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首页> 外文期刊>Journal of thermal stresses >AXISYMMETRIC AND ONE-DIMENSIONAL THERMOELASTIC FIELDS OF RADIALLY GRADED BODIES
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AXISYMMETRIC AND ONE-DIMENSIONAL THERMOELASTIC FIELDS OF RADIALLY GRADED BODIES

机译：径向梯度体的轴对称和一维热弹性场

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摘要

In this paper, both Young's modulus and Poisson's ratio along with thermal expansion coefficient are allowed to vary across the radius in a solid ring and a curved beam. Effects of non-constant Poisson's ratio on the thermoelastic field in these graded axisymmetric and one-dimensional problems are studied. A governing differential equation in terms of stress function is obtained for general axisymmetric and one-dimensional problems. Two linearly independent solutions in terms of hypergeometric functions are then attained to calculate the stresses and the strains. Using Green's function method, a form of a solution for the stress functions in terms of integral equations for a curved beam and a solid ring are obtained. Specifically, closed form solutions for the stress functions, when Young's modulus and Poisson's ratio are expressed as power law functions across the radius, are calculated. The results show that the effect of varying Poisson's ratio upon the thermal stresses is considerable for the solid ring. In addition, a non-constant Poisson's ratio has significant influences on the thermal strain field in solid rings. The effect of varying Poisson's ratio upon the thermal stresses is negligible for the curved beam. However, non-constant Poisson's ratios have substantial effects on the thermal strain field in curved beams. Finally, the effects of varying Poisson's ratio on the thermal stresses in thick solid rings and curved beams are also investigated.
机译：在本文中，允许杨氏模量和泊松比以及热膨胀系数沿实心环和弯曲梁的半径变化。研究了在这些渐变的轴对称和一维问题中非恒定泊松比对热弹性场的影响。对于一般的轴对称和一维问题，获得了基于应力函数的控制微分方程。然后，根据超几何函数获得了两个线性独立的解，以计算应力和应变。使用格林函数方法，获得了针对弯曲梁和实心环的积分方程的应力函数解的形式。具体来说，当杨氏模量和泊松比表示为半径范围内的幂律函数时，计算应力函数的封闭形式解。结果表明，对于固体环而言，改变泊松比对热应力的影响相当大。另外，非恒定泊松比对实心环中的热应变场有重要影响。对于弯曲梁，改变泊松比对热应力的影响可以忽略不计。但是，非恒定泊松比对弯曲光束中的热应变场有很大影响。最后，还研究了变泊松比对厚实心环和弯曲梁中热应力的影响。

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