364 S. Tornincasa et al. 0 100 101 102 103 104 105 106 107 108 109 110 201 202 203 204 205 206 300 301 302 303 304 305 306 307 308 309 310 311 401 402 403 404 405 406 407 501 502 503 504 505 506 507 508 509 510 511 601 602 603 604 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.1 0 Axis z [m] Axis y [m] Axis x [m] 0 −0.1 −0.1 Fig. 34.2 LUPOS test-rig model with node numbering Fig. 34.3 Details of the test-rig: (a) first added mass with rotating graduated device; (b) second added mass with fixing device; (c) third added mass 34.3 Nurbs-Based IGA and Test-Rig Model In Isogeometric Analysis, applied to solid structural mechanics, use trivariate NURBS (all the details about are widely explained in [29]) to define the discretization in a Finite Elements environment. The basic concept is to use a set of NURBS instead of the usual Lagrange basis functions. Being NURBS rational B-Splines, the latter is to be considered. B-Spline basis functions are defined by a knot vector, which is a vector of parameters in ascending order „D˚ 1 2 nCpC1 , where nis the number of basis functions andp is the polynomial degree. A particular case (and mostly used in CAD) of knot vector is the open knot vector, which is a knot vector where the first and last knots are repeatedpC1 times. A B-Spline basis functions is defined using the following recursive formula, starting from the order pD0 Ni;0 . / D 1 if i iC1 0 otherwise (34.1) Ni;p . / D i iCp i Ni;p 1 . / C iCpC1 iCpC1 iC1 NiC1;p 1 . / (34.2) In Fig. 34.4 the elements of a cubic (pD2) B-spline generated with an open knot vector are displayed.
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