This research improves the theoretical foundations for structural optimization and clarifies controversies on existing solutions available for multimodel optimization. The research develops a new and simpler solution for the optimal design of a doubly clamped column and re-examines other optimization problems in which multiple Eigen values occur such as vibrating shafts and beams. Multimodel optimization is an effective approach to improve the reliability in the design of structures, such as columns, frames, and arches. This research will help to validate and assess the theoretical disparities, if any, of the approaches currently used for multimodel optimization. The results has a good potential to increase the confidence of the theoretical approaches that are used for structural optimization.
