Efficient technique for optimal design changes to FEM of structural dynamic systems

The primary concern of this work is to improve the efficiency by which optimal design changes can be made to finite element models (FEM) of undamped structural dynamic systems. An optimal design change is one in which there is a minimum change in the design parameters. Because of the very large number of degrees of freedom which normally comprise a practical finite element model, it is generally impractical to conduct an optimization of design changes for prescribed design objectives. This is due to the excessive computer time required for the necessary iterations of the optimizing scheme. To facilitate identification of the optimum design, the optimizing algorithm is applied to a generalized coordinate representation of the FEM by identifying and altering the available design parameters in a manner which is consistent with the imposed design constraints. These constraints are prescribed in terms of eigenvectors and/or eigen-values of the modified system. Various illustrations of the proposed technique's validity and versatility are presented for a FEM of a flat plate. One important aspect of the work presented here is the generality of the approach, thus permitting the application to any kind of finite element model and to a large variety of design parameters.