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Abstract <p>This study investigates the buckling behaviour of functionally graded material (FGM) beams through an analytical–numerical framework that incorporates both Poisson’s effect and nonlocal elasticity theory. An original warping shape function and a refined higher-order transverse shear deformation field are introduced to improve the accuracy of the displacement model. The equilibrium equations are derived using the principle of minimum potential energy, and the Ritz method is employed to solve them numerically. The study first considers a simply supported FGM beam composed of metal and ceramic constituents, allowing comparison of the dimensionless critical buckling loads predicted by various higher-order deformation theories. A second application focuses on a sandwich beam with a ceramic core, where both non-local and Poisson’s effects are simultaneously considered. The analysis explores a range of beam slenderness ratios and volume fraction indices. The&#xa0;results demonstrate that Poisson’s effect significantly influences the critical buckling load, while the non-local effect exhibits strong dependence on the beam’s slenderness. Specifically, the non-local influence intensifies in shorter beams due to the enhanced role of shear deformations. These findings underline the necessity of including both Poisson’s and non-local effects for accurate modeling of FGM beam stability.</p>

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Analytical and Numerical Approach on Coupled Non-Local and Poisson Effects on the Buckling of Engesser Higher-Order FGM Beams

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • M. Hamhami,
  • N. Elmeiche,
  • I. Mechab,
  • B. Mechab

摘要

Abstract

This study investigates the buckling behaviour of functionally graded material (FGM) beams through an analytical–numerical framework that incorporates both Poisson’s effect and nonlocal elasticity theory. An original warping shape function and a refined higher-order transverse shear deformation field are introduced to improve the accuracy of the displacement model. The equilibrium equations are derived using the principle of minimum potential energy, and the Ritz method is employed to solve them numerically. The study first considers a simply supported FGM beam composed of metal and ceramic constituents, allowing comparison of the dimensionless critical buckling loads predicted by various higher-order deformation theories. A second application focuses on a sandwich beam with a ceramic core, where both non-local and Poisson’s effects are simultaneously considered. The analysis explores a range of beam slenderness ratios and volume fraction indices. The results demonstrate that Poisson’s effect significantly influences the critical buckling load, while the non-local effect exhibits strong dependence on the beam’s slenderness. Specifically, the non-local influence intensifies in shorter beams due to the enhanced role of shear deformations. These findings underline the necessity of including both Poisson’s and non-local effects for accurate modeling of FGM beam stability.