Shape optimization of rigid inclusions for elastic plates with cracks

In the paper, we consider an optimal control problem of finding the most safe rigid inclusion shapes in elastic plates with cracks from the viewpoint of the Griffith rupture criterion. We make use of a general Kirchhoff–Love plate model with both vertical and horizontal displacements, and nonpenetra...

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Bibliographic Details
Published inZeitschrift für angewandte Mathematik und Physik Vol. 67; no. 3; pp. 1 - 12
Main Author Shcherbakov, Viktor
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2016
Subjects
Applications of mathematics
Cracks
Derivatives
Elastic plates
Engineering
Inclusions
Mathematical Methods in Physics
Mathematical models
Optimal control
Perturbation methods
Theoretical and Applied Mechanics
Rigid inclusion
74K20
Nonpenetration conditions
Derivative of energy functional
Griffith rupture criterion
49J20
Variational inequality
49J40
Shape optimization
Kirchhoff–Love plate
74A45
Crack
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Summary:In the paper, we consider an optimal control problem of finding the most safe rigid inclusion shapes in elastic plates with cracks from the viewpoint of the Griffith rupture criterion. We make use of a general Kirchhoff–Love plate model with both vertical and horizontal displacements, and nonpenetration conditions are fulfilled on the crack faces. The dependence of the first derivative of the energy functional with respect to the crack length on regular shape perturbations of the rigid inclusion is analyzed. It is shown that there exists a solution of the optimal control problem.
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ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-016-0666-7