Computer Aided Design of Cable Membrane Structures by B. H. V. Topping

By B. H. V. Topping

This instruction manual concentrates at the computational elements of study and layout of cable membrane buildings utilizing the dynamic leisure technique with a finite point idealization.

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Extra resources for Computer Aided Design of Cable Membrane Structures (Saxe-Coburg Publications on Computational Engineering)

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In NURBS, the basis functions are usually not interpolatory. There are two notions of meshes, the control mesh2 and the physical mesh. The control points define the control mesh, and the control mesh interpolates the control points. The control mesh consists of multilinear elements, in two dimensions they are bilinear quadrilateral elements, and in three dimensions they are trilinear hexahedra. The control mesh does not conform to the actual geometry. Rather, it is like a scaffold that controls the geometry.

Unlike in standard finite element analysis, the B-spline parameter space is local to patches rather than elements. 1. 2. Each element in the physical space is the image of a corresponding element in the parameter space, but the mapping itself is global to the whole patch, rather than to the elements themselves. Patches play the role of subdomains within which element types and material models are assumed to be uniform. Many simple domains can be represented by a single patch. 1 Knot vectors A knot vector in one dimension is a non-decreasing set of coordinates in the parameter space, written = {ξ1 , ξ2 , .

20 Knot insertion. Control points are denoted by . The knots, which define a mesh by partitioning the curve into elements, are denoted by . Each element has been evenly split in the parametric domain. mesh, and basis functions of the unrefined curve are shown on the left. 5. The new curve, shown on the right, is geometrically and parametrically identical to the original curve, but the control points are changed, the mesh is partitioned, and the basis is richer. There is one more control point, one more element, and one more basis function than in the unrefined case.

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