In the present work, isogeometric analysis in 3D linear elasticity problem is conducted using the basis functions from NURBS. The objective of isogeometric analysis introduced by Hughes is to integrate both geometric modeling (CAD) and computational analysis (CAE). This can be accomplished from direct usage of geometric modeling by NURBS as the computational mesh that means isogeometric analysis. NURBS surface are able to represent exact geometry from the control points and knot vectors. Also subsequent refinement is so simple relatively. The test geometries are the solid circular cylinder subjected to the constant internal pressure loading and the infinite plate with circular hole and the results are compared with the exact solution. Quadratic, cubic and quartic NURBS are considered. After generating the circular cylinder geometry based on the control points and knot vectors, the effects of the knot insertion (h-refinement) and the order elevation of the basis (p-refinement) are investigated. Meshes produced by h-refinement and the contours of the radial displacement are presented. The convergence rate of the calculated variables is checked with respect to some discretization orders and various mesh sizes.
The basic concept of the isogeometric analysis is to use the same functions between the solution space and the geometric modeling. This isogeometric analysis was introduced conceptually by Cho and Roh (2003) and NURBS based isogeometric analysis was developed by Hughes et al. (2005). Through isogeometric analysis, the geometric modeling from Computer Aided Design (CAD) is directly adopted to the mesh for Computer Aided Engineering (CAE) without the extra regeneration process. The omission of this extra job can save the time by about 80% of overall analysis time (Hughes et al., 2005). NURBS basis is able to generate the exact geometry when compared with other basis functions.
