On rigid inclusions of minimum stress concentration
On rigid inclusions of minimum stress concentration
- Journal of the Mechanics and Physics of Solids, 34(1), p.19-28, 1986 .
The three-dimensional problem of finding the shape of minimum stress concentration for a rigid inclusion imbedded in an elastic matrix is analyzed and solved. The matrix extends to infinity, filling the space exterior to the inclusion. Loading consists of uniform stress applied at infinity, so that in the absence of the inclusion the medium would be homogeneously stressed. The optimum inclusions are found to be ellipsoidal in shape, and conditions on the loading are found under which these ellipsoids can be rigorously proven to be optimal.
The three-dimensional problem of finding the shape of minimum stress concentration for a rigid inclusion imbedded in an elastic matrix is analyzed and solved. The matrix extends to infinity, filling the space exterior to the inclusion. Loading consists of uniform stress applied at infinity, so that in the absence of the inclusion the medium would be homogeneously stressed. The optimum inclusions are found to be ellipsoidal in shape, and conditions on the loading are found under which these ellipsoids can be rigorously proven to be optimal.