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.
An actual structural design, especially that of lightweight structures, must evaluate strength, stiffness and stability constraints. A designed structure must satisfy optimality criteria. One faces known difficulties when trying to implement several from above mentioned requirements into optimization problem for further successful numerical realisation. A method to formulate the optimization problem, incorporating all above described criterions, mathematical model and algorithm to solve it numerically, taking into account the geometrically non‐linear structural behaviour are presented for truss type structure. In each optimization cycle the member forces obtained in the previous optimization cycle via elastic‐plastic non‐linear analysis procedure are employed to obtain the new optimal design values. During the optimization procedures, the tension members are assumed to be loaded up to the yield limit, compression members are assumed to be stressed up to their critical limits, the nodal displacements are restricted to limited magnitudes in prescribed directions. Design examples are presented to demonstrate the application of the algorithm.
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