Optimisation of Geometrically Non-linear Elastic-plastic Structures in the State Prior To Plastic Collapse

A mathematical model and calculation algorithm for geometrically non‐linear structure cross‐sectional optimisation are developed. Inelastic strains in the state prior to plastic collapse are evaluated. The algorithm is obtained combining the extreme energy principle for minimum value dissipated power and mathematical programming theory in concert with a large displacement analysis. An evaluation of dissipative features by employing inelastic strains finally results in a significant reducement of structure carrying capacity resource versus accounting its elastic response only. The safety requirements of structure involve stability conditions in addition to the strength ones. Stability conditions define the minimum cross‐sectional and slenderness values of structural members. An evaluation of the above‐mentioned factors restrict a free development of plastic strains, thus an optimal structure generally is in a state prior to plastic failure. The problem is solved iteratively, as the employed values of structural elastic response are functionally related with the optimised parameters ones. During iterative calculus process the design parameters are defined applying the non‐linear analysis and the tangent stiffness computational procedures. A simulation of 16‐storey steel optimal frame created from standard profiles is presented.