Optimal control and optimum design of elasticity system: Topological derivative method for control problem

We consider a class of boundary dynamic optimal control problems for elasticity systems in the geometric domain. The class of control problems admits the so-called Turnpike Property. The relation of optimal controls for static problems and dynamic problems is investigated. Thus, we consider the steady state problem in order to compute the optimal control. The cost is minimized with respect to boundary controls. Meanwhile, the optimal cost of control is minimized with respect to the shape and topology of its domain of integration. The topological optimum design problem is solved by the topological derivative method for the steady-state model. The level set function for the purposes of topology optimization is defined. Numerical results for topology optimization are presented.