薄壁壳体的屈曲问题一直受到广泛关注，其对于几何缺陷的敏感性一直是壳体稳定性研究的重点。使用传统有限元方法对壳体真实几何缺陷表面进行面片化离散时，会不可避免地产生误差，从而导致所预测的屈曲载荷值的较大偏差。.本项目拟结合逆向工程、等几何方法及随机分析研究具有精确几何缺陷描述的壳体概率屈曲问题。主要内容为：采用基于NURBS的曲面重构方法对壳体真实的几何缺陷点云数据进行逆向建模，建立精确的壳体几何模型，消除了几何离散误差；巧妙地结合等几何方法研究具有精确几何缺陷描述的壳体前、后屈曲规律以及对缺陷的敏感度；建立壳体几何缺陷随机场模型，结合蒙特卡洛模拟，统计屈曲载荷值的分布特征，并进行壳体屈曲的可靠性分析。.本项目预期得到更为可靠的屈曲载荷，揭示精确几何缺陷描述对壳体屈曲的影响及规律，为设计人员提供优于NASA SP-8007准则的参考，提升壳体屈曲设计的精度，具有较为重要的科学研究价值。

The buckling problems of thin-walled shell structures received considerable amount of attention in the past century. The sensitivity of shell structures to its geometric imperfections is one of the key points of shell buckling research. In traditional finite element framework, the geometries of imperfect shell structures are approximated using facet faces which will lead to discretization errors, and these errors sometimes have great influences on the final buckling loads of shell structures..In this research project, we propose a NURBS-based surface reconstruction method to fit the point cloud data of real shell geometric imperfections, by which the geometric discretization errors of shells can be naturally avoided. The reconstructed real shell surfaces will be utilized directly in the framework of isogeometric analysis without further need of meshing. The high-order and high-continuity NURBS basis will be fully exploited to the study of buckling of shell structures with real geometric imperfections. An arc-length path following technique will be developed to trace both the pre- and post-buckling phenomena of such shell structures, and the sensitivity of shell buckling to the geometric imperfections will be carried out. In addition, by introducing the concept of random fields, a set of shell samples with random geometric imperfections can be generated. Then the probability features of shell buckling loads can be obtained using direct Monte Carlo simulation, based on which, the reliability analysis can be conducted..Based on the accurate reconstruction and spectra representation of random geometric imperfections of shell structures, more reliable and accurate buckling loads can be obtained using direct Monte Carlo simulation. The proposed research framework could provide the shell designers with a better guideline than the well-known NASA SP-8007, and resulting in a more robust and accurate shell design.