Static and dynamic convergence studies of a four-noded membrane finite element with rotational degrees of freedom based on displacement superposition

2008 ◽  
Vol 26 (10) ◽  
pp. 1263-1275 ◽  
Author(s):  
Ülkü H. Çalık Karaköse ◽  
Harm Askes
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Rotational Degrees Of Freedom

Beam Element Structural Dynamics Modification Using Experimental Modal Rotational Data

1995 ◽  
Vol 117 (3A) ◽  
pp. 265-271 ◽  
Author(s):  
John A. Cafeo ◽  
Martin W. Trethewey ◽  
H. Joseph Sommer
Keyword(s):  
Finite Element ◽  
Cantilever Beam ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Structural Dynamic ◽  
Modal Data ◽  
Structural Dynamic Modification ◽  
Dynamic Modification ◽  
Rotational Degrees Of Freedom ◽  
Fixed Beam

Structural dynamic modification (SDM) of a fixed-free (cantilever) beam to convert it into a fixed-fixed beam with experimental modal data is presented. The SDM focuses on incorporating experimental rotational degrees-of-freedom (DOF) measured with a novel laser measurement technique. A cantilever beam is tested to develop the experimental modal database including rotational degrees of freedom. A modal database from a finite-element model also is developed for comparison. A structural dynamic modification, with both databases, is performed using a Bernoulli-Euler beam to ground the free end of the cantilever beam. The hardware is then modified and a second experimental modal analysis of the resulting fixed-fixed beam performed. A finite-element model of the fixed-fixed beam also was created. Comparison of results from these four tests are used to assess the effectiveness of SDM using experimental modal rotational data. The evaluation shows that provided high quality experimental rotational modal data can be acquired, SDM work with beam elements can be effective in yielding accurate results.

scholarly journals Consistent coupling of positions and rotations for embedding 1D Cosserat beams into 3D solid volumes

2021 ◽  
Author(s):  
Ivo Steinbrecher ◽  
Alexander Popp ◽  
Christoph Meier
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Lagrange Multiplier ◽  
Degrees Of Freedom ◽  
Element Discretization ◽  
Geometrically Exact Beam ◽  
Coupling Constraints ◽  
Rotational Degrees Of Freedom ◽  
3D Solid ◽  
Cosserat Continua

AbstractThe present article proposes a mortar-type finite element formulation for consistently embedding curved, slender beams into 3D solid volumes. Following the fundamental kinematic assumption of undeformable cross-section s, the beams are identified as 1D Cosserat continua with pointwise six (translational and rotational) degrees of freedom describing the cross-section (centroid) position and orientation. A consistent 1D-3D coupling scheme for this problem type is proposed, requiring to enforce both positional and rotational constraints. Since Boltzmann continua exhibit no inherent rotational degrees of freedom, suitable definitions of orthonormal triads are investigated that are representative for the orientation of material directions within the 3D solid. While the rotation tensor defined by the polar decomposition of the deformation gradient appears as a natural choice and will even be demonstrated to represent these material directions in a $$L_2$$ L 2 -optimal manner, several alternative triad definitions are investigated. Such alternatives potentially allow for a more efficient numerical evaluation. Moreover, objective (i.e. frame-invariant) rotational coupling constraints between beam and solid orientations are formulated and enforced in a variationally consistent manner based on either a penalty potential or a Lagrange multiplier potential. Eventually, finite element discretization of the solid domain, the embedded beams, which are modeled on basis of the geometrically exact beam theory, and the Lagrange multiplier field associated with the coupling constraints results in an embedded mortar-type formulation for rotational and translational constraint enforcement denoted as full beam-to-solid volume coupling (BTS-FULL) scheme. Based on elementary numerical test cases, it is demonstrated that a consistent spatial convergence behavior can be achieved and potential locking effects can be avoided, if the proposed BTS-FULL scheme is combined with a suitable solid triad definition. Eventually, real-life engineering applications are considered to illustrate the importance of consistently coupling both translational and rotational degrees of freedom as well as the upscaling potential of the proposed formulation. This allows the investigation of complex mechanical systems such as fiber-reinforced composite materials, containing a large number of curved, slender fibers with arbitrary orientation embedded in a matrix material.

A Four-Node Tetrahedral Finite Element Based on Space Fiber Rotation Concept

2019 ◽  
Vol 11 (1) ◽  
pp. 67-78
Author(s):  
Kamel Meftah ◽  
Lakhdar Sedira
Keyword(s):  
Finite Element ◽  
Strain Field ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Field Tensor ◽  
Tetrahedral Element ◽  
Numerical Studies ◽  
Rotational Degrees Of Freedom ◽  
Tensor Approximation

Abstract The paper presents a four-node tetrahedral solid finite element SFR4 with rotational degrees of freedom (DOFs) based on the Space Fiber Rotation (SFR) concept for modeling three-dimensional solid structures. This SFR concept is based on the idea that a 3D virtual fiber, after a spatial rotation, introduces an enhancement of the strain field tensor approximation. Full numerical integration is used to evaluate the element stiffness matrix. To demonstrate the efficiency and accuracy of the developed four-node tetrahedron solid element and to compare its performance with the classical four-node tetrahedral element, extensive numerical studies are presented.

