Correction of node mapping distortions using universal serendipity elements in dynamical problems

2011 ◽  
Vol 40 (2) ◽  
pp. 245-256
Author(s):  
Semih Kucukarslan ◽  
Ali Demir
Keyword(s):  
Serendipity Elements

NURBS-based geometries: A mapping approach for virtual serendipity elements

2021 ◽  
Vol 378 ◽  
pp. 113732
Author(s):  
Peter Wriggers ◽  
Blaž Hudobivnik ◽  
Fadi Aldakheel
Keyword(s):  
Mapping Approach ◽  
Serendipity Elements

AN ALGORITHM FOR GENERATION OF SHAPE FUNCTIONS IN SERENDIPITY ELEMENTS

1991 ◽  
Vol 8 (1) ◽  
pp. 19-31 ◽  
Author(s):  
G. ZAVARISE ◽  
R. VITALIANI ◽  
B. SCHREFLER
Keyword(s):  
Shape Functions ◽  
Serendipity Elements

FINITE ELEMENT MODELING OF ACOUSTICS USING HIGHER ORDER ELEMENTS PART I: NONUNIFORM DUCT PROPAGATION

2004 ◽  
Vol 12 (03) ◽  
pp. 397-429 ◽  
Author(s):  
EIVIND LISTERUD ◽  
WALTER EVERSMAN
Keyword(s):  
Finite Element ◽  
Acoustic Pressure ◽  
Preliminary Assessment ◽  
Numerical Accuracy ◽  
Error Norm ◽  
One Dimensional ◽  
Wave Approximation ◽  
Potential Formulation ◽  
Serendipity Elements ◽  
Analytical Expressions

Cubic serendipity elements have been implemented into a nonuniform duct model of acoustic propagation in a moving medium. This model uses a convective potential formulation derived from the inviscid linearized mass and momentum equations. The model requires post-processing to calculate acoustic pressure. These elements outperform the quadratic serendipity elements in terms of computational efficiency based on visual observations and error norm analysis of acoustic pressure. CPU time reduction of up to 40% has been observed without sacrificing accuracy. Any penalty in numerical accuracy incurred by using serendipity elements rather than Lagrangian elements is far outweighed by the gains in dimensionality. The computational gains for calculation of acoustic potential are considerably less. Analytical expressions for the modal and convective effects on the propagating wavelength have been formulated and compared to numerical results. Preliminary assessment of alternative finite element approaches to model the convective potential formulation has been conducted. Stabilization and wave approximation methods have been implemented to solve simple one-dimensional problems.

THE USE OF ENRICHED HEXAHEDRAL ELEMENTS WITH BUBBLE FUNCTIONS FOR FINITE ELEMENT ANALYSIS

2006 ◽  
Vol 30 (4) ◽  
pp. 495-509
Author(s):  
Shi-Pin Ho ◽  
Yen-Liang Yeh
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Three Dimensional ◽  
Computation Time ◽  
System Of Equations ◽  
Error Norm ◽  
Element Analysis ◽  
Hexahedral Elements ◽  
Static Condensation ◽  
Serendipity Elements

In this paper, the concept that adds the interior nodes of the Lagrange elements to the serendipity elements is described and a family of enriched elements is presented to improve the accuracy of finite element analysis. By the use of the static condensation technique at the element level, the extra computation time in using these elements can be ignored. Three-dimensional elastic problems are used as examples in this paper. The numerical results show that these enriched elements are more accurate than the traditional serendipity elements. The convergence rate of the enriched elements is the same as the traditional serendipity elements. In the numerical example, the error norm of the first order enriched elements can be reduced when compared with the use of the traditional serendipity element, but the computation time is increased a little. The use of enriched second and third order hexahedral elements does not only improve accuracy, but also saves the computation time for solving the system of equations, when the precondition conjugate gradient method is used to solve the system of equations. The saving of computation time is due to the decrease in the number of iteration for the iteration method.

On the Construction of Diagonal Mass Matrices for Serendipity Elements

PAMM ◽  
2018 ◽  
Vol 18 (1) ◽  
Author(s):  
Sascha Duczek ◽  
Hauke Gravenkamp
Keyword(s):  
Mass Matrices ◽  
Serendipity Elements

FINITE ELEMENT MODELING OF ACOUSTICS USING HIGHER ORDER ELEMENTS PART II: TURBOFAN ACOUSTIC RADIATION

2004 ◽  
Vol 12 (03) ◽  
pp. 431-446 ◽  
Author(s):  
EIVIND LISTERUD ◽  
WALTER EVERSMAN
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Acoustic Pressure ◽  
Acoustic Radiation ◽  
Near Field ◽  
Element Formulation ◽  
Computational Accuracy ◽  
Element Modeling ◽  
Quadratic Performance ◽  
Serendipity Elements

A study is made of computational accuracy and efficiency for finite element modeling of acoustic radiation in a nonuniform moving medium. For a given level of accuracy for acoustic pressure, cubic serendipity elements are shown to require a less dense mesh than quadratic elements. These elements have been applied to the near field of inlet and aft acoustic radiation models for a turbofan engine and they yield considerable reduction in the dimensionality of the problem without sacrificing accuracy. The results show that for computation of acoustic pressure the cubic element formulation model is superior to the quadratic. Performance gains in computation of acoustic potential are not as significant. In the external radiated field, improved convergence using cubic serendipity elements is shown by comparison of contours of constant pressure magnitude.

scholarly journals Analysis of Distortion Parameters of Eight node Serendipity Element on the Elements Performance

2013 ◽  
pp. 226-233
Author(s):  
Vishal Jagota ◽  
A. P. S. Sethi
Keyword(s):  
Grid Generation ◽  
Computer Programs ◽  
Complex Shapes ◽  
Serendipity Elements ◽  
Automatic Mesh ◽  
Distortion Parameters

Often the result produced using FEM technique on the distorted shaped element gives poor result. Moreover if the results are poor then the design will fail. Eight noded serendipity elements is the most widely used element in 2-D analysis of structures. But despite its benefits it remains distortion sensitive. In the majority of computer programs, automatic mess generation is an integral part of the program. For complex shapes, the automatic grid generation will result in distorted quadrilateral shapes. Thus the solution obtained by using these meshes will produce erroneous results so it becomes necessary to incorporate the distortion measures in to these automatic mesh generations to limit the errors. Here in this paper distortion parameters are defined in terms of the coefficient of the element’s shape polynomials and are tested for a range of distortion.

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