Efficient Algorithms for Large-Scale Linear and Nonlinear Finite Element Computations with Applications to Thin Shell Structures

研究者和他的同事专注于高性能计算环境下非线性弹性静力学问题全局解的有效数值计算。特别关注对称无缺陷弹性壳结构的全局后临界行为，对其分析对于理解现实工程结构的大变形响应和最终崩溃场景具有重要意义。工作的一个主要主题是利用自然并行性，通过群论技术，在一类重要的工程问题的特点是潜在的对称性。他们还调查了在这些问题的背景下使用自动区分软件。最后，他们在Krylov迭代子空间方法的背景下，研究了对称驱动预条件对结构力学中一类“几乎对称”问题的有效性。由于其高强度重量比，薄壳结构在航空航天、民用、机械和核工程应用中得到了广泛的应用，例如圆顶屋顶、航空航天飞行器、压力容器、安全壳等。然而，迄今为止，工程师预测此类系统最终失效的能力更多的是一门艺术，而不是一门科学（严重依赖于昂贵的实验验证——参见D. Bushnell， Martinus Nijhoff 1985年的“计算机化壳体屈曲分析”）。研究人员将对称和非线性分析的新数学思想与高性能计算方法相结合，以有效和系统地分析这些系统。长期目标是为工程师提供有用的工具，对这类重要的结构进行系统分析（并最终更好地设计）。本项目由MPS计算数学项目和多学科活动办公室以及CISE新技术项目提供资金。

Coleman 9704509 The investigator and his colleagues focus on the efficient numerical computation of global solutions of problems of nonlinear elastostatics in a high-performance computational environment. Particular attention is paid to the global post-critical behavior of symmetric imperfection-free elastic shell structures --- the analysis of which has great significance in understanding the large deformation response and ultimate collapse scenario of realistic engineering structures. A major theme of the work is to exploit the natural parallelism, via group theoretic techniques, in an important class of engineering problems characterized by underlying symmetries. They also investigate the use of automatic differentiation software in the context of those problems. Finally, they study the effectiveness of symmetry-motivated preconditioners, within the context of Krylov iterative subspace methods, for a class of ``almost-symmetric'' problems in structural mechanics. Due to their high strength-to-weight ratios, thin shell structures have been used extensively in aerospace, civil, mechanical and nuclear engineering applications, e.g., dome roofs, aerospace vehicles, pressure vessels, containment vessels, etc. Yet the ability of engineers to predict the ultimate failure of such systems has heretofore been more of an art than a science (relying heavily upon costly experimental verification -- see "Computerized Buckling Analysis of Shells", by D. Bushnell, Martinus Nijhoff 1985). The investigators combine new mathematical ideas of symmeytry and nonlinear analysis with high-performance computing methodology to analyze such systems efficiently and systematically. A long-term goal is to provide engineers with useful tools for the sytematic analysis (and ultimately better design) for this important class of structures. Funding for the project is provided by the Computational Mathematics program and the Office of Multidisciplinary Activities in MPS and b y the New Technologies program in CISE.