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An efficient method for solving the structural dynamics of finite elastic structures containing discontinuities using analytical/numerical matching with finite element analysis.

机译：通过有限元分析/数值匹配，解决包含不连续性的有限弹性结构的动力学问题的有效方法。

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摘要

Analytical/Numerical Matching (ANM) is a method designed to efficiently solve many types of problems containing discontinuities. The method separates local and global effects, and solves separate sub-problems using high resolution around the discontinuity and low resolution away from the discontinuity. This work demonstrates the methodology for applying ANM to 2D and 3D finite dynamic structures using finite element analysis (FEA) and hybrid modal/FEA methods for the solution of the high-resolution (local) and low-resolution (global) subproblems. The ANM method is illustrated on a thick 2D beam having several displacement constraints attached to the lower surface of the beam and a 3D cylindrical shell excited by various forcing functions and displacement constraints. Ordinarily (and here, for verification purposes) these problems would be solved using high-resolution finite element analysis due to the local discontinuities around the applied forcing and displacement constraints. Using ANM, these discontinuities and through-the-thickness effects are modeled separately in the geometrically compact local sub-problem using a high-resolution mesh of 2D plane or 3D solid finite elements. The much larger global sub-problem contains no discontinuities and is reduced to a low-resolution finite element problem or one that rapidly converges when using a modal approach. The third sub-problem (matching) is solved analytically and therefore carries no computational burden. The agreement between the ANM solutions and the traditional FEA (or modal/FEA) solutions is excellent. Furthermore, the computational savings are significant. Finally, a method for efficiently implementing fluid-loading effects into the in-vacuo ANM methodology is demonstrated for the 2D thick beam and 3D cylindrical shell problems.
机译：分析/数字匹配（ANM）是一种旨在有效解决许多类型的包含不连续性问题的方法。该方法将局部和全局效应分开，并使用围绕不连续点的高分辨率和远离不连续点的低分辨率来解决单独的子问题。这项工作演示了使用有限元分析（FEA）和混合模态/ FEA方法将ANM应用于2D和3D有限动态结构的方法，用于解决高分辨率（局部）和低分辨率（全局）子问题。在厚2D梁上显示了ANM方法，该厚2D梁具有附加到梁下表面的多个位移约束和3D圆柱壳，并通过各种强制函数和位移约束激发。通常（出于验证目的）（由于验证目的），这些问题将使用高分辨率有限元分析解决，原因是所施加的力和位移约束周围存在局部不连续性。使用ANM，可以使用2D平面或3D实体有限元的高分辨率网格在几何紧凑的局部子问题中分别对这些不连续性和整个厚度效应进行建模。更大的全局子问题不包含任何不连续性，并且简化为低分辨率有限元问题，或者使用模态方法时会迅速收敛的问题。第三个子问题（匹配）通过解析解决，因此不承担计算负担。 ANM解决方案与传统FEA（或模态/ FEA）解决方案之间的协议非常出色。此外，计算上的节省是可观的。最后，针对2D厚梁和3D圆柱壳问题，论证了一种有效地将流体加载效果应用于真空ANM方法的方法。

著录项

  • 作者

    Park, Christopher Douglas.;

  • 作者单位

    Duke University.;

  • 授予单位 Duke University.;
  • 学科 Engineering Mechanical.
  • 学位 Ph.D.
  • 年度 2001
  • 页码 168 p.
  • 总页数 168
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 机械、仪表工业;
  • 关键词

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