scholarly journals Kane’s Method-Based Simulation and Modeling Robots with Elastic Elements, Using Finite Element Method

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 805 ◽  
Author(s):  
Sorin Vlase ◽  
Iuliu Negrean ◽  
Marin Marin ◽  
Silviu Năstac
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Computational Effort ◽  
Element Analysis ◽  
Lagrange’S Equation ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
The Matrix ◽  
Element Method

The Lagrange’s equation remains the most used method by researchers to determine the finite element motion equations in the case of elasto-dynamic analysis of a multibody system (MBS). However, applying this method requires the calculation of the kinetic energy of an element and then a series of differentiations that involve a great computational effort. The last decade has shown an increased interest of researchers in the study of multibody systems (MBS) using alternative analytical methods, aiming to simplify the description of the model and the solution of the systems of obtained equations. The method of Kane’s equations is one possibility to do this and, in the paper, we applied this method in the study of a MBS applying finite element analysis (FEA). The number of operations involved is lower than in the case of Lagrange’s equations and Kane’s equations are little used previously in conjunction with the finite element method (FEM). Results are obtained regardless of the type of finite element used. The shape functions will determine the final form of the matrix coefficients in the equations. The results are applied in the case of a planar mechanism with two degrees of freedom.

Free Vibration Analysis of Frame Structures Using BSWI Method

2008 ◽  
Author(s):  
Farhang Daneshmand ◽  
Abdolaziz Abdollahi ◽  
Mehdi Liaghat ◽  
Yousef Bazargan Lari
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Frame Structures ◽  
Shape Functions ◽  
Element Analysis ◽  
B Spline ◽  
Multi Level ◽  
Element Method

Vibration analysis for complicated structures, or for problems requiring large numbers of modes, always requires fine meshing or using higher order polynomials as shape functions in conventional finite element analysis. Since it is hard to predict the vibration mode a priori for a complex structure, a uniform fine mesh is generally used which wastes a lot of degrees of freedom to explore some local modes. By the present wavelets element approach, the structural vibration can be analyzed by coarse mesh first and the results can be improved adaptively by multi-level refining the required parts of the model. This will provide accurate data with less degrees of freedom and computation. The scaling functions of B-spline wavelet on the interval (BSWI) as trial functions that combines the versatility of the finite element method with the accuracy of B-spline functions approximation and the multiresolution strategy of wavelets is used for frame structures vibration analysis. Instead of traditional polynomial interpolation, scaling functions at the certain scale have been adopted to form the shape functions and construct wavelet-based elements. Unlike the process of wavelets added directly in the other wavelet numerical methods, the element displacement field represented by the coefficients of wavelets expansions is transformed from wavelet space to physical space via the corresponding transformation matrix. To verify the proposed method, the vibrations of a cantilever beam and a plane structures are studied in the present paper. The analyses and results of these problems display the multi-level procedure and wavelet local improvement. The formulation process is as simple as the conventional finite element method except including transfer matrices to compute the coupled effect between different resolution levels. This advantage makes the method more competitive for adaptive finite element analysis. The results also show good agreement with those obtained from the classical finite element method and analytical solutions.

Towards Predicting Relative Belt Edge Endurance With the Finite Element Method

1990 ◽  
Vol 18 (4) ◽  
pp. 216-235 ◽  
Author(s):  
J. De Eskinazi ◽  
K. Ishihara ◽  
H. Volk ◽  
T. C. Warholic
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Shear Deformations ◽  
Element Analysis ◽  
Vertical Loading ◽  
Predicted Values ◽  
Element Method

Abstract The paper describes the intention of the authors to determine whether it is possible to predict relative belt edge endurance for radial passenger car tires using the finite element method. Three groups of tires with different belt edge configurations were tested on a fleet test in an attempt to validate predictions from the finite element results. A two-dimensional, axisymmetric finite element analysis was first used to determine if the results from such an analysis, with emphasis on the shear deformations between the belts, could be used to predict a relative ranking for belt edge endurance. It is shown that such an analysis can lead to erroneous conclusions. A three-dimensional analysis in which tires are modeled under free rotation and static vertical loading was performed next. This approach resulted in an improvement in the quality of the correlations. The differences in the predicted values of various stress analysis parameters for the three belt edge configurations are studied and their implication on predicting belt edge endurance is discussed.

