Get Advanced numerical simulation methods : from CAD data PDF

By Gernot Beer

ISBN-10: 1138026344

ISBN-13: 9781138026346

ISBN-10: 1315766310

ISBN-13: 9781315766317

This publication is an enjoyable, effortless to learn advent to complicated numerical modeling. the purpose of the ebook is to steer the reader on a trip in the direction of the ‘holy grail’ of numerical simulation, particularly one with out the requirement of mesh iteration, that takes info without delay from CAD courses. in this trip readers will realize the wonderful thing about Non-uniform Rational B-Splines or NURBS and notice how good they're suited to describing geometry, notice how CAD courses paintings and the way their facts can be utilized for simulation. The implementation of NURBS-based simulation is mentioned utilizing Finite point and Boundary point know-how. this can be a hands-on booklet with emphasis on implementation and examples of programming in a better point language are given. it's been written for clients of simulation software program, to allow them to comprehend the advantages of this new know-how and insist growth from a a little bit conservative undefined, for software program builders, to allow them to see that it is a know-how with a major destiny and for researchers, within the wish that it'll allure extra humans to paintings during this intriguing new box.

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Sample text

We keep here to the definition in the book Isogeometric Analysis. Stage 1: Basis functions 19 Figure 2 Lagrange function derivatives for orders 2 to 4. Substitution of the ξ1 = −1 and ξ2 = 1 into equation 5 gives 1 (1 − ξ) 2 1 N2 (ξ) = (1 + ξ) 2 N1 (ξ) = (6) For a quadratic interpolation we have p = 2 and I = 3: N1 (ξ) = ξ − ξ1 ξ − ξ3 ξ − ξ2 ξ − ξ3 ξ − ξ1 ξ − ξ2 · ; N2 (ξ) = · ; N3 (ξ) = · (7) ξ 2 − ξ 1 ξ1 − ξ 3 ξ1 − ξ 2 ξ 2 − ξ 3 ξ3 − ξ 1 ξ 3 − ξ 1 20 Advanced numerical simulation methods Figure 3 Example of interpolation between 4 points with Lagrange polynomials of order 3.

Here we only introduce the OCTAVE functions for determining the values of NURBS at parametric points. Other functions will be introduced in the next chapters as required. A few remarks on the software are appropriate here. The functions take homogeneous coordinates/parameters at the control points as input. This means that they have to be multiplied by the weights before being supplied to the function. The functions assume that the entries in knot vector range from 0 to 1. Knot vectors can be supplied with different range of entries but are changed internally.

Parametric points % For individual points: % NURBS curves: % Array of size (number of points= npoints) % t (n)=u 50 Advanced numerical simulation methods % NURBS surfaces: Array of size (2, npoints) % t (1, n)= u, t (2, n)= v % Points on a grid nu*nv % 2 arrays of size (number of points in u/v directions) % {u(n), v(n)} % nurbs ... NURBS structure % % Output: % Ru(1:npoints,1:nbf) ... first derivative to u of basis functions % NURBS surfaces only: % Rv(1:points,1:nbf) ... first derivative to v of basis functions % idx(1:npnts,1:nbf) ...

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Advanced numerical simulation methods : from CAD data directly to simulation results by Gernot Beer

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