Joint and Cross Acceptances for Cross-Flow-Induced Vibration—Part I: Theoretical and Finite Element Formulations

2000 ◽  
Vol 122 (3) ◽  
pp. 349-354 ◽  
Author(s):  
M. K. Au-Yang
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Cross Flow ◽  
Theoretical Development ◽  
Element Formulation ◽  
Flow Induced Vibration ◽  
Arbitrary Boundary ◽  
One Dimensional ◽  
Closed Form Solutions ◽  
Special Cases

The theoretical development of the acceptance integral method to estimate the random vibration of structures subject to turbulent flow is critically reviewed and put onto a firm mathematical basis. Closed-form solutions for the joint acceptances for cross-flow-induced vibration of one-dimensional structures are derived for two special cases of spring-supported and simply supported beams. These are used to check results from a finite element formulation of the acceptance integrals for one-dimensional structures with arbitrary boundary conditions, and for arbitrary correlation lengths. Agreements between the finite element and closed-form solutions are excellent. [S0094-9930(00)02303-9]

Validation of Nitinol SMA Characteristics Using Finite Element Analysis and Closed Form Solutions

2013 ◽  
Vol 856 ◽  
pp. 147-152
Author(s):  
S.H. Adarsh ◽  
U.S. Mallikarjun
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fe Analysis ◽  
Element Analysis ◽  
Complex Behaviour ◽  
Closed Form Solutions

Shape Memory Alloys (SMA) are promising materials for actuation in space applications, because of the relatively large deformations and forces that they offer. However, their complex behaviour and interaction of several physical domains (electrical, thermal and mechanical), the study of SMA behaviour is a challenging field. Present work aims at correlating the Finite Element (FE) analysis of SMA with closed form solutions and experimental data. Though sufficient literature is available on closed form solution of SMA, not much detail is available on the Finite element Analysis. In the present work an attempt is made for characterization of SMA through solving the governing equations by established closed form solution, and finally correlating FE results with these data. Extensive experiments were conducted on 0.3mm diameter NiTinol SMA wire at various temperatures and stress conditions and these results were compared with FE analysis conducted using MSC.Marc. A comparison of results from finite element analysis with the experimental data exhibits fairly good agreement.

scholarly journals Transient Solutions for One-Dimensional Problems With Strain Softening

1987 ◽  
Vol 54 (3) ◽  
pp. 513-518 ◽  
Author(s):  
T. Belytschko ◽  
Xiao-Jun Wang ◽  
Z. P. Bazant ◽  
Y. Hyun
Keyword(s):  
Strain Rate ◽  
Closed Form ◽  
Transient Response ◽  
Softening Point ◽  
Strain Softening ◽  
Stress Strain ◽  
One Dimensional ◽  
Closed Form Solutions ◽  
Transient Solutions

Closed-form solutions are presented for the transient response of rods in which strain softening occurs and the stress-strain laws exhibit nonvanishing stresses after the strain-softening regime. It is found that the appearance of any strain softening results in an infinite strain rate if the material is inviscid. For a stress-strain law with a monotonically decreasing stress the strains are infinite also. If the stress increases after the strain-softening portion, the strains remain finite and the strain-softening point moves through the rod.

A Conical Beam Finite Element for Rotor Dynamics Analysis

1985 ◽  
Vol 107 (4) ◽  
pp. 421-430 ◽  
Author(s):  
L. M. Greenhill ◽  
W. B. Bickford ◽  
H. D. Nelson
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Cross Section ◽  
Rotor Dynamics ◽  
General Purpose ◽  
Closed Form Expression ◽  
Dynamics Analysis ◽  
Closed Form Solutions ◽  
Analysis Computer ◽  
Rotor Dynamic

The development of finite element formulations for use in rotor dynamics analysis has been the subject of many recent publications. These works have included the effects of rotatory inertia, gyroscopic moments, axial load, internal damping, and shear deformation. However, for most closed-form solutions, the element geometry has been limited to a cylindrical cross-section. This paper extends these previous works by developing a closed-form expression including all of the above effects in a linearly tapered conical cross-section element. Results are also given comparing the formulation to previously published examples, to stepped cylinder representations of conical geometry, and to a general purpose finite element elasticity solution. The elimination of numerical integration in the generation of the element matrices, and the ability of the element to represent both conical and cylindrical geometries, make this formulation particularly suited for use in rotor dynamic analysis computer programs.

