The algorithm of the cross-section optimization of inelastic geometrical nonlinear steel frame structures

Abstract

The purpose of the problem of optimization is introducing a project on the structure satisfying the limit requirements of the safety and usability conditions of the various eff ects of external actions. It can be provided by disposing comprehensive information about the real behaviour of construction under all working conditions and at any period of occurrence. Such problem cannot be solved applying the methods of the linear theory of structural mechanics because the form and dimensions of construction under assorted loads essentially change and the principle of small displacement becomes unreliable. In addition, starting from certain stress conditions, Hook’s law for majority materials is ineligible and changing by nonlinear relation. It is necessary to refuse the linear theory assumptions and change over to considerably wide and complex nonlinear theory generalizations. Abandoning calculation by unstrained condition tolerating small displacements allow changes in the infl uence of construction geometry on its defl ected mode, proceed to nonlinear tensions and relations with deformations and allow incipient plastic deformations because some materials of construction close to plastic collapse receive very large displacements and do not satisfy requirements for successful exploitation. Th ereby, the above mentioned causes must be allowed developing the mathematical models of solving the problems of construction optimization. A developed mathematical model and calculation algorithm with material inelastic properties as well as the evaluation of maintenance requirements are presented for the cross-sections optimization of geometrically nonlinear frames. Th e evaluation of dissipative features when employing inelastic steel stains results in a signifi cant reduction of reserve in carrying capacity in respect of the optimal elastic state of the structure. Maintenance requirements for the structure introduced to its operation time involve not only strength constraints but also stiff ness, stability and structural constraints defi ning minimal cross-section parameters and the ration of element slenderness. Th e aforementioned factors limit the free development of plastic stains, and therefore the optimal structure is considered in the state prior to plastic collapse. Th e used elastic response values are related to the optimal parameters of standard profi le cross-sections by nonlinear functional relation. Th erefore, this problem has to be solved using the iterative method. Th e procedure of forming a new beam element tangent stiff ness matrix considered by internal forces stimulated by diff erent element alterations is presented. Th e effi ciency of the developed algorithm exemplifi ed by calculating the optimal values of the cross-section involving 16-stroyed steel frame beam elements is obeyed by minimum volume requirements when node horizontal displacements are limited.

Netamprių geometriškai netiesinių plieninių rėminių konstrukcijų skerspjūvių optimizavimo algoritmas

Santrauka. Straipsnyje pateikiamas patobulintas plieninių rėmų kaip geometriškai netiesinių sistemų strypų skerspjūvių optimizacijos uždavinio matematinis modelis ir skaičiavimo algoritmas, įvertinantis medžiagos netampriąsias savybes bei eksploatacinius reikalavimus. Disipacinių savybių įvertinimas, naudojant netampriąsias plieno deformacijas, lemia reikšmingą laikomosios galios rezervo sumažinimą optimalios tamprios būklės konstrukcijos atžvilgiu. Eksploataciniai reikalavimai, keliami konstrukcijai jos naudojimo laikotarpiu, apima ne tik stiprumo, bet ir deformatyvumo, stabilumo ir konstrukcinius apribojimus. Jie apibrėžia minimalius skerspjūvių parametrus ir elementų ribinius liaunius. Visa tai riboja laisvą plastinių deformacijų plitimą, todėl optimali konstrukcija yra neyramoji tamprioji plastinė. Naudojami tampraus atsako dydžiai susieti netiesiniu funkciniu ryšiu su standartinių profi lių skerspjūvių optimizuojamais parametrais, todėl uždavinys sprendžiamas iteracijų būdu. Pateikta nauja rėminio strypinio elemento tangentinės standumo matricos sudarymo metodika. Atliktas 16 aukštų rėmo iš standartinių profi liuočių skerspjūvių optimizacijos uždavinio skaitinis eksperimentas.

Reikšminiai žodžiai: optimizacija, tamprioji plastinė konstrukcija, geometrinis netiesiškumas, tangentinė standumo matrica, geometrinis standumas, plastiškoji irtis.

First Published Online: 16 May 2013

Keyword : optimization, elastic plastic structure, geometrical nonlinearity, tangent stiff ness matrix, geometrical stiff ness, plastic collapse