A Comparison of a Penalty Finite Element Model with the Stream Function-Vorticity Model of Natural Convection in Enclosures

1980 ◽  
Vol 102 (4) ◽  
pp. 659-666 ◽  
Author(s):  
J. N. Reddy ◽  
Akio Satake
Keyword(s):  
Finite Element ◽  
Natural Convection ◽  
Finite Element Model ◽  
Stream Function ◽  
Penalty Function ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Flow And Heat Transfer ◽  
Natural Connection ◽  
Function Formulation

This paper is concerned with a comparative study of the stream function-vorticity formulation and penalty function formulation of the two-dimensional equations governing natural connection in enclosures. The penalty function formulation presented herein is the only correct way of describing it for the problem at hand. The penalty-finite element model developed herein is novel with this work, and involves two velocities, temperature, and stream function as degrees of freedom at each node. The model includes, as a special case, the penalty-finite element model of natural convection in enclosures reported in the literature. Numerical results obtained using the two formulations are compared for several geometries, and boundary conditions, and the effects of Rayleigh number and Prandtl number on the flow and heat transfer are studied.

Finite Element Model of the Human Knee Joint to Study Tibio-Femoral Contact Mechanics

2000 ◽  
Author(s):  
Tammy Haut Donahue ◽  
Maury L. Hull ◽  
Mark M. Rashid ◽  
Christopher R. Jacobs
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Soft Tissues ◽  
Element Model ◽  
Human Knee ◽  
Human Knee Joint ◽  
Solid Models ◽  
Flexion Extension ◽  
A New Technique

Abstract A finite element model of the tibio-femoral joint in the human knee was created using a new technique for developing accurate solid models of soft tissues (i.e. cartilage and menisci). The model was used to demonstrate that constraining rotational degrees of freedom other than flexion/extension when the joint is loaded in compression markedly affects the load distribution between the medial and lateral sides of the joint. The model also was used to validate the assumption that the bones can be treated as rigid.

Modeling of fast pre-joining processes optimization for skin-stringer panels

2014 ◽  
Vol 34 (4) ◽  
pp. 323-332 ◽  
Author(s):  
Gang Liu ◽  
Wei Tang ◽  
Ying-Lin Ke ◽  
Qing-Liang Chen ◽  
Yunbo Bi
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Traditional Approach ◽  
Element Model ◽  
Optimal Number ◽  
Neighborhood Search ◽  
Adaptive Genetic Algorithm ◽  
Time Saving ◽  
Content Type

Purpose – The purpose of this paper is to propose a new model for optimizing pre-joining processes quickly and accurately, guiding workers to standardized operations. For the automatic riveting in panel assemblies, the traditional approach of determination of pre-joining processes entirely rests on the experience of workers, which leads to the improper number, location and sequence of pre-joining, the low quality stability and the high repair rate in most cases. Design/methodology/approach – The clearances computation with the complete finite element model for every process combination is time-consuming. Therefore a fast pre-joining processes optimization model (FPPOM) is proposed. This model treats both the measured initial clearances and the stiffness matrices of key points of panels as an input; considers the permissive clearances as an evaluation criterion; regards the optimal number, location and sequence as an objective; and takes the neighborhood-search-based adaptive genetic algorithm as a solution. Findings – A comparison between the FPPOM and complete finite element model with clearances (CFEMC) was made in practice. Further, the results indicate that running the FPPOM is time-saving by >90 per cent compared with the CFEMC. Practical implications – This paper provides practical insights into realizing the pre-joining processes optimization quickly. Originality/value – This paper is the first to propose the FPPOM, which could simplify the processes, reduce the degrees of freedom of nodes and conduct the manufacturers to standardized manipulations.

Verification of Predicted Knee Replacement Kinematics During Simulated Gait in the Kansas Knee Simulator

2010 ◽  
Vol 132 (8) ◽  
Author(s):  
Jason P. Halloran ◽  
Chadd W. Clary ◽  
Lorin P. Maletsky ◽  
Mark Taylor ◽  
Anthony J. Petrella ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Knee Replacement ◽  
Degrees Of Freedom ◽  
Computational Models ◽  
Evaluation Process ◽  
Element Model ◽  
Explicit Finite Element ◽  
Knee Simulator ◽  
Flexion Extension

Evaluating total knee replacement kinematics and contact pressure distributions is an important element of preclinical assessment of implant designs. Although physical testing is essential in the evaluation process, validated computational models can augment these experiments and efficiently evaluate perturbations of the design or surgical variables. The objective of the present study was to perform an initial kinematic verification of a dynamic finite element model of the Kansas knee simulator by comparing predicted tibio- and patellofemoral kinematics with experimental measurements during force-controlled gait simulation. A current semiconstrained, cruciate-retaining, fixed-bearing implant mounted in aluminum fixtures was utilized. An explicit finite element model of the simulator was developed from measured physical properties of the machine, and loading conditions were created from the measured experimental feedback data. The explicit finite element model allows both rigid body and fully deformable solutions to be chosen based on the application of interest. Six degrees-of-freedom kinematics were compared for both tibio- and patellofemoral joints during gait loading, with an average root mean square (rms) translational error of 1.1 mm and rotational rms error of 1.3 deg. Model sensitivity to interface friction and damping present in the experimental joints was also evaluated and served as a secondary goal of this paper. Modifying the metal-polyethylene coefficient of friction from 0.1 to 0.01 varied the patellar flexion-extension and tibiofemoral anterior-posterior predictions by 7 deg and 2 mm, respectively, while other kinematic outputs were largely insensitive.

