Razvoj izogeometrijske metode konačnih elemenata i njena primena u strukturnoj analizi nosećih struktura transportnih mašina

Abstract

The subject of doctoral dissertation is the isogeometric structural analysis. The isogeometric analysis represents a special approach in the finite element method (FEM) which aims at closing the gap between the actual geometry of modeled structures and the geometry generated upon the finite element discretization. In the isogeometric FE analysis, NURBS (non-uniform rational basis spline) functions usually form the basis for the definition of both the geometric models and interpolation functions of the FE models. Regardless of the mesh density, the geometry is exactly described in the FE model. The aim of the dissertation is the systematization of procedures and methods necessary for isogeometric analysis by creating general mathematical forms and program procedures. Isogeometric FE models are defined by using the NURBS and T-spline basis functions. An isogeometric solid element is formulated as well as a Kirchhoff-Love shell element with the NURBS basic functions. The method of modeling complex structures formed from several surfaces by using Kirchhoff-Love elements is presented. The results of the performed isogeometric analyses were compared with analytical results, the results yielded by the classical finite element method and experimental results. The developed isogeometric models were tested in the field of linear static, modal and explicit dynamic analyses. A particular part of the dissertation is dedicated to the benefits of isogeometric analysis in the field of structural analysis of transport machines complex structures. The conclusions related to advantages and disadvantages of NURBS ant Tsplines basis functions in the finite element method are presented through examples and tests done in this dissertation. The directions of further research are proposed.