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.

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

2012 ◽  
Vol 8 (2) ◽  
Author(s):  
Karin Nachbagauer ◽  
Peter Gruber ◽  
Johannes Gerstmayr
Keyword(s):  
Finite Element ◽  
Continuum Mechanics ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Geometrically Nonlinear ◽  
Finite Element Software ◽  
Rod Theory ◽  
Elastic Forces ◽  
Nonlinear Rod Theory ◽  
Shear Deformable

In the present paper, a three-dimensional shear deformable beam finite element is presented, which is based on the absolute nodal coordinate formulation (ANCF). The orientation of the beam’s cross section is parameterized by means of slope vectors. Both a structural mechanics based formulation of the elastic forces based on Reissner’s nonlinear rod theory, as well as a continuum mechanics based formulation for a St. Venant Kirchhoff material are presented in this paper. The performance of the proposed finite beam element is investigated by the analysis of several static and linearized dynamic problems. A comparison to results provided in the literature, to analytical solutions, and to the solution found by commercial finite element software shows high accuracy and high order of convergence, and therefore the present element has high potential for geometrically nonlinear problems.

Transient Response Analysis of Geometrically Nonlinear Laminated Composite Shell Structures

1996 ◽  
Author(s):  
Cho W. S. To ◽  
Bin Wang
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Composite Shell ◽  
Laminated Composite ◽  
Shell Structures ◽  
Response Analysis ◽  
Hybrid Strain ◽  
Drilling Degree Of Freedom ◽  
Shell Finite Element ◽  
Shear Deformable

Abstract The investigation reported in this paper is concerned with the prediction of geometrically large nonlinear responses of laminated composite shell structures under transient excitations by employing the hybrid strain based flat triangular laminated composite shell finite element presented here. Large deformation of finite strain and finite rotation are considered. The finite element has eighteen degrees-of-freedom which encompass the important drilling degree-of-freedom at every node. It is hinged on the first order shear deformable lamination theory. Various laminated composite shell structures have been studied and for brevity only two are presented here. It is concluded that the element proposed is very accurate and efficient. Shear locking has not appeared in the results obtained thus far. There is no zero energy mode detected in the problems studied. For nonlinear dynamic response computations, the full structural system has to be considered if accurate results are required.

Three-Dimensional Solid Brick Element Using Slopes in the Absolute Nodal Coordinate Formulation

2013 ◽  
Vol 9 (2) ◽  
Author(s):  
Alexander Olshevskiy ◽  
Oleg Dmitrochenko ◽  
Chang-Wan Kim
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Absolute Nodal Coordinate Formulation ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Test Problems ◽  
Absolute Nodal Coordinate ◽  
Highly Nonlinear ◽  
Brick Element ◽  
The Absolute

The present paper contributes to the field of flexible multibody systems dynamics. Two new solid finite elements employing the absolute nodal coordinate formulation are presented. In this formulation, the equations of motion contain a constant mass matrix and a vector of generalized gravity forces, but the vector of elastic forces is highly nonlinear. The proposed solid eight node brick element with 96 degrees of freedom uses translations of nodes and finite slopes as sets of nodal coordinates. The displacement field is interpolated using incomplete cubic polynomials providing the absence of shear locking effect. The use of finite slopes describes the deformed shape of the finite element more exactly and, therefore, minimizes the number of finite elements required for accurate simulations. Accuracy and convergence of the finite element is demonstrated in nonlinear test problems of statics and dynamics.

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.

Optimization Analysis for Radial Support by Finite Elements Method

2012 ◽  
Vol 466-467 ◽  
pp. 734-738
Author(s):  
Cheng Ming Li ◽  
Yi Fan Wang
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Optimal Solution ◽  
Support Point ◽  
Mirror Surface ◽  
Optimization Analysis ◽  
Primary Mirror ◽  
Finite Element Software ◽  
The Relationship ◽  
Surface Figure

Primary mirror’ surface figure is affected by supporting structure obviously. Especially for large-aperture telescope, the surface figure is significant because of primary mirror’ self-weight. For the requirement of the usage, it’s necessary to minimize the surface figure from self-weight by reasonable supporting scheme. The text optimized support point and force of radial support to minimize the surface figure by finite-element software. At the same time, it studied the relationship between support point and counterweight to reduce the weight of support structure. At last, it gave the optimal solution.

