Об особенностях идентификации переменных термомеханических характеристик функционально-градиентного прямоугольника

Александр Ованесович Ватульян, Сергей Анатольевич Нестеров
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引用次数: 1

Abstract

The inverse thermoelastic problem of identification of the variable properties of a functionally graded rectangle is studied. Unsteady vibrations are excited by applying mechanical and thermal loads to the upper side of the rectangle. To solve the direct problem in Laplace transforms, the method of separation of variables and the shooting method for harmonics are used. Transformants are inverted by expanding the origin in terms of shifted Legendre polynomials. The method proposed for solving the direct problem is verified by comparison with a finite element solution. The influence of the laws of change of variable characteristics on the boundary physical fields is analyzed. The displacement components give additional information on the mechanical loading, and the temperature measured on the upper side of the rectangle over a certain time interval – on the thermal loading. Assuming that the additional information admits expansion in Fourier series, the two-dimensional inverse problem is reduced to one-dimensional problems for various harmonics. The solution of the obtained nonlinear inverse problems is carried out on the basis of an iterative process, at each stage of which, in order to find corrections for thermomechanical characteristics, systems of Fredholm integral equations of the 1st kind are solved. The possibility of simultaneous reconstruction of several characteristics is investigated. The results of computational experiments on the phased reconstruction of thermomechanical characteristics are presented. The influence of the thermomechanical coupling parameter on the results of the thermal stress coefficient reconstruction was clarified.
关于识别功能梯度矩形可变热力学特性的特殊性
本文研究了识别功能分级矩形的可变特性的逆热弹性问题。通过在矩形上侧施加机械和热载荷来激发非稳态振动。为了解决拉普拉斯变换中的直接问题,使用了变量分离法和谐波射击法。通过将原点展开为移位 Legendre 多项式,对变换子进行反演。通过与有限元解法的比较,验证了所提出的直接问题求解方法。分析了变量特性变化规律对边界物理场的影响。位移分量提供了机械载荷的附加信息,而矩形上侧在一定时间间隔内测得的温度则提供了热载荷的附加信息。假设附加信息可以用傅里叶级数展开,那么二维逆问题就可以简化为各种谐波的一维问题。所获得的非线性逆问题的求解是在迭代过程的基础上进行的,在每一阶段,为了找到热机械特性的修正,都要求解第一类弗雷德霍姆积分方程系统。研究了同时重建多个特性的可能性。介绍了分阶段重建热力学特性的计算实验结果。阐明了热力学耦合参数对热应力系数重建结果的影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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