圆环壳几何非线性问题的摄动渐近解

Perturbed Asymptotic Solution of Geometrically Nonlinear Problem of Toroidal Shells under Axial Symmetric Loading

在应变ε＜＜１，转角β＜１，β～ε的假设下用工程方法导出了轴对称旋转壳几何非线性问题的平衡方程和变形几何关系。在此基础上，导出了圆环壳复变量非线性二阶常微分方程，并采用摄动法给出了方程的渐近解。最后同实验进行了比较。

The nonlinear equilibrium equations and geometrical relations of axially symmetrical toroidal shells are derived under the assumption of the little deformation ε<<1, the moderate rotation β<1 and . The nonlinear ordinary differential equations of the second order with complex variables for the axially symmetrical problems are also derived. The paper gives the asymptotic solution of the nonlinear equation with perturbation method and its comparision with experiment.