An optimal design problem has been formulated for lightly damped structures under random excitations.
The finite element method and a normal mode method have been adopted to obtain modal responses of structures to random excitations. The structural damping required has been introduced in terms of modal damping ratios.
Constraints have been mainly imposed on the variances of displacements and stresses of structures when the generalized steepest descent method was utilized in the optimal design process.
To illustrate the optimization process developed, simple structures subject to earthquake and wind force were considered and optimally designed, minimizing weights.