Thermoelastic Response of Fractional-Order Nonlocal and Geometrically Nonlinear Beams
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This study presents both the theoretical framework and the finite element solution to the fractional-order nonlocal thermoelastic response of beams. The constitutive relations of the fractional-order medium are developed based on thermodynamic principles. Remarkably, it is shown that the fractional model allows the rigorous application of thermodynamic balance principles at every point within the domain. The theory is applied to the analysis of the nonlocal response of Euler-Bernoulli beams under combined thermo-mechanical loads. The governing fractional-differential equations and the associated boundary conditions for the elastic field variables are derived using variational principles. The fractional finite element method (f-FEM) is used to numerically solve the linear and nonlinear fractional-order system of equations. Further, the numerical model is used to study the thermoelastic response of the nonlocal beam subject to various thermo-mechanical loads and boundary conditions. The fractional thermoelasticity framework is expected to provide consistent models for nonlocal interactions in complex nonlocal structures exposed to a thermo-mechanical environment.
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