Second-order sensitivity of smart structures

This paper presents a second-order sensitivity analysis for a smart structural system formulated in terms of multiobjective optimization where structural design variables and control parameters are equally treated as design variables. The analytical derivatives of various objectives and constraints are obtained. These expressions provide a complete sensitivity package for the multidisciplinary analysis and optimization problem. An example truss regulated using four actuators is presented as verification of the derivations. This includes the optimal designs achieved using sequential linear and quadratic programming methods. Numerical results show the advantages of using high-order derivatives for the solution of a problem of such complexity and confirm that a systematic sensitivity analysis is essential, as the performance of the controller relies heavily on the structural design variables as well as feedback control logic.