scholarly journals Maggi’s Equations Used in the Finite Element Analysis of the Multibody Systems with Elastic Elements

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 399 ◽  
Author(s):  
Sorin Vlase ◽  
Marin Marin ◽  
Maria Luminița Scutaru
Keyword(s):  
Finite Element ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Main Method ◽  
The Finite Element Analysis ◽  
Elastic Systems ◽  
Lagrange’S Multipliers ◽  
Elastic Elements

The main method used to determine the equations of motion of a multibody system (MBS) with elastic elements is the method of Lagrange’s multipliers. The assembly of equations for the whole system represents an important step in the elastodynamic analysis of such a system. This paper presents a new method of approaching this stage, by applying Maggi’s equations. In this way, the links that exist between the finite elements and the connections that exist between different bodies of the MBS system are conveniently taken into account, each body having a distinct velocity and acceleration field. Although Maggi’s equations have been used, sporadically, in some applications so far, we are not aware that they have been used in the study of elastic systems using the finite element method. Finally, an algorithm is presented that uses the Maggi formalism to obtain the equations of motion for an MBS system.

scholarly journals Energy of Accelerations Used to Obtain the Motion Equations of a Three- Dimensional Finite Element

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 321 ◽  
Author(s):  
Sorin Vlase ◽  
Iuliu Negrean ◽  
Marin Marin ◽  
Maria Luminița Scutaru
Keyword(s):  
Finite Element ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Method Of Calculation ◽  
Elastic Systems ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element ◽  
Multi Body ◽  
Elastic Elements

When analyzing the dynamic behavior of multi-body elastic systems, a commonly used method is the finite element method conjunctively with Lagrange’s equations. The central problem when approaching such a system is determining the equations of motion for a single finite element. The paper presents an alternative method of calculation theses using the Gibbs–Appell (GA) formulation, which requires a smaller number of calculations and, as a result, is easier to apply in practice. For this purpose, the energy of the accelerations for one single finite element is calculated, which will be used then in the GA equations. This method can have advantages in applying to the study of multi-body systems with elastic elements and in the case of robots and manipulators that have in their composition some elastic elements. The number of differentiation required when using the Gibbs–Appell method is smaller than if the Lagrange method is used which leads to a smaller number of operations to obtain the equations of motion.

scholarly journals The Finite Element Analysis of High Precision Positioning System

2018 ◽  
Vol 68 (4) ◽  
pp. 41-48 ◽  
Author(s):  
Trebuňa František ◽  
Bocko Jozef ◽  
Pástor Miroslav ◽  
Lengvarský Pavol ◽  
Prada Erik
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Applied Load ◽  
Positioning System ◽  
The Finite Element Method ◽  
Correct Position ◽  
Element Analysis ◽  
Precise Positioning ◽  
The Finite Element Analysis ◽  
Elastic Elements

AbstractThe paper deals with design and computation of precise positioning mechanism. The aim of mechanism is to transfer applied load without any change of position of parts in question. The stabilization of position is assured by elastic elements connected to reductor which is adjusted into correct position by an actuator. The functionality of mechanism and its stiffness and strength characteristics were checked by the finite element method. The computations were accomplished for prescribed displacement of reductor. On the base of this type of loading the behaviour of the structure was evaluated.

Analysis of Hydroelectric Unit’s Upper Bracket Based on Test and FEM

2014 ◽  
Vol 721 ◽  
pp. 131-134
Author(s):  
Mi Mi Xia ◽  
Yong Gang Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Element Model ◽  
The Finite Element Method ◽  
Ansys Software ◽  
Element Analysis ◽  
Hydroelectric Unit ◽  
The Finite Element Analysis ◽  
Strain Rosette ◽  
The Finite Element Model

To research the load upper bracket of Francis hydroelectric unit, then established the finite-element model, and analyzed the structure stress of 7 operating condition points with the ANSYS software. By the strain rosette test, acquired the data of stress-strain in the area of stress concentration of the upper bracket. The inaccuracy was considered below 5% by analyzing the contradistinction between the finite-element analysis and the test, and match the engineering precision and the test was reliable. The finite-element method could be used to judge the stress of the upper bracket, and it could provide reference for the Structural optimization and improvement too.

