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.

Highlights

  • Classical limit analysis has been conducted extensively in the engineering due to its sound theoretical fundamental and practicability since 1950s. e upper and lower bound theorems provide the basis for bracketing the plastic limit load of a structural system that consists of the perfectly plastic materials subjected to small strain [1,2,3,4,5]

  • For the system consisting of perfectly plastic materials without geometric nonlinearities, Ponter et al [6] demonstrated that the displacement field generated from an elastic solution can be treated as a plastic displacement field in the limiting case. erefore, the upper and lower bound solutions can be obtained simultaneously through the linear matching method (LMM), and the exact solution associated with the displacement field allowed by the finite element (FE) formation is guaranteed by the convergence of the upper and lower bound solutions with certain restrictions on the yield surface

  • A case study is conducted on an actual offshore platform failed in pile foundation overturning in Hurricane Ike [16,17,18]. e proposed method falls into the general group of determining the load multiplier in global displacement-softening problems in FE analysis. e novel features of the proposed method on the potential energy-based kinematic solution and the yield criteria-based static solution for bracketing the exact load-displacement response are discussed

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Summary

Introduction

Classical limit analysis has been conducted extensively in the engineering due to its sound theoretical fundamental and practicability since 1950s. e upper and lower bound theorems provide the basis for bracketing the plastic limit load of a structural system that consists of the perfectly plastic materials subjected to small strain [1,2,3,4,5]. As the first step in extending the LMM to strain-softening materials, this paper focuses on a classical problem, i.e., the static response of a beam column with nonlinear springs, to demonstrate the potential of the proposed method. E objective of this paper is to derive FE-based kinematic and static solutions for bounding the load-displacement responses of pile foundations under monotonic loading by adopting the extended linear matching method (LMM). E proposed method falls into the general group of determining the load multiplier in global displacement-softening problems in FE analysis. E novel features of the proposed method on the potential energy-based kinematic solution (mimic to the upper bound solution in limit analysis) and the yield criteria-based static solution (mimic to the lower bound solution in limit analysis) for bracketing the exact load-displacement response are discussed A case study is conducted on an actual offshore platform failed in pile foundation overturning in Hurricane Ike [16,17,18]. e proposed method falls into the general group of determining the load multiplier in global displacement-softening problems in FE analysis. e novel features of the proposed method on the potential energy-based kinematic solution (mimic to the upper bound solution in limit analysis) and the yield criteria-based static solution (mimic to the lower bound solution in limit analysis) for bracketing the exact load-displacement response are discussed

Description of the Extended LMM Method
Convergence Discussion
Findings
Case Study
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