【摘要】 本文用三维弹性理论研究横观各向同性球体的轴对称弯曲问题.用分离变量法直接从轴对称问题的微分方程得到位移和应力的通解.以球面应力的齐次边界条件,推导了特征方程,并用Muller方法求解特征方程.本文还给出了特征根的排列关系式,以判断是否有漏根现象发生.对于锥面边界条件,用最小二乘法构造出关于特征函数系数的代数方程组. 对于球体的边值问题作了数值计算,给出了应力和位移的分布曲线.误差分析表明,边界条件得到很好的满足.更多还原

【Abstract】 In this paper, the axisymmetrically bending problem for the transversely isotropic spherical shells are studied by the three-dimensional elasticity theory. Using the Navier’s equations of the transversely isotropio spherical shell, the general solutions of the axisymmetric problems are obtained. The particular solutions of the surfaces stresses conditions and the derivation of the eigenequations are discussed in details. Muller’s method is adopled to solve the eigon-equation. The permuting relation for eigenvalues is presented. This relation can be used to judge the leak information of the eigenvalues. According to the edge boundary conditions of the shell, the linear algebraic equations for the coefficients of eigen functions are derived by the point collocation least square method.The numerical solution of the axisymmetrically bending problem is calculated. The distributions of the stresses and displacements in the shell are given in the figures. The error analysis shows that the boundary conditions are fitted excellently. In oan be said that the solution is an exact solution for this problem.更多还原