Topology optimization of structures under dynamic response constraints

Structural optimization subjected to dynamic responses constraints is of great importance in the aeronautical and automobile industries. Topology optimization problem with the weight reduction as the objective function and the mean square response of the specified locations on the structure as design constraints is studied under white-noise force excitation. In order to avoid the occurrence of localized mode, the pseudo-density based optimization method is established by means of the rational approximation of material properties, and the relationship between design variables and material properties as well as design functions is formulated. In the developed optimization procedure, the mean square response of the system is calculated by means of frequency domain analysis. The sensitivity analysis is formulated for the mean square response, and sensitivity analyses of the circular frequency and vibration mode are simplified according to the expressions of element kinematic energy and strain energy of each mode. The dual algorithm with convex linearity is used to solve the optimization problem. Three typical topology optimization examples are solved to demonstrate the validity and the advantage as well as the adaptability of the proposed optimization procedure in solving complicated problems.