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

研究人员科尔曼·9704509和他的同事们致力于在高性能计算环境中高效地计算非线性弹性静力学问题的整体解。重点研究了对称无缺陷弹性壳结构的整体后临界行为-其分析对于了解实际工程结构的大变形响应和最终倒塌情况具有重要意义。这项工作的一个主要主题是通过群论技术开发以潜在对称性为特征的一类重要工程问题的自然并行性。他们还在这些问题的背景下调查了自动区分软件的使用情况。最后，在Krylov迭代子空间方法的背景下，他们研究了对称性激励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，薄壳结构已被广泛应用于航空航天、土木、机械和核工程应用，例如，穹顶屋顶、航空航天飞行器、压力容器、安全壳容器等。然而，迄今为止，工程师预测这类系统的最终失效的能力更像是一门艺术而不是一门科学(严重依赖昂贵的实验验证--见D.Bushnell，Martinus Nijhoff 1985年的《壳体的计算机化屈曲分析》)。研究人员将对称性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类系统。一个长期目标是为工程师提供有用的工具，以便对这类重要的结构进行系统分析(并最终进行更好的设计)。该项目的资金由MPS的计算数学计划和多学科活动办公室以及CEISE的新技术计划提供。

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.