scholarly journals FE approximation for an hybrid Naghdi equations for shells with G 1 -midsurface

2018 ◽  
Vol Volume 22 - 2016-2018 ◽  
Author(s):  
Barbouche Refka
Keyword(s):  
Finite Elements ◽  
Degrees Of Freedom ◽  
Well Posedness ◽  
Numerical Tests ◽  
Nous Permet ◽  
Hybrid Formulation ◽  
Éléments Finis

The purpose of this present work is to consider an hybrid formulation of Naghdi’s shell with G1-midsurface of the model already introduced by H. Le Dret in [1] and prove its well-posedness. Here, the displacement and the rotation of the normal to the midsurface are respectively given in Cartesian and local covariant or contravariant basis. This new version enables us, in particular, to approximate by conforming finite elements the solution with less degrees of freedom. Numerical tests are given to illustrate the efficiency of our approach. Le but de ce travail est de considérer une formulation hybride de la coque de Naghdi avec une surface moyenne G 1 du modèle déjà introduit par H. Le Dret dans [1] et de prouver sa bonne posture. Ici, le déplacement et la rotation de la normale à la surface moyenne sont donnés respectivement en une base cartésienne et une base locale covariante ou contravariante. Cette nouvelle version nous permet, en particulier, d'approximer la solution par des éléments finis conformes avec moins degrés de liberté. Des tests numériques sont donnés pour illustrer l'efficacité de notre approche.

scholarly journals Régularisation de l'équation de Galbrun pour l'aéroacoustique en régime transitoire

2006 ◽  
Vol Volume 5, Special Issue TAM... ◽  
Author(s):  
Anne Sophie Bonnet-Bendhia ◽  
Kamel Berriri ◽  
Patrick Joly
Keyword(s):  
Numerical Analysis ◽  
Finite Elements ◽  
Variational Formulation ◽  
Acoustic Propagation ◽  
Well Posedness ◽  
Nous Proposons ◽  
Régime Transitoire ◽  
Nous Montrons ◽  
International Audience ◽  
Éléments Finis

International audience In this paper we are interested in the mathematical and numerical analysis of the timedependent Galbrun equation in a rigid duct. This equation modelizes the acoustic propagation in presence of flow. We prove the well-posedness of the problem for a subsonic uniform flow. Besides, we propose a regularized variational formulation of the problem suitable for an approximation by Lagrange finite elements. Dans ce papier, nous nous intéressons à l'analyse mathématique et à l'approximation numérique de l'équation de Galbrun en régime transitoire dans un conduit rigide. Cette équation modélise la propagation d'ondes acoustiques en présence d écoulement. Nous montrons pour un écoulement porteur uniforme subsonique que ce modèle a une solution unique. En outre, nous proposons une formulation variationnelle régularisée qui se prête à une approximation par éléments finis de Lagrange.

A Discretization Scheme for a Quasi-Hydrodynamic Semiconductor Model

1997 ◽  
Vol 07 (07) ◽  
pp. 935-955 ◽  
Author(s):  
Ansgar Jüngel ◽  
Paola Pietra
Keyword(s):  
Finite Elements ◽  
Mixed Finite Elements ◽  
Exponential Fitting ◽  
Discretization Scheme ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
Current Conservation ◽  
Numerical Tests ◽  
Finite Elements Methods ◽  
Degenerate Type

A discretization scheme based on exponential fitting mixed finite elements is developed for the quasi-hydrodynamic (or nonlinear drift–diffusion) model for semiconductors. The diffusion terms are nonlinear and of degenerate type. The presented two-dimensional scheme maintains the good features already shown by the mixed finite elements methods in the discretization of the standard isothermal drift–diffusion equations (mainly, current conservation and good approximation of sharp shapes). Moreover, it deals with the possible formation of vacuum sets. Several numerical tests show the robustness of the method and illustrate the most important novelties of the model.

