scholarly journals General polytopal H(div)-conformal finite elements and their discretisation spaces.

2020 ◽  
Author(s):  
Elise Le Meledo ◽  
Philipp Öffner ◽  
Remi Abgrall
Keyword(s):  
Finite Elements ◽  
Degrees Of Freedom ◽  
General Setting ◽  
Basis Functions ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Wide Range ◽  
Virtual Element ◽  
Set Up

We present a class of discretisation spaces and H(div) - conformal elements that can be built on any polytope. Bridging the flexibility of the Virtual Element spaces towards the element's shape with the divergence properties of the Raviart - Thomas elements on the boundaries, the designed frameworks offer a wide range of H(div) - conformal discretisations. As those elements are set up through degrees of freedom, their definitions are easily amenable to the properties the approximated quantities are wished to fulfil. Furthermore, we show that one straightforward restriction of this general setting share its properties with the classical Raviart - Thomas elements at each interface, for any order and any polytopial shape. Then, to close the introduction of those new elements by an example, we investigate the shape of the basis functions corresponding to particular elements in the two dimensional case.

Isogeometric Stress, Vibration and Stability Analysis of In-Plane Laminated Composite Structures

2018 ◽  
Vol 18 (05) ◽  
pp. 1850070 ◽  
Author(s):  
S. Faroughi ◽  
E. Shafei ◽  
D. Schillinger
Keyword(s):  
Stability Analysis ◽  
Finite Elements ◽  
Isogeometric Analysis ◽  
Composite Structures ◽  
Degrees Of Freedom ◽  
Computational Study ◽  
Laminated Composite ◽  
Basis Functions ◽  
Energy Error ◽  
Laminated Composite Structures

We present a computational study that develops isogeometric analysis based on higher-order smooth NURBS basis functions for the analysis of in-plane laminated composites. Focusing on the stress, vibration and stability analysis of angle-ply and cross-ply 2D structures, we compare the convergence of the strain energy error and selected stress components, eigen-frequencies and buckling loads according to overkill solutions. Our results clearly demonstrate that for in-plane laminated composite structures, isogeometric analysis is able to provide the same accuracy at a significantly reduced number of degrees of freedom with respect to standard [Formula: see text] finite elements. In particular, we observe that the smoothness of spline basis functions enables high-quality stress solutions, which are superior to the ones obtained with conventional finite elements.

On Higher Order Pyramidal Finite Elements

2011 ◽  
Vol 3 (2) ◽  
pp. 131-140 ◽  
Author(s):  
Liping Liu ◽  
Kevin B. Davies ◽  
Michal Křížek ◽  
Li Guan
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Degrees Of Freedom ◽  
Higher Order ◽  
Basis Functions ◽  
Quadratic Functions ◽  
Polynomial Basis

AbstractIn this paper we first prove a theorem on the nonexistence of pyramidal polynomial basis functions. Then we present a new symmetric composite pyramidal finite element which yields a better convergence than the nonsymmetric one. It has fourteen degrees of freedom and its basis functions are incomplete piecewise triquadratic polynomials. The space of ansatz functions contains all quadratic functions on each of four subtetrahedra that form a given pyramidal element.

scholarly journals Scalability of high-performance PDE solvers

2020 ◽  
Vol 34 (5) ◽  
pp. 562-586 ◽  
Author(s):  
Paul Fischer ◽  
Misun Min ◽  
Thilina Rathnayake ◽  
Som Dutta ◽  
Tzanio Kolev ◽  
...  
Keyword(s):  
Finite Elements ◽  
High Performance ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Fixed Number ◽  
Peak Performance ◽  
Trade Offs ◽  
Wide Range ◽  
P Type ◽  
Pde Solvers

Performance tests and analyses are critical to effective high-performance computing software development and are central components in the design and implementation of computational algorithms for achieving faster simulations on existing and future computing architectures for large-scale application problems. In this article, we explore performance and space-time trade-offs for important compute-intensive kernels of large-scale numerical solvers for partial differential equations (PDEs) that govern a wide range of physical applications. We consider a sequence of PDE-motivated bake-off problems designed to establish best practices for efficient high-order simulations across a variety of codes and platforms. We measure peak performance (degrees of freedom per second) on a fixed number of nodes and identify effective code optimization strategies for each architecture. In addition to peak performance, we identify the minimum time to solution at 80% parallel efficiency. The performance analysis is based on spectral and p-type finite elements but is equally applicable to a broad spectrum of numerical PDE discretizations, including finite difference, finite volume, and h-type finite elements.

