A numerical-computational model for static analysis of plane frames with semirigid connections and geometric nonlinear behavior is presented. The set of nonlinear equations governing the structural system is solved by the Potra–Pták method in an incremental procedure, with order of cubic convergence, combined with the linear arc-length path-following technique. The algorithm pseudo-code is presented, and the finite element corotational method is used for the discretization of the structures. The equilibrium paths with load and displacement limit points are obtained. The semirigidity is simulated by a linear connection element of null length, which considers the axial, tangential, and rotational stiffness. Nonlinear analyses of 2D frame structures are carried out with the free Scilab program. The results show that the Potra–Pták procedure can decrease the number of iterations and the computing time in comparison with the standard and modified Newton–Raphson iterative schemes. Also, the simulations show that the connection flexibility has a strong influence on the nonlinear behavior and stability of the structural systems.

中文翻译：

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半刚性连接框架非线性分析的数值计算模型

提出了一种用于半刚性连接和几何非线性行为的平面框架静态分析的数值计算模型。用Potra–Pták方法以逐步收敛的方式（按三次收敛顺序）结合线性弧长路径跟踪技术，可解决控制结构系统的非线性方程组。给出了算法的伪代码，并使用有限元校正法对结构进行离散化。获得具有载荷和位移极限点的平衡路径。半刚性由零长度的线性连接元件模拟，该元件考虑了轴向，切向和旋转刚度。使用免费的Scilab程序对2D框架结构进行非线性分析。结果表明，与标准和改进的Newton-Raphson迭代方案相比，Potra-Pták过程可以减少迭代次数和计算时间。仿真还表明，连接的柔性对结构系统的非线性行为和稳定性有很大的影响。