| The basic idea of isogeometric analysis is using language of CAD system, namely NURBS, to substitute lagrangian interpolation as the basis of mechanics calculation, which has been shown to be very effective to eliminate errors brought by the geometric approximation in the finite element discretization, and suitable for contact problems especially. This thesis was concerned with the investigation on NURBS geometry discretization of barrel and isogeometric contact analysis of barrel and projectile.NURBS rational basis functions were defined by the Cox-de Boor recursion formula, and their derivatives were calculated for analysis. The knot vector, control point and weight were studied on their effect on the continuity of NURBS, respectively. Three different refine methods including knot insert, order elevation, and k-refine which remain the geometry and parameters unchanged were compared in details.The modeling of barrel was done in CAD system, and exported as an IGES file. Through analyzing the NURBS data structure of IGES, an IGESREADER program used for extracting NURBS geometry information was developed. The coarse mesh was formed with these original NURBS information, and refined by knot insert.Taking control points as degrees of freedom, the algorithm of isogeometric analysis has been derived based on the Galerkin method, which was quite similar to the framework of traditional FEA. The efficacy of isogeometric analysis was also verified by some classical numerical examples.For2D frictionless contact problems, contact detection was carried out on NURBS curves of contact body. The impenetration conditions were weakened by penalty approach, and then the patch test was passed. With the NURBS model exist, the contact between barrel and projectile was seen as interference fitting simply. The correctness of isogeometric contact analysis was verified by the numerical results compared with theoretical solution and finite element analysis results. |
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