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运用加权最小二乘配点法解决了具有初始几何缺陷的双向加肋旋转壳的小应变、大转动、大位移问题。借助于微分几何、矢量分析的工具导出了壳、子午向肋、环向肋的高精度下的非线性几何方程.推出了一套对壳、板、梁等结构具有通用性的考虑几何缺陷的应变公式,由此进一步导出了带几何缺陷的壳、子午肋、环肋的高精度下的非线性几何方程和其对应的内力公式.在此基础上得到了权残法的带几何缺陷的组合壳体的控制方程.最后给出了几个例题,结果证明,公式系统、算法及程序都是令人满意的.
Using the weighted least-squares collocation method, the problem of small-strain, large-rotation and large-displacement of bidirectional ribbed rotating shells with initial geometrical defects was solved. By means of differential geometry and vector analysis tools, the nonlinear geometric equations of the shell, meridional ribs, and hoop ribs are derived with high precision. A set of geometrical defects that are universal for shells, plates, beams, etc. are introduced. Strain formula, which further derived the high-precision nonlinear geometric equations and its corresponding internal force formulas for shells, meridional ribs, and ring ribs with geometrical imperfections. Based on this, a geometrically flawed combination of weighted residual methods was obtained. The control equations of the shell. Finally, several examples are given. The results prove that the formula system, algorithm and program are all satisfactory.