article · Alexandria Engineering Journal
An analytical framework evaluates thermal stress and deformation in curved nanobeams resting on a Pasternak foundation. The structure undergoes both transverse mechanical forces and thermal loading. To model the displacement field accurately, sinusoidal shear deformation theory is combined with nonlocal thermoelasticity principles, using the principle of virtual work to formulate the governing equations. The resulting solutions, demonstrated for simply-supported boundary conditions, show how structural behaviour responds to variations in key factors. These influences include the spring and shear parameters of the supporting foundation, the magnitude of the thermal loads, the nanoscale size effect represented by the nonlocal parameter, and the curvature radius of the beam. The findings provide theoretical insights directly relevant to calculating load responses in curved nanoscale structures.
Nanoscale structural components often experience extreme temperature variations and mechanical forces in tiny devices. Standard macroscopic theories fail to account for nanoscale physical behaviours. By accurately capturing how curvature, foundational support, and size effects influence thermal stresses, this analytical model helps engineers understand the mechanical integrity and deformation patterns of curved components before they are built.
The analytical model is early-stage theoretical research intended to inform the design of curved nanobeams operating under combined mechanical and thermal stress. Potential users include micro- and nanoscale mechanical designers and engineering analysts. Because the study focuses on mathematical derivations and analytical results rather than physical device fabrication, the work remains at a fundamental modelling stage and requires experimental testing before practical implementation.
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In this paper, the analytical approach for thermal stress and deformation analysis of a curved nanobeam is presented. The nanobeam is subjected to transverse mechanical and thermal loads while resting on Pasternak's foundation. Sinusoidal shear deformation theory is employed to derive displacement field of curved nanobeam. In addition, nonlocal thermo-elasticity relations are employed to derive governing equations of thermal analysis based on principle of virtual work. The analytical results are presented for simply-supported curved nanobeam to discuss the influence of important parameters on the results of thermal stress. The important parameters include spring and shear parameters of foundation, thermal loads, nonlocal parameter and radius of curvature of curved nanobeam. The results of our problem are applicable to design of curved nanobeams subjected to thermal and mechanical loads. Keywords: Sinusoidal shear deformation theory, Thermal loads, Curved nanobeam, Pasternak's foundation, Nonlocal parameter
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DOI: 10.1016/j.aej.2017.07.003
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