2D Quasi-Static Accurate Solutions for Isotropic Thermoelastic Materials with Applications

Wen-Ying Xiao,Ying-Jie Liu,Jiang Su,Jian-Ping Li,Jie Tong,Vasilios Spitas

doi:10.1155/2021/8825226

Wen-Ying Xiao, Ying-Jie Liu + Show 4 more

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https://doi.org/10.1155/2021/8825226

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Abstract

Thermally induced stress is an important scientific problem in engineering applications. In this paper, an accurate and efficient method for the two-dimensional quasi-static thermal elastic problem is established to explore the thermal stress problem. First, the compact quasi-static two-dimensional general solution is derived in terms of simple potential functions. The general solution is simple in form and can be derived for arbitrary boundary problems subjected to a line heat load. This is completely new to the literature. Second, Green’s function solutions of an infinite plane under the line pulse heat source based on the general solutions are presented to analyze the thermal stress field. Lastly, numerical results are taken into account to study the temperature and stress field induced by the dynamic heat source load. The corresponding analysis can constitute to reveal the mechanism of thermal elastic problems and provide some guidance for experiments or engineering structural design in the future work.

Highlights

E main analytical methods are the integral transformation method, complex variable method, and classical general solution method
Integral transformation is a common method to solve differential equations. e Laplace and Hankel transform techniques have been used for the transversely isotropic thermoelastic thin plate [20]. e method of Fourier transformation is used to obtain an analytical expansion for the temperature and thermal stresses [21]
By virtue of Almansi’s theorem, the three general solutions can be transformed to the general solution which is expressed in terms of two harmonic functions and a function which satisfies the quasi-static heat conduction equation, respectively. irdly, the integral general solution expressed in one harmonic function and one function which satisfies the quasi-static heat conduction equation is obtained

Summary

Introduction

E main analytical methods are the integral transformation method, complex variable method, and classical general solution method. Irdly, the integral general solution expressed in one harmonic function and one function which satisfies the quasi-static heat conduction equation is obtained. The suitable functions for a quasi-static line heat source in the interior of the infinite steel plane are constructed, and the corresponding Green’s solutions are presented by virtue of the obtained general solutions. 3. Two-Dimensional Quasi-Static General Solutions for the Isotropic Thermoelastic Material

Results

Conclusion