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Solution of the Thermoelastic Problem for a Two-Dimensional Curved Beam with Bimodular Effects

Authors :
Xiao-Ting He
Meng-Qiao Zhang
Bo Pang
Jun-Yi Sun
Source :
Mathematics, Vol 10, Iss 16, p 3002 (2022)
Publication Year :
2022
Publisher :
MDPI AG, 2022.

Abstract

In classical thermoelasticity, the bimodular effect of materials is rarely considered. However, all materials will present, in essence, different properties in tension and compression, more or less. The bimodular effect is generally ignored only for simple analysis. In this study, we theoretically analyze a two-dimensional curved beam with a bimodular effect and under mechanical and thermal loads. We first establish a simplified model on a subarea in tension and compression. On the basis of this model, we adopt the Duhamel similarity theorem to change the initial thermoelastic problem as an elasticity problem without the thermal effect. The superposition of the special solution and supplement solution of the Lamé displacement equation enables us to satisfy the boundary conditions and stress continuity conditions of the bimodular curved beam, thus obtaining a two-dimensional thermoelastic solution. The results indicate that the solution obtained can reduce to bimodular curved beam problems without thermal loads and to the classical Golovin solution. In addition, the bimodular effect on thermal stresses is discussed under linear and non-linear temperature rise modes. Specially, when the compressive modulus is far greater than the tensile modulus, a large compressive stress will occur at the inner edge of the curved beam, which should be paid with more attention in the design of the curved beams in a thermal environment.

Details

Language :
English
ISSN :
22277390
Volume :
10
Issue :
16
Database :
Directory of Open Access Journals
Journal :
Mathematics
Publication Type :
Academic Journal
Accession number :
edsdoj.22c72d51040e44d6b364aa0dd33d601b
Document Type :
article
Full Text :
https://doi.org/10.3390/math10163002