Rigid inclusions in frictionless unilateral contact with the matrix: identification of maximum stiffness structures by means of BEM formulations and sensitivity analyses

Abstract

The Authors present a Boundary Element procedure for the solution of 2D optimisation problems in the presence of unilateral contact interfaces. The position which a rigid inclusion must occupy within the matrix in order to maximise the structural stiffness of the matrix-inclusion system under prescribed external loads is identified. The matrix is considered linear elastic. A minimisation problem is stated with design variables representing the size and the shape of the inclusion. The cost function is an error function which evaluates the strain energy accumulated by the matrix-inclusion system. The minimisation is performed by using a first-order nonlinear optimisation technique in which the cost function gradient is computed by implicit differentiation. Two numerical examples are presented and discussed. In the first example a comparison between the proposed procedure, the finite difference technique and the analytical strategy is performed, whereas the second example deals with the determination of the position of an internal circular inclusion such as to maximise the structural stiffness of a plane strain plate under a prescribed load.