Nonlinear Optimum Design of Dynamic Damped Frames

A method to optimize the weight of plane frames subjected to dynamic loads is presented. Various considerations for rigid frame design include damping, the P? effect, static girder loads, static column loads and girder shears transferred to the columns. A finite difference approach is presente to evaluate a shock spectrum which is used in conjunction with modal superposition to obtain the peak upper bound dynamic displacements and stresses for multistory and multibay frames. The displacement method is used for the structural matrix formulation from which the optimization process is shown in relation to the change of the design variables in the condensed stiffness matrix. A direct, nonlinear mathematical programming method of feasible directions is used to minimize the weight of the structure subject to the aforementioned linear and nonlinear constraints. Several applications of the proposed method are presented to show the design process related to the active constraints and the significant effects of various considerations on optimum design.