Tire Cornering Simulation Using an Explicit Finite Element Analysis Code

1998 ◽  
Vol 26 (2) ◽  
pp. 109-119 ◽  
Author(s):  
M. Koishi ◽  
K. Kabe ◽  
M. Shiratori
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Test System ◽  
Experimental Results ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Explicit Finite Element ◽  
Explicit Finite Element Analysis ◽  
Element Method

Abstract The finite element method has been used widely in tire engineering. Most tire simulations using the finite element method are static analyses, because tires are very complex nonlinear structures. Recently, transient phenomena have been studied with explicit finite element analysis codes. In this paper, the authors demonstrate the feasibility of tire cornering simulation using an explicit finite element code, PAM-SHOCK. First, we propose the cornering simulation using the explicit finite element analysis code. To demonstrate the efficiency of the proposed simulation, computed cornering forces for a 175SR14 tire are compared with experimental results from an MTS Flat-Trac Tire Test System. The computed cornering forces agree well with experimental results. After that, parametric studies are conducted by using the proposed simulation.

FINITE ELEMENT ANALYSIS OF RECTANGULAR RESONATORS WITH METAL INCLUSIONS

2019 ◽  
Author(s):  
Sergey Bushanskiy ◽  
Vyacheslav Komarov ◽  
A. Churkin
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Electrodynamic Characteristic ◽  
Metallic Inclusions ◽  
Element Method

Electrodynamic characteristic of two rectangular resonators with metallic inclusions are analyzed by using the finite element method.

scholarly journals Shape Sensing of a Complex Aeronautical Structure with Inverse Finite Element Method

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1388
Author(s):  
Daniele Oboe ◽  
Luca Colombo ◽  
Claudio Sbarufatti ◽  
Marco Giglio
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Strain Field ◽  
Element Analysis ◽  
Inverse Finite Element Method ◽  
Shape Sensing ◽  
Definition Of ◽  
High Level ◽  
Element Method

The inverse Finite Element Method (iFEM) is receiving more attention for shape sensing due to its independence from the material properties and the external load. However, a proper definition of the model geometry with its boundary conditions is required, together with the acquisition of the structure’s strain field with optimized sensor networks. The iFEM model definition is not trivial in the case of complex structures, in particular, if sensors are not applied on the whole structure allowing just a partial definition of the input strain field. To overcome this issue, this research proposes a simplified iFEM model in which the geometrical complexity is reduced and boundary conditions are tuned with the superimposition of the effects to behave as the real structure. The procedure is assessed for a complex aeronautical structure, where the reference displacement field is first computed in a numerical framework with input strains coming from a direct finite element analysis, confirming the effectiveness of the iFEM based on a simplified geometry. Finally, the model is fed with experimentally acquired strain measurements and the performance of the method is assessed in presence of a high level of uncertainty.

Application of Extended Finite Element Method (XFEM) to Stress Intensity Factor Calculations

2015 ◽  
Author(s):  
Do-Jun Shim ◽  
Mohammed Uddin ◽  
Sureshkumar Kalyanam ◽  
Frederick Brust ◽  
Bruce Young
Keyword(s):  
Finite Element Method ◽  
Stress Intensity Factor ◽  
Finite Element ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Degrees Of Freedom ◽  
Extended Finite Element Method ◽  
Partition Of Unity ◽  
Extended Finite Element ◽  
Element Method

The extended finite element method (XFEM) is an extension of the conventional finite element method based on the concept of partition of unity. In this method, the presence of a crack is ensured by the special enriched functions in conjunction with additional degrees of freedom. This approach also removes the requirement for explicitly defining the crack front or specifying the virtual crack extension direction when evaluating the contour integral. In this paper, stress intensity factors (SIF) for various crack types in plates and pipes were calculated using the XFEM embedded in ABAQUS. These results were compared against handbook solutions, results from conventional finite element method, and results obtained from finite element alternating method (FEAM). Based on these results, applicability of the ABAQUS XFEM to stress intensity factor calculations was investigated. Discussions are provided on the advantages and limitations of the XFEM.

