A Two-Dimensional Thermoelasticity Solution for Bimodular Material Beams under the Combination Action of Thermal and Mechanical Loads

Si-Rui Wen, Xiao-Ting He, Hao Chang and Jun-Yi Sun
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Si-Rui Wen: School of Civil Engineering, Chongqing University, Chongqing 400045, China
Xiao-Ting He: School of Civil Engineering, Chongqing University, Chongqing 400045, China
Hao Chang: School of Civil Engineering, Chongqing University, Chongqing 400045, China
Jun-Yi Sun: School of Civil Engineering, Chongqing University, Chongqing 400045, China

Mathematics, 2021, vol. 9, issue 13, 1-20

Abstract: A typical characteristic of bimodular material beams is that when bending, the neutral layer of the beam does not coincide with its geometric middle surface since the mechanical properties of materials in tension and compression are different. In the classical theory of elasticity, however, this characteristic has not been considered. In this study, a bimodular simply-supported beam under the combination action of thermal and mechanical loads is theoretically analyzed. First, a simplified mechanical model concerning the neutral layer is established. Based on this mechanical model, Duhamel’s theorem is used to transform the thermoelastical problem into a pure elasticity problem with imaginary body force and surface force. In solving the governing equation expressed in terms of displacement, a special solution of the displacement equation is found first, and then by utilizing the stress function method based on subarea in tension and compression, a supplement solution for the displacement governing equation without the thermal effect is derived. Lastly, the special solution and supplement solution are superimposed to satisfy boundary conditions, thus obtaining a two-dimensional thermoelasticity solution. In addition, the bimodular effect and temperature effect on the thermoelasticity solution are illustrated by computational examples.

Keywords: thermoelasticity; bimodular material beams; thermal load; tension and compression; neutral layer (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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