具有薄壳理论同样精度的圆锥壳简化解

Simplified Solution Having the Same Accuracy as Thin Walled Shell Theory for Conical Shells

采用新的变量转换公式 ,通过量级分析 ,略去 h/R量级的小量 ,从而将圆锥壳有矩问题求解的基本微分方程式转换成一个二阶复常系数的常微分方程式 .求解该方程式 ,导出了具有薄壳理论同样精度的圆锥壳的简化解 .这一简化解较圆锥壳的精确解简单 ,无须利用复杂的贝塞尔函数 ,与具有 h/R精度的等效圆柱壳的解相比 ,其精度同精确解一样为 h/R.该简化解可用于圆锥壳的边界效应 ,以及锥 -柱、锥

Using new variable transformation formulas, performing magnitude analysis and neglecting the quantities with h/R magnitude, the basic governing equations for conical shells are transformed into a second order differential equation with complex constant coefficients. By solving this equation, a simplified solution having the same accuracy as thin walled shell theory for conical shells is derived. The simplified solution is simpler than the exact solution for conical shells because it does not use Bessel's functions. Also, it is more accurate than the equivalent cylinder solution with h/R accuracy. The simplified solution is useful in analyzing the stresses at junctions of cylinder cone and cone cone or at boundaries for conical shells.