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<p>This study develops a <b>nonlinear coupled thermoelastic</b> formulation tailored for functionally graded beams subjected to large deflections under transient thermal conduction. The beam behavior is modeled using first-order shear deformation theory (FSDT) in conjunction with von Kármán strain–displacement relations to capture geometric nonlinearity. The governing equations are derived via Hamilton’s principle and discretized using the <b>variational differential quadrature</b> (VDQ) method. Time integration is performed through the Newmark-beta scheme. Thermo-mechanical properties of the functionally graded material are considered <b>temperature-dependent</b> and are dynamically updated to reflect realistic thermal behavior. The formulation is validated against benchmark solutions in both linear and uncoupled regimes to ensure accuracy. Parametric studies reveal that power-law index of functionally graded materials, geometric dimensions, boundary conditions, beam thickness, and heat flux intensity significantly influence the nonlinear thermoelastic response. Results indicate that geometric nonlinearity mitigates stress fluctuations and moderates’ deflection growth. Moreover, the interaction between power-law index and structural geometry plays a decisive role in balancing stiffness, thermal resistance, and deformation capacity. The proposed framework offers a reliable and adaptable computational tool for analyzing advanced FGM structures under complex thermal environments, with direct implications for high-performance engineering applications.</p>

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On nonlinear coupled thermoelastic analysis of functionally graded beams

  • 期刊论文

  • 发表日期：

    2026年6月29日

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  • Ali Talebian,
  • Mohammad Faraji Oskouie,
  • Reza Ansari

摘要

This study develops a nonlinear coupled thermoelastic formulation tailored for functionally graded beams subjected to large deflections under transient thermal conduction. The beam behavior is modeled using first-order shear deformation theory (FSDT) in conjunction with von Kármán strain–displacement relations to capture geometric nonlinearity. The governing equations are derived via Hamilton’s principle and discretized using the variational differential quadrature (VDQ) method. Time integration is performed through the Newmark-beta scheme. Thermo-mechanical properties of the functionally graded material are considered temperature-dependent and are dynamically updated to reflect realistic thermal behavior. The formulation is validated against benchmark solutions in both linear and uncoupled regimes to ensure accuracy. Parametric studies reveal that power-law index of functionally graded materials, geometric dimensions, boundary conditions, beam thickness, and heat flux intensity significantly influence the nonlinear thermoelastic response. Results indicate that geometric nonlinearity mitigates stress fluctuations and moderates’ deflection growth. Moreover, the interaction between power-law index and structural geometry plays a decisive role in balancing stiffness, thermal resistance, and deformation capacity. The proposed framework offers a reliable and adaptable computational tool for analyzing advanced FGM structures under complex thermal environments, with direct implications for high-performance engineering applications.