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Computational methods for the direct solution of inverse problems in finite elasticity.

机译：直接求解有限弹性反问题的计算方法。

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摘要

This thesis addresses current research in inverse methods for finite elastostatics and prescribes a new method for solving these problems. In these well-posed inverse problems, the undeformed shape is the unknown, while the deformed shape, Cauchy tractions, and displacement boundary conditions are known. Current research in this area uses conservation laws based on Eshelby's energy momentum tensor. A finite element formulation using this tensor is shown to be very limited. By using the inverse motion composed with the standard equations of equilibrium, a simple algorithm is developed which allows for the direct solution of the inverse problem. Quasi-incompressibility is incorporated into the formulation to solve common elastomeric design problems. Numerical examples are presented and compared to known solutions.; An ill-posed problem is considered for the steady state spinning of a cylinder in contact with a rigid surface. The 3D cylinder is analyzed and the deformed shape determined. The solution of the ill-posed problem utilizes the new inverse method and regularization to enforce an a priori condition of circularity of the cylinder. Numerical examples computing the undeformed profile through the axis of the cylinder are shown.
机译：本文针对当前有限弹性静力学反方法的研究现状，提出了解决这些问题的新方法。在这些适当摆放的逆问题中，未变形的形状是未知的，而变形的形状，柯西牵引力和位移边界条件是已知的。目前该领域的研究使用基于埃舍尔比的能量动量张量的守恒定律。使用此张量的有限元公式显示非常有限。通过使用由标准平衡方程组成的逆运动，开发了一种简单算法，可以直接求解逆问题。准不可压缩性已纳入配方中，以解决常见的弹性体设计问题。给出了数值示例并将其与已知解决方案进行比较。对于与刚性表面接触的气缸的稳态旋转，考虑了不适定的问题。分析3D圆柱体并确定变形的形状。不适定问题的解决方案利用新的逆方法和正则化来强制圆柱体的圆度先验条件。显示了通过圆柱轴计算未变形轮廓的数值示例。

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  • 作者

    Mihalic, Paul Andrew, Jr.;

  • 作者单位

    University of California, Berkeley.;

  • 授予单位 University of California, Berkeley.;
  • 学科 Engineering Civil.; Engineering Mechanical.; Applied Mechanics.
  • 学位 Ph.D.
  • 年度 1999
  • 页码 117 p.
  • 总页数 117
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 建筑科学;机械、仪表工业;应用力学;
  • 关键词

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