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丁皓江, 任永坚, 邹道勤, 陈伟球. 球面各向同性弹性力学的位移解法[J]. 力学学报, 1994, 26(2): 186-197. DOI: 10.6052/0459-1879-1994-2-1995-536
引用本文: 丁皓江, 任永坚, 邹道勤, 陈伟球. 球面各向同性弹性力学的位移解法[J]. 力学学报, 1994, 26(2): 186-197. DOI: 10.6052/0459-1879-1994-2-1995-536
DISPLACEMENT METHOD OF ELASTICITY PROBLEMS IN SPHERICALLY ISOTROPIC MEDIA[J]. Chinese Journal of Theoretical and Applied Mechanics, 1994, 26(2): 186-197. DOI: 10.6052/0459-1879-1994-2-1995-536
Citation: DISPLACEMENT METHOD OF ELASTICITY PROBLEMS IN SPHERICALLY ISOTROPIC MEDIA[J]. Chinese Journal of Theoretical and Applied Mechanics, 1994, 26(2): 186-197. DOI: 10.6052/0459-1879-1994-2-1995-536

球面各向同性弹性力学的位移解法

DISPLACEMENT METHOD OF ELASTICITY PROBLEMS IN SPHERICALLY ISOTROPIC MEDIA

  • 摘要: 本文引入三个位移函数(w,G,ψ),将球面各向同性弹性力学运动方程,简化为关于ψ的二阶偏微分方程,和关于W和G的联立方程。在静力学问题中,联立方程可进一步简化,w和G可用另一位移函数F表示,而F满足一个四阶偏微分方程。在球壳固有振动问题中,则简化为一个独立的二阶常微分方程,和另两个二阶的联立的常微分方程,证明了在多层球壳中,它们分别对应独立的两类振动。改进了常微分方程的解法,并计算了一个二层球壳的频率。

     

    Abstract: Three displacement functions w,Gand ψare introduced in this paper tosimplify motion equations of elasticity problenis in spherically isotropic media to an indepen-dent partial differential equation concerning one displacement function ψand simultaneous equations concerning two other displacement functions w and G.For static elasticity,thesimultaneous equations can be further simplified through another function F,which is gov-erned by a four-order partial differential equation,In free vibration problems of s...

     

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