SPECTRAL APPROXIMATION OF A SCHRÖDINGER TYPE EQUATION

1994 ◽  
Vol 04 (01) ◽  
pp. 49-88 ◽  
Author(s):  
CHRISTINE BERNARDI ◽  
MARIE-CLAUDE PELISSIER
Keyword(s):  
Numerical Analysis ◽  
Type Equation ◽  
Neumann Boundary ◽  
Rectangular Domain ◽  
The Other ◽  
Well Posedness ◽  
Discrete Problem ◽  
Spectral Approximation ◽  
Numerical Tests ◽  
Continuous Problem

This paper deals with a linear Schrödinger type equation in a rectangular domain with mixed Dirichlet-Neumann boundary conditions. The well-posedness of the continuous problem is proved, then a discrete problem is defined by combining a Legendre type spectral method in the first direction and a leap-frog scheme in the other one. The numerical analysis of the discretization is performed and error estimates are given. Numerical tests are presented.

Three-Dimensional Solutions for Rotor Blades Using High-Order Geometrical Nonlinear Beam Finite Elements

2019 ◽  
Vol 64 (3) ◽  
pp. 1-10
Author(s):  
Matteo Filippi ◽  
Alfonso Pagani ◽  
Erasmo Carrera
Keyword(s):  
Finite Elements ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
High Order ◽  
Rotor Blades ◽  
Constitutive Law ◽  
Displacement Fields ◽  
Cross Sectional ◽  
The Cross

This paper proposes a geometrically nonlinear three-dimensional formalism for the static and dynamic study of rotor blades. The structures are modeled using high-order beam finite elements whose kinematics are input parameters of the analysis. The displacement fields are written using two-dimensional Taylor- and Lagrange-like expansions of the cross-sectional coordinates. As far as the Taylor-like polynomials are concerned, the linear case is similar to the first-order shear deformation theory, whereas the higher-order expansions include additional contributions that describe the warping of the cross section. The Lagrange-type kinematics instead utilizes the displacements of certain physical points as degrees of freedom. The inherent three-dimensional nature of the Carrera unified formulation enables one to include all Green–Lagrange strain components as well as all coupling effects due to the geometrical features and the three-dimensional constitutive law. A number of test cases are considered to compare the current solutions with experimental and theoretical results reported in terms of large deflections/rotations and frequencies related to small amplitude vibrations.

Structural and Continuum Mechanics Approaches for a 3D Shear Deformable ANCF Beam Finite Element: Application to Buckling and Nonlinear Dynamic Examples

2013 ◽  
Vol 9 (1) ◽  
Author(s):  
Karin Nachbagauer ◽  
Johannes Gerstmayr
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Continuum Mechanics ◽  
Degrees Of Freedom ◽  
Mass Matrix ◽  
Finite Element Software ◽  
High Order Convergence ◽  
Dynamics Problems ◽  
Transverse Slope ◽  
Shear Deformable

For the modeling of large deformations in multibody dynamics problems, the absolute nodal coordinate formulation (ANCF) is advantageous since in general, the ANCF leads to a constant mass matrix. The proposed ANCF beam finite elements in this approach use the transverse slope vectors for the parameterization of the orientation of the cross section and do not employ an axial nodal slope vector. The geometric description, the degrees of freedom, and a continuum-mechanics-based and a structural-mechanics-based formulation for the elastic forces of the beam finite elements, as well as their usage in several static problems, have been presented in a previous work. A comparison to results provided in the literature to analytical solution and to the solution found by commercial finite element software shows accuracy and high order convergence in statics. The main subject of the present paper is to show the usability of the beam finite elements in dynamic and buckling applications.

New mixed finite elements for the discretization of piezoelectric structures or macro-fiber composites

2018 ◽  
Vol 29 (16) ◽  
pp. 3266-3283 ◽  
Author(s):  
Astrid S Pechstein ◽  
Martin Meindlhumer ◽  
Alexander Humer
Keyword(s):  
Finite Elements ◽  
Normal Stress ◽  
Degrees Of Freedom ◽  
Piezoelectric Materials ◽  
Normal Component ◽  
Mixed Finite Elements ◽  
Fiber Composites ◽  
Tangential Component ◽  
Tangential Displacement ◽  
Thin Elements

We propose a new three-dimensional formulation based on the mixed tangential-displacement normal-normal-stress method for elasticity. In elastic tangential-displacement normal-normal-stress elements, the tangential component of the displacement field and the normal component of the stress vector are degrees of freedom and continuous across inter-element interfaces. Tangential-displacement normal-normal-stress finite elements have been shown to be locking-free with respect to shear locking in thin elements, which makes them suitable for the discretization of laminates or macro-fiber composites. In the current paper, we extend the formulation to piezoelectric materials by adding the electric potential as degree of freedom.

