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<p>L-shaped and stepped plates are widely adopted in engineering applications due to their ability to meet strict assembly requirements while achieving significant reductions in weight and material usage. This work derives analytical solutions for the buckling of clamped L-shaped functionally graded material (FGM) stepped thick plates using a symplectic approach within the framework of Hamiltonian system. Three material models are considered to describe the continuous variation of properties through the plate thickness, i.e., the power-law (P-FGM), sigmoid (S-FGM), and exponential (E-FGM) distributions. The overall plate is divided into three rectangular regions with uniform thickness, and the symplectic superposition method is applied to each region, with continuity conditions ensuring compatibility at the interfaces. The accuracy of the analytical solutions is verified through comparisons with literature and finite element results. The effects of step thickness ratio, material gradation laws and material gradient index on the buckling behavior of L-shaped FGM stepped thick plates are discussed. New benchmark data are presented to validate future numerical methods.</p>

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Symplectic buckling solutions of L-shaped functionally graded stepped thick plates

  • 期刊论文

  • 发表日期：

    2026年7月10日

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  • Yingrui Zhang,
  • Zhenhuan Zhou,
  • Yuhang Li,
  • Andi Lai,
  • Jianlong Qu,
  • Xinsheng Xu

摘要

L-shaped and stepped plates are widely adopted in engineering applications due to their ability to meet strict assembly requirements while achieving significant reductions in weight and material usage. This work derives analytical solutions for the buckling of clamped L-shaped functionally graded material (FGM) stepped thick plates using a symplectic approach within the framework of Hamiltonian system. Three material models are considered to describe the continuous variation of properties through the plate thickness, i.e., the power-law (P-FGM), sigmoid (S-FGM), and exponential (E-FGM) distributions. The overall plate is divided into three rectangular regions with uniform thickness, and the symplectic superposition method is applied to each region, with continuity conditions ensuring compatibility at the interfaces. The accuracy of the analytical solutions is verified through comparisons with literature and finite element results. The effects of step thickness ratio, material gradation laws and material gradient index on the buckling behavior of L-shaped FGM stepped thick plates are discussed. New benchmark data are presented to validate future numerical methods.