横观各向同性轴对称圆柱的精化理论

为获得精确的应力场和位移场,将扭转圆轴的精化理论研究方法推广到横观各向同性材料的轴对称圆柱研究.利用横观各向同性材料的轴对称通解以及Bessel函数,在不做任何预先假设的情况下,给出了横观各向同性材料的轴对称圆柱的精化理论.根据柱面齐次边界条件获得精确的精化方程,精化方程可以分解为一阶方程和超越方程,从而将横观各向同性圆柱的轴对称变形问题分解为轴向拉压问题和超越问题,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.

Refined Theory of Axisymmetric Circular Cylinder with Transversely Isotropic

To analyze the exact stress field and displacement field in axisymmetric circular cylinder with transversely isotropic, the refined theory of torsional deformation of a circular shaft was converted for being applicable to the case of axisymmetric circular cylinder with transversely isotropic. Without employing ad hoc assumptions, the refined theory of an axisymmetric circular cylinder with transversely isotropic could be applied, which would yield the solution of the cylinder directly from the general solution and Bessel function. With the homogenous boundary condition, the refined theory provided exact solutions which satisfied all of the governing equations. The exact solutions could be decomposed into two parts: the 1-orders equation and the transcendental equation. The solutions of two equations reflected directly the axially loading solution and the transcendental solution, respectively. The transcendental solution satisfied the boundary condition under self-equilibrated end loading, and the stress distribution on the end of the stress field could be known clearly.