多层横观各向同性圆柱壳的三维弹性理论解

本文从三维弹性理论出发,用特征函数法研究多层横观各向同性圆柱壳的轴对称问题.把位移和应力分量的齐次解表达成特征函数展开式,并把特解部分用Fourier级数表示.以多层圆柱壳的内、外柱面作为齐次边界,同时考虑层间的连续条件,推导出问题的特征方程并用Muller法求解.文中运用传递矩阵技术处理多层问题,并用边界型最小二乘配点法处理端部边界条件.作为实例,对双层圆柱壳作了数值计算.

Elasticity Solusion for a Finite Multilayered Transversely Isotropic Circular Cylindrical shell

In this paper, by using the three-dimensional elastic theory, the problem of a finite multilayered transversely isotropic cylindrical shell subjected to an axisymmetric load is solved. The homogeneous solution is obtained in the form of an eigenfunction expansion, which satisfy the homogeneous boundary and the continuity conditions. A Fourier type analysis is used to solve the particular problem. The characteristic equation for multilayered cylindrical shell is obtained and the eigenvalues are computed. A transfer matrix method is used for ease of computations. Because of the lack of orthogonality relations for eigenfunctions, the arbitrary boundary condition at the end face is satisfied by using the leastsquare point collocated technique. An example problem for a two layered shell is solved and the numerical results are presented in the graphical form.