New PDF release: Advanced numerical simulation methods : from CAD data

By Gernot Beer

ISBN-10: 1138026344

ISBN-13: 9781138026346

ISBN-10: 1315766310

ISBN-13: 9781315766317

This e-book is an exciting, effortless to learn advent to complex numerical modeling. the purpose of the publication is to steer the reader on a trip in the direction of the ‘holy grail’ of numerical simulation, specifically one with out the requirement of mesh iteration, that takes facts 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 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 expertise. it is a hands-on e-book 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 expertise and insist development from a just a little conservative undefined, for software program builders, to allow them to see that this can be a expertise with a tremendous destiny and for researchers, within the desire that it'll allure extra humans to paintings during this fascinating new box.

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Extra resources for Advanced numerical simulation methods : from CAD data directly to simulation results

Example text

The number of control points and the order of the basis functions is deduced from the size of the array supplied in the input. Care has to be taken when these arrays are reused with different sizes (in this case a clear command must be used). The toolkit always demands 3 coordinates. For plane curves the z-coordinate is set to zero. As will be pointed out in the detailed description of the toolkit, there are a number of inconsistencies. For example different definitions of order or degree of the basis functions are used.

The next function computes first derivatives of basis functions. function [Ru,Rv,idx] = nrbbasisfunder(points, nurbs) % --------------------------------------------------------% Evaluate non-zero NURBS function derivatives at parametric points. % % Input: % points ... 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 ...

5: This means that the blue basis function has only C 0 continuity (see Figure 15) and all other basis functions only span half of the parameter space. For this case, two knots are located at the same location. It is noted that the same result can be achieved if the parameter space is split into two and Bernstein polynomials are used for each subspace. We re-plot the function in Figure 7 with the modified knot vectors in Figures 16 and 17. It can be seen that the shape of the curve has been altered when compared to Bernstein polynomials.

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


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