On the Continuous Coupling of Finite Elements with Holomorphic Basis Functions

2013 ◽  
pp. 167-180 ◽  
Author(s):  
Klaus Gürlebeck ◽  
Dmitrii Legatiuk
Keyword(s):  
Finite Elements ◽  
Basis Functions

scholarly journals Polyhedral Finite Elements Using Harmonic Basis Functions

2008 ◽  
Vol 27 (5) ◽  
pp. 1521-1529 ◽  
Author(s):  
Sebastian Martin ◽  
Peter Kaufmann ◽  
Mario Botsch ◽  
Martin Wicke ◽  
Markus Gross
Keyword(s):  
Finite Elements ◽  
Basis Functions

Layer-adapted methods for a singularly perturbed singular problem

2011 ◽  
Vol 11 (2) ◽  
pp. 192-205
Author(s):  
Christian Grossmann ◽  
Lars Ludwig ◽  
Hans-Görg Roos
Keyword(s):  
Boundary Layer ◽  
Finite Elements ◽  
Boundary Value Problem ◽  
Bessel Functions ◽  
Basis Functions ◽  
Singularly Perturbed ◽  
Singular Problem ◽  
Dimensional Problem ◽  
Modified Bessel Functions ◽  
One Dimensional

Abstract In the present paper we analyze linear finite elements on a layer adapted mesh for a boundary value problem characterized by the overlapping of a boundary layer with a singularity. Moreover, we compare this approach numerically with the use of adapted basis functions, in our case modified Bessel functions. It turns out that as well adapted meshes as adapted basis functions are suitable where for our one-dimensional problem adapted bases work slightly better.

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.

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.

Timoshenko beam finite elements using trigonometric basis functions

AIAA Journal ◽  
1988 ◽  
Vol 26 (11) ◽  
pp. 1378-1386 ◽  
Author(s):  
G. R. Heppler ◽  
J. S. Hansen
Keyword(s):  
Finite Elements ◽  
Timoshenko Beam ◽  
Basis Functions ◽  
Trigonometric Basis Functions

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.

On trigonometric basis functions for C1 curved beam finite elements

1992 ◽  
Vol 45 (2) ◽  
pp. 405-413 ◽  
Author(s):  
J.E.F. Guimaraes ◽  
Heppler G.R
Keyword(s):  
Finite Elements ◽  
Basis Functions ◽  
Curved Beam ◽  
Trigonometric Basis Functions
Sign in / Sign up

Export Citation Format

Share Document