Benchmark Problems for Shape Optimization in Plane Stress or Strain

by Gordon S. Bjorkman, Jr., ABB Impell Corp, Framingham, United States,

Document Type: Proceeding Paper

Part of: Electronic Computation


The purpose of this paper is to bring to the attention of engineers and researchers who are working with finite element shape optimization techniques, the closed-form solutions for a unique class of optimum shapes for plane stress and plane strain. These shapes for holes and rigid inclusions not only minimize the maximum principle stress but also minimize the Von Mises stress. Furthermore, they do not change the volume strain energy, the first invariant, or the rotations at any point in the field from the values which existed in the original stress field prior to the introduction of the hole or inclusion shape. These special holes and inclusions, called harmonic shapes, exist for biaxial and linearly varying stress fields. By use of the finite element method this paper demonstrates some of the unique properties of these shapes.

Subject Headings: Stress strain relations | Plane strain | Finite element method | Benchmark | Strain | Closed form solutions | Rotation | Biaxial strength

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