THE CAVITY OF THE OPTIMAL SHAPE UNDER THE SHEAR STRESSES

The problem of optimal shape of a single cavity in an infinite 2-D ela stic domain is analyzed. An elastic plane is subjected to a uniform lo ad at infinity. The cavity of the fixed area is said to be optimal if it provides the minimal energy change between the homogeneous plane an d the plane with the cavity. We show that for the case of shear loadin g the contour of the optimal cavity is not smooth but is shaped as a c urved quadrilateral. The shape is specified in terms of conformal mapp ing coefficients, and explicit analytical representations for componen ts of the dipole tensor associated with the cavity are employed. We al so find the exact values of angles at the corners of the optimal conto ur. The applications include the problems of optimal design for dilute composites. (C) 1998 Elsevier Science Ltd. All rights reserved.