The Application of Harmonic Finite Elements in the Seismic Response Spectrum Analysis of a Skirt Supported Vessel

2010 ◽  
Author(s):  
Bikramjit Singh Antaal ◽  
Yogeshwar Hari ◽  
Dennis K. Williams
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Seismic Response ◽  
Spectrum Analysis ◽  
Degrees Of Freedom ◽  
Response Spectrum ◽  
Response Spectrum Analysis ◽  
Element Analysis ◽  
Structure Interaction ◽  
Input Response

This paper describes the finite element considerations employed in a seismic response spectrum analysis of a skirt supported, liquid containing pressure vessel. Like many axisymmetric cylindrical vessels, the gross seismic response to an input response spectrum can be categorized by a simplified lump mass model that includes both the mass of the vessel proper in combination with the associated mass of multiple fluid levels. This simplified response may be utilized to determine the initial sizing of the supporting configuration, such as a skirt, but lacks the ability to properly address the fluid-structure interaction that creates sloshing loads on the vessel walls. The most obvious method to address the fluid-structure interaction when considering the finite element method is to build a three-dimensional model of the vessel proper, including, but not limited to the shell courses, the top and bottom heads (for a vertical vessel), and the support skirt. The inclusion of the fluid effects may now be incorporated with a “contained fluid” finite element, however, for vessels of any significant volume, the number of finite elements can easily exceed 100,000 and the number of degrees of freedom can sore from as few as 300,000 to as many as 500,000 or more. While these types of finite element analysis problems can be solved with today’s computer hardware and software, it is not desirable in any analysis to have that volume of information that has to be reviewed and approved in a highly regulated nuclear QA environment (if at all possible). With these items in mind, the methodology described in this paper seeks to minimize the number of degrees of freedom associated with a response spectrum analysis of a liquid filled, skirt supported vertical pressure vessel. The input response spectra are almost always provided in Cartesian coordinates, while many, if not most liquid containing pressure vessels are almost always axisymmetric in geometry without having benefit of being subjected to an axisymmetric load (acceleration in this case) due to the specified seismic event. The use of harmonic finite elements for both the vessel structure and the contained fluid medium permit the efficiencies associated with an axisymmetric geometry to be leveraged when the seismic response spectrum is formulated in terms of a Fourier series and combined to regain the effects of the two orthogonal, horizontally applied accelerations as a function of frequency. The end result as discussed and shown in this paper is a finite element model that permits a dense mesh of both the fluid and the structure, while economizing on the number of simultaneous equations required to be solved by the chosen finite element analysis.

A CRITICAL EVALUATION OF VARIOUS NONLINEAR BEAM FINITE ELEMENTS

2012 ◽  
Vol 09 (04) ◽  
pp. 1250045
Author(s):  
A. LAULUSA ◽  
J. N. REDDY
Keyword(s):  
Finite Elements ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Critical Evaluation ◽  
Quadrature Rules ◽  
Nonlinear Beam ◽  
Lagrange Polynomials ◽  
Reduced Integration ◽  
Uniform Interpolation

The characteristics of interdependent interpolation and mixed interpolation nonlinear beam finite elements are investigated in comparison with the equal-order interpolation element with uniform reduced integration. The stiffness matrix of the 3-noded and 4-noded equal order interpolation elements is identical to that of the 2-noded interdependent interpolation element if the internal nodal degrees-of-freedom are eliminated. The extension of the latter to include nonlinear kinematics by approximating the extensional displacement and the twist rotation with quadratic and cubic Lagrange polynomials yields unsatisfactory results. The 2-noded, 3-noded, and 4-noded mixed interpolation elements using one-, two-, and three-point quadrature rules, respectively, are shown to be equivalent to the corresponding uniform interpolation elements employing the same quadrature rules. The equivalence is established in the framework of nonlinear kinematics and anisotropic couplings.

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.

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