Kinematic and Static Solutions for Beam Column with Nonlinear Springs Using the Extended Linear Matching Method

Abstract

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.