scholarly journals Adaptive modelling of variably saturated seepage problems

2021 ◽  
Author(s):  
B Ashby ◽  
C Bortolozo ◽  
A Lukyanov ◽  
T Pryer
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
A Priori ◽  
Water Flux ◽  
Posteriori Error ◽  
Adaptive Finite Element Method ◽  
Posteriori Error Estimate ◽  
Adaptive Finite Element ◽  
Element Method

Summary In this article, we present a goal-oriented adaptive finite element method for a class of subsurface flow problems in porous media, which exhibit seepage faces. We focus on a representative case of the steady state flows governed by a nonlinear Darcy–Buckingham law with physical constraints on subsurface-atmosphere boundaries. This leads to the formulation of the problem as a variational inequality. The solutions to this problem are investigated using an adaptive finite element method based on a dual-weighted a posteriori error estimate, derived with the aim of reducing error in a specific target quantity. The quantity of interest is chosen as volumetric water flux across the seepage face, and therefore depends on an a priori unknown free boundary. We apply our method to challenging numerical examples as well as specific case studies, from which this research originates, illustrating the major difficulties that arise in practical situations. We summarise extensive numerical results that clearly demonstrate the designed method produces rapid error reduction measured against the number of degrees of freedom.

Teaching the Finite Element Method As a Design Tool for Mechanical Engineering

1993 ◽  
Author(s):  
T. R. Grimm
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Solution Process ◽  
Thinking Skills ◽  
Design Tool ◽  
Basic Solution ◽  
The Finite Element Method ◽  
The Matrix ◽  
Analysis Of Results ◽  
Element Method

Abstract The importance of the finite element method as an engineering tool for design and analysis is emphasized in a senior level elective course taught at Michigan Technological University. The course emphasizes hands-on experience with computers and the pre- and post-analysis of results to establish confidence in solutions obtained. The students learn by using the finite element method to “solve” several design projects, rather than by being told about the method without significant actual experience. They also learn about the basis of the method, including formation of the matrix equations required and the numerical methods used in their solution. Intelligent use of the method requires that engineers understand both the mechanics of how to apply the method, i.e modeling requirements, and the limitations imposed by the basic solution process. The course provides the students with important experience in using the powerful finite element method as a design tool. It requires a strong background of fundamentals and stimulates the problem solving thinking skills so essential to industry.

scholarly journals Quasi-3-D spectral wavelet method for a thermal quench simulation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jonas Bundschuh ◽  
Laura A. M. D’Angelo ◽  
Herbert De Gersem
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Spectral Method ◽  
Degrees Of Freedom ◽  
Hot Spot ◽  
Longitudinal Direction ◽  
Particle Accelerators ◽  
Wavelet Basis ◽  
Element Simulation ◽  
Element Method

AbstractThe finite element method is widely used in simulations of various fields. However, when considering domains whose extent differs strongly in different spatial directions a finite element simulation becomes computationally very expensive due to the large number of degrees of freedom. An example of such a domain are the cables inside of the magnets of particle accelerators. For translationally invariant domains, this work proposes a quasi-3-D method. Thereby, a 2-D finite element method with a nodal basis in the cross-section is combined with a spectral method with a wavelet basis in the longitudinal direction. Furthermore, a spectral method with a wavelet basis and an adaptive and time-dependent resolution is presented. All methods are verified. As an example the hot-spot propagation due to a quench in Rutherford cables is simulated successfully.

scholarly journals COMPARISON OF SAW BLADE NATURAL FREQUENCIES AND CRITICAL SPEEDS USING CSAW AND FINITE ELEMENT ANALYSIS

2011 ◽  
Author(s):  
J. Poirier ◽  
P. Radziszewski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Frequencies ◽  
Element Model ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Saw Blade ◽  
Circular Saws ◽  
The Finite Element Model ◽  
Element Method

The natural frequencies of circular saws limit the operating speeds of the saws. Current industry methods of increasing natural frequency include pretensioning, where plastic deformation is induced into the saw. To better model the saw, the finite element model is compared to current software for steel saws; C-SAW, a software program that calculates frequencies for stiffened circular saws. Using C-SAW and the finite element method the results are compared and the finite element method is validated for steel saws.

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