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Fully automatic evaluation of local mechanisms in masonry aggregates through a NURBS-based limit analysis procedure
Published in Jan Kubica, Arkadiusz Kwiecień, Łukasz Bednarz, Brick and Block Masonry - From Historical to Sustainable Masonry, 2020
N. Grillanda, M. Valente, G. Milani, A. Chiozzi, A. Tralli
On the frontier of limit analysis tools, the Authors have recently proposed a new limit analysis procedure initially applied to masonry vaults. Such a method, the so-called GA-NURBS limit analysis (Chiozzi, Milani & Tralli, 2017), apply an upper bound formulation on a model discretized through NURBS (Non-Uniform Rational B-Spline) surfaces. NURBS surfaces are common in the CAD environment and are particularly suited to represent curved geometries. Since the method uses an upper bound limit analysis, a mesh adaptation through Genetic Algorithm is implemented in order to optimize the load multiplier by finding the real collapse mechanisms. Some applications of this procedure can be found in (Chiozzi, Grillanda et al., 2018; Chiozzi, Milani et al., 2018; Grillanda, Chiozzi, Bondi, Tralli, Manconi, Stochino, Cazzani et al., 2019; Grillanda, Chiozzi, Milani , Tralli et al., 2019).
Reference Individuals Defined for External and Internal Radiation Dosimetry
Published in Shaheen A. Dewji, Nolan E. Hertel, Advanced Radiation Protection Dosimetry, 2019
As both existing phantom types have their own distinct drawbacks regarding both anatomical realism and flexibility in morphometry alteration, investigators have sought new methods for anatomical modeling that provide and preserve both of these important features. Phantoms developed under this new approach can thus be termed “hybrid phantoms,” as they retain both the anatomic realism of voxel phantoms and the flexibility of stylized phantoms. In one approach to hybrid phantom construction, the three-dimensional surface equations used to define organ boundaries within existing stylized phantoms are replaced with NURBS (non-uniform rational basis-spline) surfaces (Piegl 1991). NURBS is a mathematical modeling technique widely used in three-dimensional computer graphics and film animation. NURBS surfaces can precisely represent not only standard analytic shapes (as needed to model organs in low-contrast images), but they can additionally define complex free-form surfaces required for certain intricately shaped internal organs and organ systems.
Direct digital prototyping and manufacturing
Published in Fuewen Frank Liou, Rapid Prototyping and Engineering Applications, 2019
This section helps answer the following questions: What is a solid model?Why is a solid model needed in digital manufacturing?What is a constructive solid geometry (CSG) model? What is a boundary representation (B-rep) model?How is a curved surface represented in a solid model?What is B-spline? What is nonuniform rational B-splines (NURBS)? How is a curved surface represented in a B-spline or NURBS?
A novel approach to the analysis of spatial and functional data over complex domains
Published in Quality Engineering, 2020
In most applications we use finite elements over triangular meshes. Figure 4 illustrates a linear finite element basis on a planar and on a non-planar triangulation. Wilhelm et al. (2016) explores instead the use of isogeometric analysis based on Non-Uniform Rational B-Splines (NURBS), that are advanced non-tensor product splines with high smoothness. The latter numerical solution is particularly interesting for engineering applications. Indeed, NURBS are extensively used in computer-aided design (CAD), manufacturing, and engineering, to represent the three-dimensional surface of the designed item. Moreover, when optimizing the design, especially in the space, aircraft, naval and automotive sectors, it is crucial to study the distribution of some quantity of interest over the surface of the designed item. Consider for instance the pressure exerted by air over the surface of a shuttle winglet; see Figure 2. In this respect SR-PDE based on NURBS can offer important in-built tools for uncertainty quantification and for prediction, exploiting the same basis representation that is used to design the object.
Static and transient analysis of sandwich composite plates using isogeometric analysis
Published in Mechanics of Advanced Materials and Structures, 2018
NURBS curves and surfaces are generalizations of both B-splines and Bezier curves and surfaces [3], the primary difference being the weighting of the control points, which makes NURBS curves/surfaces rational. Weighting of the each control point allows for more control over the shape of the curve without unduly raising the number of control points. The geometric flexibility of the NURBS basis allows for the exact representation of a much larger class of geometric variation than standard finite element technology [4]. NURBS are obtained by augmenting every point in control mesh with the weights . The weighting function is constructed as follow:
Curve-based image editing for product styling
Published in Computer-Aided Design and Applications, 2018
Bo Wang, Bao-Jun Li, Franca Giannini, Marina Monti, Ping Hu, Ji-Cai Liang
Usually, the sparse matrix is large with size . With the regular sparse structure of , the following decomposition is applied to solve the function. Where L is a lower triangular matrix, with non-zero elements only from the main diagonal to the diagonal below the main diagonal. Analogously, is an upper triangular matrix, with non-zero elements only from the main diagonal to the diagonal upper the main diagonal In this way, the points corresponding to the grid points can be computed. Fig. 8 shows the regular grid warping and the corresponding image results obtained from reshaping some curves of the window part of car body. Since cubic Bézier curve are special cases of B-splines and then of NURBS curve, this method can be used for NURBS curves as well.