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.

A Complaint Mechanism with Freedom Degrees of One Movement and Two Rotations

2014 ◽  
Vol 551 ◽  
pp. 444-447
Author(s):  
Sheng Lin ◽  
Xi Kong ◽  
Chun Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Element Model ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Compliant Mechanism ◽  
Element Model ◽  
Theory Analysis ◽  
The Finite Element Model

Based on the method of Freedom and Constraint Topology (FACT), a compliant mechanism with 3 degrees of freedom is designed. The 3 DOF are one movement and two rotations, which belongs to Case 3, Type 2. The whole stiffness matrix of the compliant mechanism is obtained. The finite element model is established for statics analysis. The results of theory analysis and finite element method are closed.

Dynamic Analysis of Flexible Structures Using Component Mode Synthesis

1989 ◽  
Vol 56 (4) ◽  
pp. 874-880 ◽  
Author(s):  
M. De Smet ◽  
C. Liefooghe ◽  
P. Sas ◽  
R. Snoeys
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Flexible Structures ◽  
Element Model ◽  
Component Mode Synthesis ◽  
Mode Shapes ◽  
Flexible Robot ◽  
Preliminary Calculation ◽  
Resonance Frequencies

In this paper a dynamic model of a flexible robot is built out of a finite element model of each of its links. The number of degrees-of-freedom of these models is strongly reduced by applying the Component Mode Synthesis technique which involves the preliminary calculation of a limited number of mode shapes of the separate links. As can be seen from examples, the type of boundary conditions thereby imposed in the nodes in which one link is connected to the others, strongly determines the accuracy of the calculated resonance frequencies of the robot. The method is applied to an industrial manipulator. The reduced finite element model of the robot is changed in order to match the numerically and experimentally (modal analysis) determined resonance data. Further, the influence of the position of the robot on its resonance frequencies is studied using the optimized numerical model.

scholarly journals Finite element model updating using Lagrange interpolation

2019 ◽  
Vol 23 (1) ◽  
pp. 228-232
Author(s):  
F. Asma
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Model Updating ◽  
Element Model ◽  
Truss Structures ◽  
Finite Element Model Updating ◽  
Initial Model ◽  
Information Matrices ◽  
Matrix Interpolation

Abstract In this paper, an iterative finite element model updating method in structural dynamics is proposed. This uses information matrices and element connectivity matrices to reconstruct the corrected model by reproducing the frequency response at measured degrees of freedom. Indicators have been proposed to quantify the mismodelling errors based on a development in Lagrange matrix interpolation. When applied on simulated truss structures, the model gives satisfactory results by detecting and quantifying the defaults of the initial model.

Identification of Free-Free Modes From Constrained Vibration Data for Flexible Multibody Models

1999 ◽  
Author(s):  
Tong Y. Yi ◽  
Parviz E. Nikravesh
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Multibody System ◽  
Element Model ◽  
Flexible Body ◽  
Fe Model ◽  
Modal Data ◽  
Vibration Data

Abstract This paper presents a method for identifying the free-free modes of a structure by utilizing the vibration data of the same structure with boundary conditions. In modal formulations for flexible body dynamics, modal data are primary known quantities that are obtained either experimentally or analytically. The vibration measurements may be obtained for a flexible body that is constrained differently than its boundary conditions in a multibody system. For a flexible body model in a multibody system, depending upon the formulation used, we may need a set of free-free modal data or a set of constrained modal data. If a finite element model of the flexible body is available, its vibration data can be obtained analytically under any desired boundary conditions. However, if a finite element model is not available, the vibration data may be determined experimentally. Since experimentally measured vibration data are obtained for a flexible body supported by some form of boundary conditions, we may need to determine its free-free vibration data. The aim of this study is to extract, based on experimentally obtained vibration data, the necessary free-free frequencies and the associated modes for flexible bodies to be used in multibody formulations. The available vibration data may be obtained for a structure supported either by springs or by fixed boundary conditions. Furthermore, the available modes may be either a complete set; i.e., as many modes as the number of degrees of freedom of the associated FE model is available, or it can be an incomplete set.

Control-Oriented Order Reduction of Finite Element Model

1993 ◽  
Vol 115 (4) ◽  
pp. 708-711 ◽  
Author(s):  
K. Harold Yae ◽  
Daniel J. Inman
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Control Design ◽  
Element Model ◽  
Reduced Model ◽  
State Variables ◽  
Dynamics Modeling ◽  
Element Analysis

In the dynamics modeling of a structure, finite element analysis employs reduction techniques, such as Guyan’s reduction, that remove some of the “insignificant” physical coordinates, that is, degrees of freedom at a node point. Despite such reduction, the resultant model is still too large for control design. This warrants further reduction as is frequently done in control design by approximating a large dynamical system with a fewer number of state variables. A problem, however, arises because a model usually undergoes, before being reduced, some form of coordinate transformations that destroy the physical meanings of the states. To correct such a problem, we developed a method that expresses a reduced model in terms of a subset of the original states. The proposed method starts with a dynamic model that is originated and reduced in finite element analysis. The model is then converted to a state-space form, and reduced further by the internal balancing method. At this stage, being in the balanced coordinate system, the states in the reduced model have no apparent resemblance to those of the original model. Through another coordinate transformation that is developed in this paper, however, this reduced model is expressed by a subset of the original states, so that the states in the reduced model can be related to the degrees of freedom of the nodes in the original finite element model.

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