Optimal shape of a grain or a fibre cross‐section in a two‐phase composite

Shenfel'D, V. S.; Givoli, Dan; Vigdergauz, Shmuel

doi:10.1002/cnm.724

Cited by 3 publications

(1 citation statement)

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“…For this reason, the third step above becomes impossible and hence the whole scheme cannot be applied, at least straightforwardly. Shenfeld et al [2005] proposed an alternative approach for use with a direct FEM solver with adaptive meshing. They performed a reanalysis inside using a specially tailored conjugate gradient method.…”

Section: Introductionmentioning

confidence: 99%

Energy-minimizing inclusion in an elastic plate under remote shear

Vigdergauz

2008

JOMMS

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A single foreign inclusion perfectly embedded in an elastic plate is considered as a bimaterial setup for finding the interface shape that minimizes the energy increment in a homogeneous shear stress field given at infinity. While simple in concept, this optimization problem is very hard computationally. For tractability, we limit our focus to a narrowed set of curves which can be conformally mapped onto a circle by an analytic function with only one nonzero Laurent term. The resultant one-parameter shape optimization problem with an integral objective functional is then accurately solved using an enhanced complex variable approach. This scheme, though seemingly restrictive, provides good qualitative insight into the optimal solution and bridges the gap between the limiting cases of the energy-minimal hole and the rigid inclusion solved previously.

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Section: Introductionmentioning

confidence: 99%