A New Rectangular Plate Element for Vibration Analysis of Laminated Composites

1998 ◽  
Vol 120 (1) ◽  
pp. 80-86 ◽  
Author(s):  
Guan-Liang Qian ◽  
Suong V. Hoa ◽  
Xinran Xiao
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Rectangular Plate ◽  
Degrees Of Freedom ◽  
Mass Matrix ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Element Model ◽  
Higher Order ◽  
Transverse Displacement

In this paper, a higher order rectangular plate bending element based on a Higher Order Shear Deformation Theory (HSDT) is developed. The element has 4 nodes and 20 degrees of freedom. The transverse displacement is interpolated by using an optimized interpolation function while the additional rotation degrees of freedom are approximated by linear Lagrange interpolation. The consistent element mass matrix is used. A damped element is introduced to the finite element model. The proposed FEM is used to calculate eigenfrequencies and modal damping of composite plates with various boundary conditions and different thicknesses. The results show that the present FEM gives excellent results when compared to other methods and experiment results, and is efficient and reliable for both thick and thin plates. The proposed finite element model does not lock in the thin plate situation and does not contain any spurious vibration mode, and converges rapidly. It will provide a good basis for the inverse analysis of vibration of a structure.

Finite Element Modeling of Dynamic Behavior of Some Basic Structural Members

1992 ◽  
Vol 114 (1) ◽  
pp. 3-9 ◽  
Author(s):  
R. C. Engels
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Finite Element Modeling ◽  
Mass Matrix ◽  
Matrix Approach ◽  
Structural Members ◽  
Shape Functions ◽  
Generalized Coordinates ◽  
Stiffness Matrices ◽  
Consistent Mass Matrix

A method is described to model the dynamics of finite elements. The assumed modes method is used to show how static shape functions approximate the element mass distribution. The deterioration of the modal content of a model can be linked to the neglect of interface restrained assumed modes. Restoration of a few of these modes leads to higher accuracy with fewer generalized coordinates compared to the standard consistent mass matrix approach. Also, no need exists for subdivision of basic elements such as rods and beams. The mass and stiffness matrices for several basic elements are derived and used in demonstration problems.

Dynamic Analysis of a Mobile Mechanical System with Deformable Elements

2012 ◽  
Vol 463-464 ◽  
pp. 1242-1245 ◽  
Author(s):  
Nicolae Dumitru ◽  
Raluca Malciu ◽  
Madalina Calbureanu ◽  
Sorin Dumitru ◽  
Gabriel Cătălin Marinescu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
System Modeling ◽  
Rigid Motion ◽  
Elastic Solid ◽  
Constant Matrix ◽  
Lagrange Formulation

The paper presents a method for studying mechanisms with deformable elements, based on overlapping the solid rigid motion over the elastic solid one, in order to identify the dynamic response of the system. Modeling was based on finite element method, so the cinematic elements were meshed in bar type finite elements and the degrees of freedom per node were settled according to the motion character (planar or spatial). A Lagrange formulation of the finite element was adopted for the deformable elements connected in multibody systems. In order to define the joints constraints, the conditions for compatibility between elements were defined using a Boolean constant matrix. Computer processed results were verified by an experimental model.

Rail Dynamic Vibration Absorber Design and Vibration Reduction Analysis

2011 ◽  
Vol 42 (11) ◽  
pp. 15-19
Author(s):  
Linya Liu ◽  
Bin Zhang ◽  
Jin Wang
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Vertical Displacement ◽  
Vibration Absorber ◽  
Vertical Acceleration ◽  
Dynamic Vibration Absorber ◽  
Finite Element Software ◽  
Dynamic Vibration ◽  
Damped System

The rail between two adjacent fasteners is regarded as the research object, and the rail is simplified as the main vibration system of undamped single degree of freedom, which supports the elastic components. The dynamic vibration absorber is simplified as a spring and damped system of 3-DOF(three degrees of freedom), to establish a mathematical model of rail dynamic vibration absorber. Through relevant theories, the parameter values of dynamic vibration absorber can be deduced when it achieves the best absorption effect. In accordance with the parameters, the scantlings of the structure of the dynamic vibration absorber can also be designed. Through the finite element software, the finite element model CRTS _ Ballastless Track system is established; with consideration of the value of irregularity, we load it variously. Analysis results showed that: compared to the rail and track where the dynamic vibration absorber is not installed, the maximum vertical displacement of the rail and track where a dynamic vibration absorber is installed was reduced by 65% and 67% respectively, the maximum vertical acceleration decreased by 75% and 70% and around, which reveals that the rail dynamic vibration absorber has a good vibration-reducing effect.

scholarly journals Implementation of a reaction-diffusion process in the Abaqus finite element software

2020 ◽  
Vol 21 (5) ◽  
pp. 508
Author(s):  
Elisabeth Vasikaran ◽  
Yann Charles ◽  
Pierre Gilormini
Keyword(s):  
Finite Element ◽  
Diffusion Process ◽  
Degrees Of Freedom ◽  
Reaction Diffusion ◽  
Finite Element Software ◽  
Complex Patterns ◽  
Complex Phenomena ◽  
Abaqus Software

To increase the Abaqus software capabilities, we propose a strategy to force the software to activate hidden degrees of freedom and to include extra coupled phenomena. As an illustration, we apply this approach to the simulation of a reaction diffusion process, the Gray-Scott model, which exhibits very complex patterns. Several setups have been considered and compared with available results to analyze the abilities of our strategy and to allow the inclusion of complex phenomena in Abaqus.

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