Application of Rotational Measurements in Stiffness Reconstruction of Beams and Frames

2009 ◽  
Vol 413-414 ◽  
pp. 189-194
Author(s):  
Zbigniew Zembaty ◽  
Seweryn Kokot
Keyword(s):  
Inverse Problem ◽  
Finite Element ◽  
Damage Detection ◽  
Minimization Problem ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Frame Structure ◽  
Reconstruction Method ◽  
Harmonic Vibrations ◽  
Rotational Degrees Of Freedom

A stiffness reconstruction method is tested when rotational degrees of freedom are added to the dynamic model of the structure. The inverse problem is formulated as a minimization problem in terms of harmonic vibrations of the structure and its finite element model. An example of frame structure is analyzed by numerical simulations. The results of these numerical analyses show that the damage detection appeared to be much more effective when the angular amplitudes of harmonic vibrations are acquired. This makes very good prospects for the future applications of angular sensors in damage detection of structures.

A Generalized Conforming Quadrilateral Membrane Element Less Sensitive to Geometric Distortion

1998 ◽  
Vol 1 (3) ◽  
pp. 185-191 ◽  
Author(s):  
Yin Xu ◽  
Zhifei Long ◽  
Yuqiu Long
Keyword(s):  
Finite Element ◽  
High Precision ◽  
Degrees Of Freedom ◽  
Geometric Distortion ◽  
Finite Element Models ◽  
Membrane Element ◽  
Mesh Distortion ◽  
Long Period ◽  
Rotational Degrees Of Freedom ◽  
General Method

Many finite element models have very acceptable performance when the computing meshes are regular. However, as the level of mesh distortion is increasing, the accuracy of the solutions deteriorates rapidly. Therefore, how to formulate an element that is less sensitive to geometric distortion is an important question for study for a long period. In this paper, a simple quadrilateral membrane element with rotational degrees-of-freedom is developed with the approach of the generalized conforming element proposed by Long Yuqiu (1989). The new element exhibits excellent feature, that is, less sensitive to geometric distortion. A general method to formulate high precision finite element less sensitive to geometric distortion is provided in this paper.

The Prediction Method on Warpage of Injection Molded Parts

2011 ◽  
Vol 317-319 ◽  
pp. 211-214
Author(s):  
Tong Chen Chang ◽  
Hong Yu Zhu ◽  
Hai Hong Wu
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Prediction Method ◽  
Element Model ◽  
Thermal Shrinkage ◽  
Injection Molding Process ◽  
Molding Process ◽  
Molded Parts ◽  
Rotational Degrees Of Freedom

Warpage is a common defect resulted from uneven thermal shrinkage during injection molding process. In this paper, the authors investigated finite element method to predict the warpage of injection moldings with thin shell theory. In order to improve calculating accuracy, discrete Kirchhoff element combined membrane element with rotational degrees of freedom was used to build finite element model. The results predicted with this model were compared with experimental data. The results showed that this finite element model was effective to increase the prediction accuracy of the warpage because of bring transfer matrices to improve the element accuracy.

On the Use of Quantum Thermal Bath in Unimolecular Fragmentation Simulations

2019 ◽  
Author(s):  
Riccardo Spezia ◽  
Hichem Dammak
Keyword(s):  
Degrees Of Freedom ◽  
Molecular Simulations ◽  
Zero Point ◽  
Thermal Bath ◽  
Unimolecular Dissociation ◽  
Point Energy ◽  
Rotational Degrees Of Freedom ◽  
The Difference ◽  
Nuclear Effects

<div> <div> <div> <p>In the present work we have investigated the possibility of using the Quantum Thermal Bath (QTB) method in molecular simulations of unimolecular dissociation processes. Notably, QTB is aimed in introducing quantum nuclear effects with a com- putational time which is basically the same as in newtonian simulations. At this end we have considered the model fragmentation of CH4 for which an analytical function is present in the literature. Moreover, based on the same model a microcanonical algorithm which monitor zero-point energy of products, and eventually modifies tra- jectories, was recently proposed. We have thus compared classical and quantum rate constant with these different models. QTB seems to correctly reproduce some quantum features, in particular the difference between classical and quantum activation energies, making it a promising method to study unimolecular fragmentation of much complex systems with molecular simulations. The role of QTB thermostat on rotational degrees of freedom is also analyzed and discussed. </p> </div> </div> </div>

The Influence of Loading Position in A Priori High Stress Detection using Mode Superposition

2020 ◽  
Vol 1 (1) ◽  
pp. 93-102
Author(s):  
Carsten Strzalka ◽  
◽  
Manfred Zehn ◽  
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
A Priori ◽  
High Stress ◽  
Von Mises Stress ◽  
Detailed Knowledge ◽  
Variable Loading ◽  
Numerical Effort ◽  
Von Mises

For the analysis of structural components, the finite element method (FEM) has become the most widely applied tool for numerical stress- and subsequent durability analyses. In industrial application advanced FE-models result in high numbers of degrees of freedom, making dynamic analyses time-consuming and expensive. As detailed finite element models are necessary for accurate stress results, the resulting data and connected numerical effort from dynamic stress analysis can be high. For the reduction of that effort, sophisticated methods have been developed to limit numerical calculations and processing of data to only small fractions of the global model. Therefore, detailed knowledge of the position of a component’s highly stressed areas is of great advantage for any present or subsequent analysis steps. In this paper an efficient method for the a priori detection of highly stressed areas of force-excited components is presented, based on modal stress superposition. As the component’s dynamic response and corresponding stress is always a function of its excitation, special attention is paid to the influence of the loading position. Based on the frequency domain solution of the modally decoupled equations of motion, a coefficient for a priori weighted superposition of modal von Mises stress fields is developed and validated on a simply supported cantilever beam structure with variable loading positions. The proposed approach is then applied to a simplified industrial model of a twist beam rear axle.

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