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THEORETICAL STRESS ANALYSIS OF ROTATING HYPERBOLIC DISK WITHOUT SINGULARITIES SUBJECTED TO THERMAL LOAD

机译:无奇异性受热负荷旋转双曲线盘的理论应力分析

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摘要

A theoretical method for the evaluation of elastic stresses and strains in rotating hyperbolic disks without singularity, also subjected to thermal load, is introduced. The differential equation governing the radial displacement field of the hyperbolic disk without singularity has been deduced from the governing equation of non-linearly variable thickness disks given by the power of a linear function of the radius. A general temperature distribution along the radius expressed by a polynomial relation is considered. To overcome convergence problems of the solution, with hypergeometric functions, analytic continuations of these series have been introduced that allow the extension the theoretical thermoelastic analysis to all cases of technical interest. Then, for the first time the authors are aware, closed-form solutions of the governing equation of hyperbolic disks without singularity are presented.
机译:介绍了一种理论上的方法来评估旋转双曲圆盘中没有奇点的弹性应力和应变,同时也要承受热负荷。已经从由半径的线性函数的幂给出的非线性可变厚度盘的控制方程推导了控制无奇异性的双曲盘的径向位移场的微分方程。考虑沿由多项式关系表示的半径的一般温度分布。为了克服具有超几何函数的解的收敛性问题,已经引入了这些系列的解析继续,从而允许将理论上的热弹性分析扩展到所有技术感兴趣的情况。然后,作者第一次意识到,提出了没有奇异性的双曲盘控制方程的闭式解。

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