ИСТИНА

Isogeometric Analysis has quickly become an attractive and exciting research topic after the publication of the seminal paper of T.J.R. Hughes et al. in 2004. In the context of this new method, mathematical approaches of two formerly independent fields of Computer-aided Design (CAD) and Finite Element Analysis (FEA) were combined together. This new paradigm promises many opportunities to any field of science and engineering where FEA was used in numerical analysis applications formerly. By using the non-uniform rational basis splines (NURBS) which are the core technology for most of the CAD packages for FEA computations, the solutions to the problems at hand can be developed and computed within the same framework seamlessly using single data set both for model generation and analysis. Some of the outstanding attractive features of this new approach can be listed as follows, the smoothness of spline functions provide additional advantages in the cases where higher order of continuity is necessary to obtain meaningful results, isogeometric analyses also offers another new higher order refinement technique called k-refinement in addition to containing the popular hp-refinement strategies commonly used in FEA, exact geometry representation and termination of the time consuming meshing step of the product development. During the past years researchers have been investigating and developing possible applications of Isogeometric Analysis on many sub-fields of mechanics. Among them, one possible field of interest is the continuum micromechanics of three dimensional textile composites. One of the possible application areas of this new analysis method is using it in effective material property determination of this kind of composites. In order to define the effective material properties of this type of materials with complex inner structures, a procedure called homogenization is applied via geometrical modeling, mesh generation, definition of the appropriate boundary conditions and computing the model in order to obtain the macroscopic mechanical response behavior of the textile composites. Textile composites have relatively more complex geometrical structure than unidirectional or particle reinforced composites, hence the exact geometrical representation offered by Isogeometric Analysis is an important advantage during the homogenization process. Here, within a three dimensional environment we face probably the most challenging problems in implementation of isogeometric analysis today, because widely used CAD packages model the solids as surfaces. This is an important shortcoming for the current state of the isogeometric analysis because the information obtained from conventional geometrical modeling packages does not possess the sufficient information for trivariate models. In this work, we develop an isogeometric analysis based homogenization method for three dimensional textile composites using classical linear materials and carry out comparison and validation processes for the results we have obtained. Already established and widely used numerical continuum micromechanis methods are used as references for the evaluation of the applicability and performance of homogenization algorithms utilizing isogeometric analysis. For developing such a comparison environment, we model representative volume elements (RVE) of textile composite specimens and under appropriate boundary conditions we analyze the RVEs and obtain the effective material properties. These results are then compared with the classical FEA approaches. As the final step of the research work, the results obtained so far are discussed and possible directions for the application of Isogeometric Analysis to textile composite modeling is determined.