Comparison of Buried Pipeline Crossing Assessments Using API RP 1102, Analytical Method and Finite Element Approach

2020 ◽  
Author(s):  
Nikhil Joshi ◽  
Pritha Ghosh ◽  
Jonathan Brewer ◽  
Lawrence Matta
Keyword(s):  
Finite Element ◽  
Analytical Method ◽  
Rapid Assessment ◽  
Buried Pipeline ◽  
The Finite Element Method ◽  
Buried Pipelines ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Element Approach ◽  
Multiple Loading

Abstract API RP 1102 provides a method to calculate stresses in buried pipelines due to surface loads resulting from the encroachment of roads and railroads. The API RP 1102 approach is commonly used in the industry, and widely available software allows for quick and easy implementation. However, the approach has several limitations on when it can be used, one of which is that it is limited to pipelines crossing as near to 90° (perpendicular crossing) as practicable. In no case can the crossing be less than 30° . In this paper, the stresses in the buried pipeline under standard highway vehicular loading calculated using the API RP 1102 method are compared with the results of two other methods; an analytical method that accounts for longitudinal and circumferential through wall bending effects, and the finite element method. The benefit of the alternate analytical method is that it is not subject to the limitations of API RP 1102 on crossing alignment or depth. However, this method is still subject to the limitation that the pipeline is straight and at a uniform depth. The fact that it is analytical in nature allows for rapid assessment of a number of pipes and load configurations. The finite element analysis using a 3D soil box approach offers the greatest flexibility in that pipes with bends or appurtenances can be assessed. However, this approach is time consuming and difficult to apply to multiple loading scenarios. Pipeline crossings between 0° (parallel) and 90° (perpendicular) are evaluated in the assessment reported here, even though these are beyond the scope of API RP 1102. A comparison across the three methods will provide a means to evaluate the level of conservatism, if any, in the API RP 1102 calculation for crossing between 30° and 90° . It also provides a rationale to evaluate whether the API RP 1102 calculation can potentially be extended for 0° (parallel) crossings.

scholarly journals Modeling of Size Effects in Bending of Perforated Cosserat Plates

2017 ◽  
Vol 2017 ◽  
pp. 1-19 ◽  
Author(s):  
Roman Kvasov ◽  
Lev Steinberg
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Numerical Study ◽  
The Finite Element Method ◽  
Classical Elasticity ◽  
Element Analysis ◽  
Plate Deformation ◽  
The Finite Element Analysis ◽  
Circular Holes ◽  
Different Shapes

This paper presents the numerical study of Cosserat elastic plate deformation based on the parametric theory of Cosserat plates, recently developed by the authors. The numerical results are obtained using the Finite Element Method used to solve the parametric system of 9 kinematic equations. We discuss the existence and uniqueness of the weak solution and the convergence of the proposed FEM. The Finite Element analysis of clamped Cosserat plates of different shapes under different loads is provided. We present the numerical validation of the proposed FEM by estimating the order of convergence, when comparing the main kinematic variables with an analytical solution. We also consider the numerical analysis of plates with circular holes. We show that the stress concentration factor around the hole is less than the classical value, and smaller holes exhibit less stress concentration as would be expected on the basis of the classical elasticity.

Large Deformation Modeling Applied to the Sheet Metal Electromagnetic Forming

2008 ◽  
Author(s):  
C. Dumitras ◽  
I. Cozminca
Keyword(s):  
Finite Element ◽  
Deformation Process ◽  
Electromagnetic Forming ◽  
Stress And Strain ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Strain Fields ◽  
The Finite Element Analysis ◽  
History Of ◽  
Free Bulging

