Optimisation of Geometrically Non‐linear Elastic‐plastic Structures in the State Prior to Plastic Collapse

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.

Discrete optimization problems of the steel bar structures

“…It is especially hardened by the nonlinear conditions (8). Therefore the problem is solved iteratively, in each iteration selecting cross-sections of bars and solving a simpler problem of nonlinear programming where only additional complementary slackness conditions are nonlinear.…”

“…While designing the structures, an additional economy of the structural material is obtained for the structures with plastic deformations with respect to optimal ones with elastic deformations. However, the optimization problems of elastic-plastic structures [6][7][8][9]15] are evaluated where not only the strength, but also stiffness and stability requirements, are complex nonlinear programming problems and the realization of them is complicated. In this paper design problems of the elastic and elastic-plastic steel structures are investigated.…”

“…The various specific algorithms for nonlinear optimization problems of structures are recently created: incremental [8], genetic [9][10][11], discrete optimization [5], evolutionary [12], homogenization [13] and other optimization algorithms [14][15][16]. The solution algorithms for nonlinear optimization problems are not as universal as the latter for the linear problems.…”

Optimization of Truss Height

“…Pastaruoju metu netiesiniams konstrukcijų optimizavimo uždaviniams spręsti yra sukurti įvairūs specifiniai algoritmai: genetiniai (Hayalioglu 2000;Zheng et al 2006), evoliuciniai (Manickarajah et al 2000;Weise 2009), etapiniai (Karkauskas 2007), diskrečiojo optimizavimo (Appa et al 2006;Gutkowski et al 1997), homogeniniai (Yuge et al 1999) ir kiti. Tačiau netiesinių optimizavimo uždavinių sprendimo algoritmai yra sudėtingi ir, be to, nėra standartinių universalių kompiuterinių programinių paketų tokiems uždaviniams spręsti.…”

“…Projektuojant konstrukcijas, kuriose galimos plastinės deformacijos, gaunama papildoma medžiagų ekonomija, lyginant su analogiškomis tampriomis konstrukcijomis. Tačiau tampriųjų ir plastinių konstrukcijų optimizavimo uždaviniai (Karkauskas 2007;Hayalioglu 2000;Grigusevičius et al 2005), kuriuose įvertinami ne tik stiprumo, bet ir standumo bei stabilumo reikalavimai, yra sudėtingi netiesinio programavimo uždaviniai ir jų realizacija nelengva.…”