Application of Finite Elements to the Analysis of Gear Tooth Stresses

1973 ◽  
Vol 95 (4) ◽  
pp. 1139-1148 ◽  
Author(s):  
L. Wilcox ◽  
W. Coleman
Keyword(s):  
Finite Elements ◽  
Gear Tooth ◽  
Tooth Surface ◽  
Two Dimensional ◽  
Loading Conditions ◽  
The Finite Element Method ◽  
Tooth Shape ◽  
Hypoid Gears ◽  
Wide Range ◽  
New Formula

This paper explains the application of the analytical method of finite elements to the analysis of gear tooth stresses. The details necessary for simulating a two-dimensional tooth shape with finite elements are outlined and a technique for determining stress values at the tooth surface in the root fillet is given. The remainder of the paper uses the finite element method to analyze tensile fillet stress in generated tooth shapes incorporating either symmetric or asymmetric profiles. Special attention has been given to the asymmetric profiles (used in Hypoid gears) since no reliable formulas are available. Stress data thus obtained are used to develop a new simplified stress formula that gives tensile fillet stress as a function of geometric tooth shape and general loading conditions. The accuracy and wide range of applicability of the new stress formula is shown by comparing the new formula to other previously accepted formulas for a variety of tooth shapes and loading conditions.

scholarly journals Two-dimensional resonant magnetic soft X-ray scattering set-up for extreme sample environment

2012 ◽  
Vol 20 (1) ◽  
pp. 181-189 ◽  
Author(s):  
Stefan Stanescu ◽  
Cristian Mocuta ◽  
Frederic Merlet ◽  
Antoine Barbier
Keyword(s):  
Magnetic Scattering ◽  
Nanometer Scale ◽  
Two Dimensional ◽  
Correlation Lengths ◽  
X Ray ◽  
X Ray Scattering ◽  
Wide Range ◽  
Set Up ◽  
Sample Environment ◽  
Ray Scattering

The newly built MagSAXS (magnetic small-angle X-ray scattering) set-up dedicated to the direct two-dimensional measurement of magnetic scattering using polarized synchrotron radiation in extreme sample environments is presented. Pure optical transport of the image is used to record the magnetic scattering with a two-dimensional CCD visible-light camera. The set-up is able to probe magnetic correlation lengths from the micrometer down to the nanometer scale. A detailed layout is presented along with preliminary results obtained at several beamlines at Synchrotron SOLEIL. The presented examples underline the wide range of possible applications spanning from correlation lengths determination to Fourier transform holography.

scholarly journals Solving the hourglass instability problem using rare mesh variation-difference schemes

2021 ◽  
Vol 2099 (1) ◽  
pp. 012003
Author(s):  
D T Chekmarev ◽  
Ya A Dawwas
Keyword(s):  
Finite Elements ◽  
High Efficiency ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Explicit Difference Scheme ◽  
Slow Convergence ◽  
Instability Problem ◽  
Instability Effect ◽  
2D And 3D

Abstract The hourglass instability effect is characteristic of the Wilkins explicit difference scheme or similar schemes based on two-dimensional 4-node or three-dimensional 8-node finite elements with one integration point in the element. The hourglass effect is absent in schemes with cells in the form of simplexes (triangles in two-dimensional case, tetrahedrons in three-dimensional case). But they have another well-known drawback - slow convergence. One of the authors proposed a rare mesh scheme, in which elements in the form of a tetrahedron are located one at a time in the centers of the cells of a hexahedral grid. This scheme showed the absence “hourglass” effect and other drawbacks with high efficiency. This approach was further developed for solving 2D and 3D problems.

Finite elements-boundary elements coupling for the movement modeling in two-dimensional structures

1992 ◽  
Vol 2 (11) ◽  
pp. 2035-2044 ◽  
Author(s):  
A. Nicolet ◽  
F. Delincé ◽  
A. Genon ◽  
W. Legros
Keyword(s):  
Finite Elements ◽  
Boundary Elements ◽  
Two Dimensional

Settlers or Movers? The Temporality of Past Migrations, Political Inaction and its Consequences, 1945–1985

2018 ◽  
Author(s):  
Jozefien De Bock
Keyword(s):  
Temporary Workers ◽  
Guest Workers ◽  
Temporary Migration ◽  
Wide Range ◽  
Settler Societies ◽  
Future Policy ◽  
Set Up ◽  
Legal Frameworks ◽  
Temporary Migrants ◽  
Multicultural Policies

Historically, those societies that have the longest tradition in multicultural policies are settler societies. The question of how to deal with temporary migrants has only recently aroused their interest. In Europe, temporary migration programmes have a much longer history. In the period after WWII, a wide range of legal frameworks were set up to import temporary workers, who came to be known as guest workers. In the end, many of these ‘guests’ settled in Europe permanently. Their presence lay at the basis of European multicultural policies. However, when these policies were drafted, the former mobility of guest workers had been forgotten. This chapter will focus on this mobility of initially temporary workers, comparing the period of economic growth 1945-1974 with the years after the 1974 economic crisis. Further, it will look at the kind of policies that were developed towards guest workers in the era before multiculturalism. This way, it shows how their consideration as temporary residents had far-reaching consequences for the immigrants, their descendants and the receiving societies involved. The chapter will finish by suggesting a number of lessons from the past. If the mobility-gap between guest workers and present-day migrants is not as big as generally assumed, then the consequences of previous neglect should serve as a warning for future policy making.

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