Form-finding of shell structures based on isogeometric analysis

Abstract

The paper reviews potentials of the application of isogeometric analysis (IGA) in the pro­cesses of form-finding of shell structures. Shaping of those specific spatial structural typolo­gies is determined by consideration of the form-structure interrelation, therefore the sustainable approach to design implies application of form-finding techniques. In this paper, we applied the frequently used form-finding principle a inverted model strategy, more precisely concept of inverted displacements. Contrary to the similar studies which apply standard finite element (FE) discretization, we proposed an application of isogeometric modeling of the structure. Isogeome­try implies analysis based on the exact definition of the initial geometry, facilitating design and analysis by application on the single data type - model. Advantage of the conservation of geometric representation is especially evident in the case of shell structure designs, bearing in mind their continuously curved geometry. We applied NURBS based isogeometric analysis in which geometry and displacement field are described by NURBS surfaces. Modeling of the structural performances was conducted by isogeometric shell elements. Presented numerical experiment has a function to confirm the effectiveness of the proposed approach.

Radom se razmatraju potencijali primene izogeometrijske analize u procesima traženja formi ljuski. Oblikovanje ovih specifičnih prostornih strukturalnih tipologija određeno je razmatranjem interrelacije forma-struktura, zbog čega održivi pristup njihovom projektovanju podra­zumeva primenu tehnika traženja forme. U okviru ovog rada primenjena je strategija obrnutog modela, često korišćen princip traženja forme, tačnije koncept obrnutih pomeranja. Za razliku od sličnih istraživanja u kojima se koristi standardna diskretizacija konačnim elementima (FE), ovim radom se predlaže izogeometrijsko modelovanje strukture. Izogeometrija podrazumeva analizu zasnovanu na egzaktnoj definiciji početne geometrije, čime je omogućeno projektovanje i analiza upotrebom jedinstvenog tipa podataka - modela. Prednost konzervacije geometrijske reprezentacije posebno dolazi do izražaja u slučaju projektovanja ljuski imajući u vidu njihovu kontinualno zakrivljenu geometriju. Primenjena je NURBS izogeometrijska analiza, u kojoj se geometrija i polje pomeranja opisuju korišćenjem NURBS površi. Modelovanje strukturalnih performansi izvršeno je korišćenjem izogeometrijskog elementa ljuske. Prikazan numerički ek­speriment u funkciji je potvrđivanja efikasnosti predloženog pristupa.