A New Class of Optimization Problems Related to Structural Control by Contact Interaction

Abstract

For some structures under service loads there is a need of precise control of local boundary displacement and/or its tangential gradient by an additional loading of one or two punches. Such problems exist in design of robot grippers or mechanical tools used in element assembling or in other mechanical processes. The punch interaction is assumed to be executed by a discrete set of pins or by a continuously distributed contact pressure. The optimal contact force and pressure distribution are defined in terms of assumed control function, for which contact shape is specified for both discrete and continuous punch action. For beam or plate structures three classes of control are considered. First, requiring by punch action the fixed load \(F_{Q}\) and displacement \(u_{Q}^{*}\) at a specified position, second, requiring the load-displacement \(F_{Q}=F_{Q}(u_{Q}^{*})\) evolution by the varying punch load and third, provide deflection and slope control at a specified position by a coordinated action of two punches. The reciprocal motion of a transverse pin attached to the beam is induced by varying punch forces. The punch position is specified by satisfying constraints on maximum punch pressure and equivalent Mises stress on the contact interface. Several illustrative examples are presented to illustrate punch control for different boundary supports and three control classes.