Discrete variable optimization of frames using a strain energy criterion

This paper reports on recent advances concerning a new method for the weight (discrete variable) optimization of frames under both stress and multi-displacement constraints using a criterion based on the distribution of the virtual strain energy density. The proposed methodology is based on an idea that has been previously demonstrated and successfully applied on truss structures. The influence of each participating beam is defined through properly normalized sensitivity factors. An iterative formula, similar to that used for trusses, is proposed for updating the second moment of inertia followed by an improvement of shape variables (e.g. height, width, thickness) on the cross-section. The proposed method is successfully compared with the sequential quadratic programming method and other techniques published in the most recent literatures.