scholarly journals Propagation of a Stress Pulse in a Heterogeneous Elastic Bar

2021 ◽  
Author(s):  
Stewart A. Silling
Keyword(s):  
Stress Pulse ◽  
Elastic Bar

Finite Deflections of a Nonlinearly Elastic Bar

1970 ◽  
Vol 37 (1) ◽  
pp. 48-52 ◽  
Author(s):  
J. T. Oden ◽  
S. B. Childs
Keyword(s):  
Differential Equations ◽  
Axial Force ◽  
Classical Theory ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Finite Deflections ◽  
Hyperbolic Tangent ◽  
Elastic Bar ◽  
Elastoplastic Materials ◽  
Nonlinearly Elastic

The problem of finite deflections of a nonlinearly elastic bar is investigated as an extension of the classical theory of the elastica to include material nonlinearities. A moment-curvature relation in the form of a hyperbolic tangent law is introduced to simulate that of a class of elastoplastic materials. The problem of finite deflections of a clamped-end bar subjected to an axial force is given special attention, and numerical solutions to the resulting system of nonlinear differential equations are obtained. Tables of results for various values of the parameters defining the material are provided and solutions are compared with those of the classical theory of the elastica.

Static and dynamic analysis of a gradient-elastic bar in tension

2002 ◽  
Vol 72 (6-7) ◽  
pp. 483-497 ◽  
Author(s):  
K. G. Tsepoura ◽  
S. Papargyri-Beskou ◽  
D. Polyzos ◽  
D. E. Beskos
Keyword(s):  
Dynamic Analysis ◽  
Static And Dynamic Analysis ◽  
Elastic Bar

Vibrations of Elastic Connecting Rod of a High-Speed Slider-Crank Mechanism

1971 ◽  
Vol 93 (2) ◽  
pp. 636-644 ◽  
Author(s):  
Peter W. Jasinski ◽  
Ho Chong Lee ◽  
George N. Sandor
Keyword(s):  
Small Parameter ◽  
High Speed ◽  
Elastic Stability ◽  
Method Of Averaging ◽  
Connecting Rod ◽  
Transverse Vibrations ◽  
Elastic Bar ◽  
The Moment ◽  
Steady State Solutions ◽  
Crank Mechanism

The research involved in this paper falls into the area of analytical vibrations applied to planar mechanical linkages. Specifically, a study of the vibrations, associated with an elastic connecting-bar for a high-speed slider-crank mechanism, is made. To simplify the mathematical analysis, the vibrations of an externally viscously damped uniform elastic connecting bar is taken to be hinged at each end (i.e., the moment and displacement are assumed to vanish at each end). The equations governing the vibrations of the elastic bar are derived, a small parameter is found, and the solution is developed as an asymptotic expansion in terms of this small parameter with the aid of the Krylov-Bogoliubov method of averaging. The elastic stability is studied and the steady-state solutions for both the longitudinal and transverse vibrations are found.

Durability of an Elastic Bar Under Tension With Linear or Nonlinear Relationship Between Corrosion Rate and Stress

2012 ◽  
Vol 79 (2) ◽  
Author(s):  
Isaac Elishakoff ◽  
Guillaume Ghyselinck ◽  
Yohann Miglis
Keyword(s):  
Corrosion Rate ◽  
Closed Form ◽  
Average Diameter ◽  
Large Error ◽  
Nonlinear Relationship ◽  
Time To Failure ◽  
Linear Quadratic ◽  
Yield Level ◽  
Elastic Bar

In this study we investigate the durability of a bar subjected to tension in the presence of corrosion. Various possible relationships are considered between the corrosion velocity and stress. We concentrate on linear, quadratic, purely cubic, and general cubic relationships. Closed-form expressions are obtained for the structure’s durability, which is identified with time to failure, with failure defined as the stress reaching the yield level. Among other things, we evaluate the validity of the assumption that the average diameter of the bar remains constant, as suggested by Dolinskii (1967, “Analysis of Loaded Tubes Subjected to Corrosion,” Khimicheskoe I Neftianoe Mashinostroenie (Chemical and Oil Machinery), 2, pp. 9–10, (in Russian)). We show that in certain circumstances this assumption may lead to an unacceptably large error.

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