单层网壳结构稳定性分析的随机缺陷模态迭加法

Stochastic Imperfection Mode Superposition Method for Stability Analysis of Single layer Lattice Domes

摘要:

根据几何非线性有限元理论，结合单层网壳结构的随机缺陷概率模型，提出了基于Timeshenko梁理论的网壳结构稳定性随机缺陷模态迭加法.推导建立空间Timeshenko梁单元的几何非线性切线刚度矩阵方程，在特征值屈曲分析基础上，建立结构缺陷模态参与系数的概率模型，采用Monte Carlo法对具有随机缺陷的结构进行稳定承载力分析，进而提出了单层网壳结构稳定性随机缺陷模态迭加法.算例分析表明，该法克服了已有传统方法随机变量过多的局限，可精确识别出结构失稳的最不利缺陷模式，获得最不利缺陷分布下的稳定承载力，并可对结构屈曲的全过程进行跟踪分析，具有良好的计算精度和计算效率.

关键词:单层网壳结构; 随机缺陷模态迭加法; 最不利缺陷模式; 稳定承载力; Timeshenko梁理论

Abstract:

Based on Timeshenko beam theory and stochastic imperfection mode, the stochastic imperfection mode superposition method was proposed for single layer lattice domes. First tangent stiffness matrix for Timeshenko beam was deduced. Then stochastic imperfection mode was set up with participating parameters of modes obtained by eigenvalue analysis. Then, a nonlinear stability analysis was made on single layer lattice dome with stochastic imperfection. And then the stochastic imperfection mode superposition method was proposed. Finally, an example verifies that compared with traditional methods, smaller samples are resorted to with the proposed method. The proposed theory and algorithm proves to be correct, effective in stability analysis of single layer lattice with dome stochastic imperfection.

Key words:single layer lattice dome; stochastic imperfection mode superposition method; the least favorable distribution of imperfection; critical buckling load; Timeshenko beam theory