By Gernot Beer
ISBN-10: 3709118425
ISBN-13: 9783709118429
ISBN-10: 3709118433
ISBN-13: 9783709118436
The publication provides the cutting-edge in isogeometric modeling and exhibits how the tactic has advantaged. First an creation to geometric modeling with NURBS and T-splines is given by means of the implementation into software program. The implementation in either the FEM and BEM is discussed.
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Extra resources for Isogeometric Methods for Numerical Simulation
Example text
An additional open source IGA code written in Matlab R is given in de Falco et al. (2011) with applications including elasticity, scalar PDEs, magnetic problems etc. Incorporating IGA within an object-oriented C++ FE code is discussed in Rypl and Patzák (2012). Implementation details for enriched formulations within an IGA framework are reported in Benson et al. (2010a) using a commercial FE software. In this chapter, an efficient easy-to-use IGA (X)FEM code for solid mechanics written in Matlab R (and some heavily used functions in C via MEX files) is presented.
For the sake of clarity, let us consider the case where there is only one collocation point and a quadratic basis (thus there are 3 non-zero ΦA at xC ). So, we have 1 ¯ (xC )||2 . ||Φ1 (xC )q1 + Φ2 (xC )q2 + Φ3 (xC )q3 − u 2 The partial derivatives of J with respect to qi are given by J= ∂J ¯ (xC )]Φ1 (xC ) = [Φ1 (xC )q1 + Φ2 (xC )q2 + Φ3 (xC )q3 − u ∂q1 ∂J ¯ (xC )]Φ2 (xC ) = [Φ1 (xC )q1 + Φ2 (xC )q2 + Φ3 (xC )q3 − u ∂q2 ∂J ¯ (xC )]Φ3 (xC ). = [Φ1 (xC )q1 + Φ2 (xC )q2 + Φ3 (xC )q3 − u ∂q3 The condition ∂J ∂q (44) (45) = 0 thus gives the following linear system ⎤ u ¯y (xC )Φ1 (xC ) u ¯y (xC )Φ2 (xC )⎦ .
We begin with some basic concepts including knot vectors, B-spline basis functions. Then, B-spline curves and surfaces are introduced. We refer to Piegl and Tiller (1996) for more details. 1 27 Parametric representation In order to present the basic concepts such as parameters, parametric space and physical space, let us consider the equation of a unit circle centered at the origin x2 + y 2 = 1 (1) which can be rewritten using the so-called parametric equation x = cos t, y = sin t 0 ≤ t ≤ 2π (2) in which t denotes a parameter ranging from 0 to 2π.
Isogeometric Methods for Numerical Simulation by Gernot Beer
by Thomas
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