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

In practical engineering problems it might be necessary to make holes in a plate subjected to boundary loads on its mid-plane. Such cavities might be left empty or they might be filled with a different material. In the latter case, during the deformation process, the initial contact surfaces between matrix and inclusion, as well as the position of the inclusion inside the hole, may change; that may affect considerably the mechanical response of the structure. Moreover, at the early stage of a design process, it might be important to know “a priori” position and size of the hole-inclusion system corresponding to the maximum structural stiffness. On the basis of their recent experiences, the Authors intend to develop a two-dimensional BEM numerical procedure to optimise the mechanical response of structures with internal inclusions by maximising their structural stiffness. In the present paper only one rigid inclusion with a prescribed area is considered; the material of the matrix is supposed linear elastic and the contact between matrix and inclusion is assumed as unilateral and frictionless.