The cavity of the optimal shape under the shear stresses

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. (C) 1998 Elsevier Science Ltd. All rights reserved.