This paper presents a new algorithm to solve the system of nonlinear equations that describes the static equilibrium of trusses with material and geometric nonlinearities, adapting a three-step method with fourth-order convergence found in the literature. The co-rotational formulation of the Finite Element Method is used in the discretization of structures. The nonlinear behavior of the material is characterized by an elastoplastic constitutive model. The equilibrium paths with limit points of load and displacement are obtained using the linearized Arc-Length path-following technique. The numerical results obtained with the free program Scilab show that the new algorithm converges faster than standard procedures and modified Newton-Raphson, since the approximate solution of the problem is obtained with a smaller number of accumulated iterations and less CPU time. The equilibrium paths show that the structures exhibit a completely different behavior when the material nonlinearity is considered in the analysis with large displacements.

本文提出了一种求解非线性方程组的新算法，该算法描述了具有材料和几何非线性的桁架的静态平衡，并采用了文献中发现的具有四阶收敛性的三步法。有限元方法的同向旋转公式用于结构离散化。材料的非线性行为由弹塑性本构模型表征。使用线性化的弧长路径跟踪技术，可以获得带有载荷和位移极限点的平衡路径。使用免费程序Scilab获得的数值结果表明，新算法的收敛速度快于标准程序，并且改进了Newton-Raphson，因为该问题的近似解决方案是通过较少的累积迭代次数和较少的CPU时间获得的。平衡路径表明，当在大位移分析中考虑材料非线性时，结构表现出完全不同的行为。