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本文首先采用了广义内力和广义形变的观念建立了一般化变分原理。其次采用了三角形单元,作出了索网的有限单元法构式,推导了刚度矩阵及荷载矩阵的表示式以及非线性问题的迭代过程。在附录中列出边缘构件曲梁的刚度矩阵的形式。将素网的刚度矩阵和曲梁的刚度矩阵结合起来可以考虑它们之间的相互作用。并用本文方法计算了振动问题。从例题中可以看出无论在静力计算或动力计算中考虑边缘构件的共同作用与不考虑共同作用其计算结果将有显著不同,这说明了考虑共同作用的重要性。
Firstly, this paper uses generalized internal force and generalized deformation to establish the generalized variational principle. Secondly, the triangular element is used to make the finite element method of the cable net. The expression of the stiffness matrix and the load matrix and the iterative process of the nonlinear problem are deduced. The form of the stiffness matrix of the edge member bending beam is listed in the appendix. Combining the stiffness matrix of the plain mesh with the stiffness matrix of the curved beam can consider the interaction between them. And using this method to calculate the vibration problem. It can be seen from the example that whether the consideration of the joint action of the edge members in the static calculation or the dynamic calculation is not significantly different from the calculation result, it shows the importance of considering the joint action.