Now showing items 1-6 of 6
Gaussian quadrature for $C^1$ cubic Clough-Tocher macro-triangles
A numerical integration rule for multivariate cubic polynomials over n-dimensional simplices was designed by Hammer and Stroud . The quadrature rule requires n + 2 quadrature points: the barycentre of the simplex and ...
Generalization of the Pythagorean Eigenvalue Error Theorem and its Application to Isogeometric Analysis
This chapter studies the effect of the quadrature on the isogeometric analysis of the wave propagation and structural vibration problems. The dispersion error of the isogeometric elements is minimized by optimally blending ...
Efficient quadrature rules for subdivision surfaces in isogeometric analysis
We introduce a new approach to numerical quadrature on geometries defined by subdivision surfaces based on quad meshes in the context of isogeometric analysis. Starting with a sparse control mesh, the subdivision process ...
On numerical quadrature for $C^1$ quadratic Powell-Sabin 6-split macro-triangles
The quadrature rule of Hammer and Stroud  for cubic polynomials has been shown to be exact for a larger space of functions, namely the $C^1$ cubic Clough-Tocher spline space over a macro-triangle if and only if the ...
Highly-accurate 5-axis flank CNC machining with conical tools
A new method for $5$-axis flank computer numerically controlled (CNC) machining using a predefined set of tappered ball-end-mill tools (aka conical) cutters is proposed. The space of lines that admit tangential motion of ...
Super Abrasive Machining of Integral Rotary Components Using Grinding Flank Tools
Manufacturing techniques that are applied to turbomachinery components represent a challenge in the aeronautic sector. These components require high resistant super-alloys in order to satisfy the extreme working conditions ...