MATLAB programming is compared with the results of the ANSYS finite element calculation with the two ends fixed curve beam. The results show that the vertical displacement and the torsion are reversed. The difference between the angle difference is within 5%, the error of both of the two is small, and the validity of the element stiffness matrix is verified. The elements in the matrix can be expressed by the explicit function with the parameters, and all the parameters can be directly referenced, which shows the correctness of the matrix.

【作者单位】：兰州交通大学土木工程学院;
【基金】：国家自然科学基金资助项目(51368032,51568036) 甘肃省科技计划资助项目(1606RJYA231)
【分类号】：U441

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