Isogeometric analysis (IGA) has been recently introduced as a viable alternative to the standard, polynomial-based finite element analysis. One of the fundamental performance issues of the isogeometric analysis is the quadrature of individual components of the discretized governing differential equation. The capability of the isogeometric analysis to easily adopt basis functions implies that high order numerical quadrature schemes must be employed. This may become computationally prohibitive because the evaluation of the high degree basis functions and/or their derivatives at individual integration points is quite demanding. The situation tends to be critical in three-dimensional space where the total number of integration points can increase dramatically. The aim of this paper is to compare computational efficiency of several numerical quadrature concepts which are nowadays available in the isogeometric analysis. Their performance is asessed on the assembly of stifness matrix of B-spline based problems with special geometrical arrangement allowing to determine minimum number of integration points leading to exact results. and Článek zahrnuje seznam literatury a na str. 257-259 Appendix
In this contribution, we present the final outcome of the program initiated in [23], aimed at the determination of a periodic unit cell for plain weave composites with reinforcement imperfections. The emphasis is put on a realistic geometrical description of these material systems utilizing the information provided by in-situ two-dimensional micrographs. Complex geometry of an analyzed composite is approximated using a two-layer periodic unit cell allowing for a mutual shift as well as nesting of individual layers. The parameters of the idealized unit cell are derived via matching appropriate statistical descriptors related to the real material and the idealized geometrical model. Once the optimal geometry of the unit cell is determined, it can be converted to a CAD model and used ot generate the periodic finite element mesh applicable in the subsequent numerical treatment. The individual steps of this procedure are demonstrated in detail for a real world carbon-carbon composite system. and Obsahuje seznam literatury