This paper deals with an optimal control problem associated to an evolution implicit quasi-variational inequality for elastic materials. Such problems describe the quasi-static process of bilateral contact with friction between an elastic body and a rigid foundation. Existence of an optimal control is proven and necessary optimality conditions are derived.

The theoretical foundation of a variant on effective medium theories for elastic constants of composites is presented and discussed. The connection between this approach and the methods of Zeller and Dederichs, Korringa, and Gubernatis and Krumhansl is elucidated. A review of the known relationships between the various effective medium theories and rigorous bounding methods for elastic constant...

The elastic instability of a circular plate adhering to an elastic foundation modeling the exposed surface of a biological cell resting on the cell interior is considered. Plate buckling occurs under the action of a uniform body force due to an overpassing simple shear flow distributed over the plate cross section. The problem is formulated in terms of the linear von Kármán plate bending equati...

Living human corneal epithelial cells have been probed in vitro via atomic force microscopy, revealing the frictional characteristics of single cells. Under cell media, measured shear stresses of 0.40 kPa demonstrate the high lubricity of epithelial cell surfaces in contact with a microsphere probe. The mechanical properties of individual epithelial cells have been further probed through nanome...

In this study, using the non-local elasticity theory, the buckling and vibration analysis of triple- walled ZnO piezoelectric Timoshenko beam on elastic Pasternak foundation is analytically investigated under magneto-electro-thermo-mechanical loadings. Using the Timoshenko beam free body diagram, the equilibrium equation of Timoshenko nano-beam model is obtained and solved by Navier’s method fo...