In this paper, the kinematic and static solutions for solving the static response of the beam column with nonlinear springs are presented by adopting the extended linear matching method (LMM). The extended LMM can be used to predict the displacement response of the beam-column system consisting of perfectly plastic and strain-softening materials. It is found that the kinematic solution generated by the extended LMM demonstrates a monotonic decrease for perfect plastic materials with certain restrictions on the yield surface. The potential energy of the system is proved to decrease with iterations for both perfect plastic and strain-softening materials if the loading multiplier remains constant. The extended LMM method is then applied to analyse the response of the pile system in a 3-leg offshore platform. An incremental procedure is recommended to determine the peak load for the soil exhibiting strain-softening. A displacement-control approach is used with the loading multiplier obtained from the variation of the potential energy. Good convergence of the method is obtained.

中文翻译：

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使用扩展线性匹配法求解具有非线性弹簧的梁柱的运动学和静态解

在本文中，采用扩展线性匹配法（LMM）提出了求解具有非线性弹簧的梁柱静态响应的运动学和静态解。扩展的 LMM 可用于预测由完美塑性和应变软化材料组成的梁柱系统的位移响应。发现由扩展的 LMM 产生的运动学解表明对于屈服面有一定限制的完美塑性材料单调递减。如果载荷乘数保持恒定，系统的势能被证明随着完美塑性和应变软化材料的迭代而降低。然后应用扩展的 LMM 方法来分析 3 腿海上平台中桩系统的响应。建议使用增量程序来确定表现出应变软化的土壤的峰值载荷。位移控制方法与从势能变化获得的载荷乘数一起使用。获得了该方法的良好收敛性。