Optimal control of memory dependent nonlocal elastic solids

Abstract

Abstract Sensitivity expressions of a general performance criterion with respect to load control functions have been derived for memory dependent nonlocal elastic solids. The memory dependence of the media has been taken in a hereditary integral form. By using nonlocal calculus of variations and the adjoint variable method of optimization, an adjoint problem is constructed in order to find the first variation of the performance criterion (i.e. a nonlocal and memory dependent integral functional) in terms of variations of the load control variables. An unconstrained optimal control example problem is provided whose solution has been obtained by using the sensitivity analysis results and also by a direct evaluation and differentiation of the relevant objective function, thereby showing the validity of the general sensitivity results derived in the present paper.