An Intelligent System for Spur Gear Design and Analysis

2001 ◽  
Author(s):  
El-Sayed Aziz ◽  
C. Chassapis
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Intelligent System ◽  
Tooth Profile ◽  
Hertzian Contact ◽  
Design Parameters ◽  
Analysis Model ◽  
Closed Form Solutions ◽  
Gear Teeth ◽  
Gear Design

Abstract A methodology for the analysis of load distribution and contact stress on gear teeth, which utilizes a combination of closed form solutions and two-dimensional finite element methods, within a constraint-based knowledge-based environment, is presented. Once the design parameters are specified, the complete process of generating the analysis model, starting from the determination of the coordinates of the tooth profile, the creation of a sector of the mating gear teeth, automatic mesh generation, boundary conditions and loading, is totally automated and transparent to the designer. The effects of non-standard geometry, load sharing on the contact zone, friction and root stresses are easily included in the model. The Finite Element Method (FEM) based results compare favorably with those obtained from closed form solutions (AGMA equations and classical Hertzian contact solution). The advantage of the approach rests in the ability to modify any of the gear design parameters such as diametral pitch, tooth profile modification etc., in an automated manner along with obtaining a better estimation of the risks of failure of the gear design on hand. The procedure may be easily extended to other types of gearing systems.

Joint and Cross Acceptances for Cross-Flow-Induced Vibration—Part II: Charts and Applications

2000 ◽  
Vol 122 (3) ◽  
pp. 355-361 ◽  
Author(s):  
M. K. Au-Yang
Keyword(s):  
Finite Element ◽  
Structural Analysis ◽  
Boundary Conditions ◽  
Computer Program ◽  
Cross Flow ◽  
Flow Induced Vibration ◽  
Modal Coupling ◽  
Analysis Computer ◽  
Flow Turbulence ◽  
Analysis Computer Program

Using closed-form and finite element solutions derived in Part I of this paper together with a standard commercial finite element structural-analysis computer program, the joint and cross acceptances for tubes and beams with different boundary conditions are calculated as a function of the correlation length up to 10 times the length of the structures. The results are presented in the form of charts. Steps are given to show how to use these charts together with standard commercial finite-element structural-analysis computer programs to estimate the responses of single and multi-span tubes and beams to cross-flow turbulence-induced vibration. The importance of cross-modal coupling for multi-supported beams is investigated. Examples are given. [S0094-9930(00)03303-5]

Analysis of Thin-Walled Closed Beams With General Quadrilateral Cross Sections

1999 ◽  
Vol 66 (4) ◽  
pp. 904-912 ◽  
Author(s):  
J. H. Kim ◽  
Y. Y. Kim
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Distortion Function ◽  
Element Formulation ◽  
Numerical Work ◽  
New Approach ◽  
One Dimensional ◽  
Static And Dynamic Analysis ◽  
Thin Walled ◽  
The One

This paper deals with the one-dimensional static and dynamic analysis of thin-walled closed beams with general quadrilateral cross sections. The coupled deformations of distortion as well as torsion and warping are investigated in this work. A new approach to determine the functions describing section deformations is proposed. In particular, the present distortion function satisfies all the necessary continuity conditions unlike Vlasov's distortion function. Based on these section deformation functions, a one-dimensional theory dealing with the coupled deformations is presented. The actual numerical work is carried out using two-node C0 finite element formulation. The present one-dimensional results for some static and free-vibration problems are compared with the existing and the plate finite element results.

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