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为了降低可带铰空间梁单元切线刚度矩阵的运算量、提高非线性计算精度,本文首先通过建立单元随转坐标系得到扣除刚体位移后结构变形与总位移之间的关系,进而基于场一致性原则导出空间梁单元的几何非线性单元切线刚度矩阵,并在此基础上根据带铰梁端弯矩为零的受力特征得到考虑梁端带铰的单元切线刚度矩阵表达式。该方法利用随转坐标系下除单元轴向相对位移外的其余五个线位移均为零的特点,降低了计算单元切线刚度矩阵所需的相关矩阵阶次,因此减少了运算量。对对角点受拉铰接的方棱形框架进行计算,得出本文结果与解析解的最大误差为0.226%;对45°弯梁和带铰平面结构的空间受力进行计算,得出前者与已有文献提供的解非常接近,误差为0.027%～2.394%,后者与ANSYS计算结果的最大误差为1.082%,表明本文算法具有良好的精度。
In order to reduce the computational complexity of tangent stiffness matrices and to improve the nonlinear calculation accuracy of the beam elements with hinged space beam, this paper first obtains the relationship between the deformation and the total displacement after deducting the rigid body displacement by establishing the unit coordinate system. Then, The tangent stiffness matrix of geometrical nonlinear element of space beam element is deduced in principle, and based on this, the expression of tangent stiffness matrix of element with the hinge of beam end is obtained based on the force characteristic with zero bending moment at the hinge end. The method uses the characteristics that the displacements of the remaining five lines except the axis relative displacement in the coordinate system are zero, which reduces the order of the correlation matrix required for calculating the tangent stiffness matrix of the unit, thereby reducing the amount of calculation. The square frame with the hinged joints is calculated. The maximum error between the result and the analytical solution is 0.226%. The calculation of the space force of the 45 ° curved beam and the hinged plane structure shows that the former The solutions provided by the literature are very close, the error is 0.027% ~ 2.394%, the maximum error between the latter and the ANSYS calculation is 1.082%, which shows that the proposed algorithm has good accuracy.