轴对称横观各向同性热弹性圆柱的分解

为了得到精确的应力场、位移场、温度场,将扭转圆轴的精化理论研究方法推广到轴对称横观各向同性热弹性圆柱。利用Bessel函数以及轴对称横观各向同性热弹性圆柱的通解,给出了轴对称横观各向同性热弹性圆柱的分解定理。根据柱面齐次边界条件获得了精确的精化方程,精化方程可以分解为一阶方程、超越方程、温度方程,从而将横观各向同性热弹性圆柱的轴对称问题分解为轴向拉压问题、超越问题、热-应力耦合问题。超越部分对应端部自平衡情况,可以清晰地了解到端部应力分布对内部应力场的影响,热-应力耦合部分对应无外加应力场时圆柱内部因温度变化引起的热应力。

A decomposed theorem of axisymmetric thermoelastic circular cylinder with transversely isotropic

For analyzing the exact stress field,the exact displacement field and the exact temperature field in axisymmetric thermoelastic circular cylinder with transversely isotropic,a decomposed theorem of axisymmetric deformation of a circular cylinder is given by using Bessel’s function and the solution of the axisymmetric thermoelastic circular cylinder with transversely isotropic directly from the general solution.Without employing ad hoc assumptions,the refined equation of an axisymmetric thermoelastic circular cylinder with transversely isotropic is obtained.The stress field satisfies the equilibrium equations without body force and the compatibility equations.In the case of homogenous boundary conditions,the refined equation provides exact solutions which satisfy all of the governing equations.The exact solutions can be decomposed into there parts: the 1st-order equation,the transcendental equation and the temperature equation.The problem of an axisymmetric thermoelastic circular cylinder with transversely isotropic is decomposed into there parts: the axially loading problem,the transcendental problem and the thermal-stress coupled problem.The exact governing equations are accurate up to the 1st-order terms with respect to the axially loading problem of the circular cylinder.The transcendental part satisfies the boundary condition under self-equilibrated end loading.That is,the stress field in any cross section is self-equilibrating,and the influence of the end stress distribution on the inner stress field can clearly be shown.The thermal-stress coupled part corresponds to the heat stress for internal temperature change of the circular cylinder without applied stress field.