Isogeometric analysis as an alternative to standard Finite element method

Structural mechanics

In the article, the modification of the Finite Element Method, the so-called Isogeometric Analysis, which employs rational B-splines (NURBS) as basis-functions is considered. The new approach is aimed to prevent approximation of the geometry and provide higher continuity on elements’ borders. A brief review of rational B- splines is made, their basic properties are described, a review of existing today software products in which the described method is implemented to some extent is executed. In the contribution, a numerical example of analysis for a simple solid body in FEAP (Finite Element Analysis Program) is given for comparing results obtained by standard and modified methods. In the Isogeometric approach, the geometry of the analysed body stays exact no matter how coarse is the computational mesh. This leads to the more robust solution of the contact problems and of the composites analysis. Non-negative basis functions increase the quality of the created continuous variable fields. Moreover, the geometry for analysis can be obtained directly from CAD graphical editors, which becomes an important step towards the introduction of BIM technology in engineering design. The advantages of this method illustrate that it can be preferred for structural analysis of solids especially in cases when complex curved geometry has to be considered.