The electromagnetic forming has the advantage of a minimum forming time, but this is a major obstacle in determining the process’s history of the forming workpiece. Both experimental and theoretical known analysis methods for this process give a discret array of data (only for the displacements). One considers it is more adequate to use the finite element method in studying this process. The main advantage of the finite element analysis is given by the fact that it shows the stress and strain fields in a continuous way during the deformation process. Also, it offers a model from which one can predict the final shape of the part and the possible crack zones. One present a compared study of the experimental and the simulated results achieved of the free bulging aluminum specimens by electromagnetic impulses.

scholarly journals New Analytical Model Used in Finite Element Analysis of Solids Mechanics

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1401 ◽  
Author(s):  
Sorin Vlase ◽  
Adrian Eracle Nicolescu ◽  
Marin Marin
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Three Dimensional ◽  
Elastic Solid ◽  
The Finite Element Method ◽  
Governing Equations ◽  
Element Analysis ◽  
Elastic Multibody System

In classical mechanics, determining the governing equations of motion using finite element analysis (FEA) of an elastic multibody system (MBS) leads to a system of second order differential equations. To integrate this, it must be transformed into a system of first-order equations. However, this can also be achieved directly and naturally if Hamilton’s equations are used. The paper presents this useful alternative formalism used in conjunction with the finite element method for MBSs. The motion equations in the very general case of a three-dimensional motion of an elastic solid are obtained. To illustrate the method, two examples are presented. A comparison between the integration times in the two cases presents another possible advantage of applying this method.

Testing of a Folded Plate Space Structure

1987 ◽  
Vol 2 (2) ◽  
pp. 115-121
Author(s):  
D. Ho ◽  
P. K. K. Lee ◽  
H. W. Chung ◽  
W. C. Keung
Keyword(s):  
Finite Element ◽  
Space Structure ◽  
Sufficient Accuracy ◽  
Design Stage ◽  
Stage Model ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Actual Structure ◽  
The Finite Element Analysis ◽  
Before And After

A reinforced concrete folded plate space structure of span 28 m and clear height 9·4 m was constructed as a games hall. The structure was analysed using the finite element method. At the design stage, model tests were carried out to check the accuracy of the method of analysis. To assess the behaviour of the actual structure subject to its self-weight, strains and deflections were monitored during construction both before and after removal of formwork. The tests confirmed that results given by the finite element analysis are of sufficient accuracy for the purpose of design, irrespective of the assumptions involved.

The Finite Element Analysis of Asphalt Pavement with Function Layer under Temperature-Load Action

2012 ◽  
Vol 468-471 ◽  
pp. 2413-2416 ◽  
Author(s):  
Chuang Du ◽  
Yan Yan Li ◽  
Rong Guo ◽  
Shi Bin Ma
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Surface Layer ◽  
Asphalt Pavement ◽  
The Finite Element Method ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Temperature Load ◽  
Load Action ◽  
Reflection Crack

In order to study the performance of asphalt pavement with function layer under temperature-load coupling action, the thickness of surface layer, the module of surface layer and was analyzed to abtain their influence on the function layer stress using the finite element method. The results clearly indicated that it is very effective to prevent the reflection crack by increasing the thickness of asphalt surface layer and it is not obvious to reduce the reflection crack through enhancing the module of asphalt surface layer.

Finite Element Numerical Analysis of the LGV Frame Based on ANSYS

2012 ◽  
Vol 590 ◽  
pp. 487-491
Author(s):  
Qin Man Fan
Keyword(s):  
Finite Element ◽  
Element Model ◽  
Mechanical Analysis ◽  
Structure Design ◽  
Frame Structure ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Static And Dynamic Characteristics ◽  
The Finite Element Analysis ◽  
Optimizing Design

The frame is the main part of the force matrix of truck vehicle and the stress state is complex and difficult to design. The finite element method is more accurate for the analysis of the static and dynamic characteristics of the frame, which provide guidance for the frame structure design. Establish finite element model of the frame with the application of ANSYS. According to the mechanical analysis of the model, impose reasonable constraints and load, the most typical of the four conditions in the frame is calculated with the finite element analysis, and predicted the weak parts of the frame according to the frame stress-strain cloud, which provided a very important theoretical basis for the improvement of the frame structure of the frame and optimizing design of the frame.

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