The cavity of the optimal shape under the shear stresses

doi:10.1016/S0020-7683(97)00214-X

International Journal of Solids and Structures

Volume 35, Issue 33, November 1998, Pages 4391-4410

https://doi.org/10.1016/S0020-7683(97)00214-X Get rights and content

Abstract

The problem of optimal shape of a single cavity in an infinite 2-D elastic domain is analyzed. An elastic plane is subjected to a uniform load at infinity. The cavity of the fixed area is said to be optimal if it provides the minimal energy change between the homogeneous plane and the plane with the cavity. We show that for the case of shear loading the contour of the optimal cavity is not smooth but is shaped as a curved quadrilateral. The shape is specified in terms of conformal mapping coefficients, and explicit analytical representations for components of the dipole tensor associated with the cavity are employed. We also find the exact values of angles at the corners of the optimal contour. The applications include the problems of optimal design for dilute composites.

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The cavity of the optimal shape under the shear stresses

Abstract

Journal of the Mechanics and Physics of Solids

Journal of Mathematical Analysis and Applications

Journal of Mechanics and Physics of Solids

Journal of Applied Mechanics

USSR Izvestiya, Mechanics of Solids

Integral characteristics in problems of elasticity

Optimization of structural topology, shape, and material

Plane strain in a wedge

Inverse problems of the plane theory of elasticity

Applied Mathematics and Mechanics (PMM)

A hole in a plate, optimal for its biaxial extension-compression

Applied Mathematics and Mechanics (PMM)

Methods of Mathematical Physics

Design of composite plates of extremal rigidity

Microstructures of composites of extremal rigidity and exact estimates of provided energy density

Design sensitivity analysis of structural system

The elastic-field behaviour in the neighbourhood of a crack of arbitrary angle

Communications on Pure and Applied Mathematics

Optimal design and relaxation of variational problems

Comm. Pure Appl. Math.

Optimal design and relaxation of variational problems

Comm. Pure Appl. Math.

Optimal design and relaxation of variational problems

Comm. Pure Appl. Math.

Some remarks on the wedge paradox and Saint-Venant's principle

Journal of Applied Mechanics

Modelling the properties of composites by laminates

On characterizing the set of possible effective tensors of composites: The variational method and the translation method

Communications on Pure and Applied Mathematics

Integral characteristics of elastic inclusions and cavities in the two-dimensional theory of elasticity

European Journal of Applied Mathematics