Abstract
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.
Highlights
The main aim of different tasks related to optimisation of building structures is to develop an optimal structure with closely related energy inputs and mass
The mathematical model and design algorithm is developed for geometrically non-linear structure crosssectional optimisation taking into account inelastic strains in the state prior to plastic collapse
The algorithm is obtained by coupling the extreme energy principle of minimum dissipated power and mathematical programming theory in concert with a large displacement analysis
Summary
The main aim of different tasks related to optimisation of building structures is to develop an optimal structure with closely related energy inputs and mass. One should employ a non-linear stress-strain relation evaluating the emerging plastic deformations It is conditioned by extremely large displacements that have been developed in structures prior to plastic collapse. It became clear that evaluation of parameters of deformed state of a structure and that of material plastic characteristics serves a more precise reflection of its behaviour at various load stages. The latter phenomenon is necessary to evaluate in mathematical models of structural optimisation problems. Karkauskas / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT – 2007, Vol XIII, No 3, 183–192 concert with actual evaluation of behaviour of the structure should be formalised mathematically during all stages of structural deforming It helps develop a more rational design of a structure.
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