By Gernot Beer
This e-book is an interesting, effortless to learn advent to complicated numerical modeling. the purpose of the e-book is to guide the reader on a trip in the direction of the ‘holy grail’ of numerical simulation, particularly one with no the requirement of mesh new release, that takes facts without delay from CAD courses. in this trip readers will detect the wonderful thing about Non-uniform Rational B-Splines or NURBS and spot how good they're fitted to describing geometry, observe how CAD courses paintings and the way their facts can be utilized for simulation. The implementation of NURBS-based simulation is mentioned utilizing Finite aspect and Boundary aspect know-how. it is a hands-on booklet with emphasis on implementation and examples of programming in the next point language are given. it's been written for clients of simulation software program, to allow them to comprehend the advantages of this new expertise and insist growth from a a little conservative undefined, for software program builders, to allow them to see that it is a expertise with an enormous destiny and for researchers, within the desire that it'll allure extra humans to paintings during this intriguing new box.
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Additional resources for Advanced numerical simulation methods : from CAD data directly to simulation results
5 Pierre Étienne Bézier (1910 to 1999) was a French engineer and one of the founders of the fields of solid, geometric and physical modeling as well as in the field of representing curves, especially in CAD/CAM systems. As an engineer at Renault, he became a leader in the transformation of design and manufacturing, through mathematics and computing tools, into computer-aided design and three-dimensional modeling. Stage 1: Basis functions Figure 8 Pierre Étienne Bézier. Figure 9 B-spline functions of order 0, 1 and 2.
Function continuity can be controlled by a repetition of values in the knot vector. e. e. continuity of function values only, not tangents). In the following we will consider only open knot vectors where the values are repeated p + 1 times at the beginning and the end6 . Furthermore, to simplify maters we will work with a parameter space that spans from 0 to 1, so that the entries in the knot vector ui will be 0 and 1. Indeed the functions of the NURBS toolkit only work with this range and knot vectors provided as input, that not comply to this will be normalised.
G. Salamon, and E. Georgiadis. A new digital method for threedimensional stress analysis in elastic media. Rock Mechanics, 5(189–202), 1973. G. J. P. Collins. The failure of an offshore platform. Concrete International, 19(8):28–35, 1997. W. Wappenhaus and J. Richter. Die erste Statik der Welt. Bautechnik, 8, 2002. C. W. Kelly, and P. Bettess. Marriage a la mode – the best of both worlds (finite elements and boundary integrals). In R. Y. C. Zienkiewicz, editors, Energy methods in finite element analysis, chapter 5, pages 82–107.
Advanced numerical simulation methods : from CAD data directly to simulation results by Gernot Beer