A two-level optimization is attempted for the design of 2 dimensional beam structures. The single level optimization problem is decomposed into a set of lower level problems and a system level problem.
In the lower level, cumulative measure of corresponding stress constraints is minimized with respect to the cross-sectional dimensions keeping the stiffness and the sub-level load vector determined in the system level unchanged. In the system level, structural weight is minimized under the constraints of displacements, the constraints on the cumulative measures of sub-level constraints and some side constraints. Quantatities representing lower level stiffnesses such as areas and sectional moments of inertia are taken as the system level design variables. The system level and the lower level are interrelated by the sensitivity analysis.
A computer program is developed and several examples are tested. The results demonstrate the applicability and the possibility of the present method, but for the practical and effective application, further researches on the decomposition method and the sensitivity analysis will be needed.
