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<p>This study investigates the dynamic consequences of rigid plastic structures under high loads, such as blasts, car crashes, and gas explosions, in which the applied load is brief but several times more than the static collapse load. Structures were traditionally intended to handle static loads of set magnitudes throughout time; however, it is now understood that structures must survive both dynamic and static loading. Frames, which are extensively utilized in civil engineering applications such as foundation building, infrastructure development, and aeronautical engineering, bear a variety of loads. As a result, a trustworthy approach for analyzing dynamic behavior needed to be devised, which would enhance engineering practice. This study uses mathematical programming approaches, notably the Linear Complementary Problem (LCP) solved using the Lemke algorithm, to address concerns with rigid-plastic constructions under dynamic stresses. The study focuses on the dynamic rigid plastic response of frame structures using computational modeling confirmed by finite element analysis (ABAQUS) and experimental testing (pendulum mass technique). LCP results closely match experimental and numerical data, with peak displacement responses of 20.77&#xa0;mm (experimental), 19.3&#xa0;mm (Lemke), and 20.3&#xa0;mm (FEM). Overall, the LCP formulation offers a systematic and effective mathematical method for capturing and solving the rigid-plastic response of skeletal systems under short-duration, high-intensity loading.</p>

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Investigation of Lemke Algorithm for Dynamic Rigid Plastic Response of Frame Structures

  • 期刊论文

  • 发表日期：

    2026年5月11日

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  • Habib Ullah,
  • Fayyaz Ullah,
  • Zia Ul Islam,
  • Irshad Ahmad,
  • Azam Khan,
  • Yazeed Abdullah Alsharedah

摘要

This study investigates the dynamic consequences of rigid plastic structures under high loads, such as blasts, car crashes, and gas explosions, in which the applied load is brief but several times more than the static collapse load. Structures were traditionally intended to handle static loads of set magnitudes throughout time; however, it is now understood that structures must survive both dynamic and static loading. Frames, which are extensively utilized in civil engineering applications such as foundation building, infrastructure development, and aeronautical engineering, bear a variety of loads. As a result, a trustworthy approach for analyzing dynamic behavior needed to be devised, which would enhance engineering practice. This study uses mathematical programming approaches, notably the Linear Complementary Problem (LCP) solved using the Lemke algorithm, to address concerns with rigid-plastic constructions under dynamic stresses. The study focuses on the dynamic rigid plastic response of frame structures using computational modeling confirmed by finite element analysis (ABAQUS) and experimental testing (pendulum mass technique). LCP results closely match experimental and numerical data, with peak displacement responses of 20.77 mm (experimental), 19.3 mm (Lemke), and 20.3 mm (FEM). Overall, the LCP formulation offers a systematic and effective mathematical method for capturing and solving the rigid-plastic response of skeletal systems under short-duration, high-intensity loading.