Springback Analysis of Rectangular Sectioned Bar of Non Linear Work-Hardening Materials under Torsional Loading

2013 ◽  
Vol 393 ◽  
pp. 422-434 ◽  
Author(s):  
Radha Krishna Lal ◽  
Vikas Kumar Choubey ◽  
J.P. Dwivedi ◽  
V.P. Singh ◽  
Sandeep Kumar
Keyword(s):  
Work Hardening ◽  
Deformation Theory ◽  
Rectangular Cross Section ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Torsional Loading ◽  
Rectangular Section ◽  
Steel Bars ◽  
Non Linear ◽  
Theoretical Results

This paper deals with the springback problems of rectangular section bars of non-linear work-hardening materials under the torsional loading. Using the deformation theory of plasticity, a numerical scheme based on the finite difference approximation has been proposed. The growth of the elastic-plastic boundary and the resulting stresses while loading, and the springback and the residual stresses after unloading are calculated. The results are verified experimentally with mild steel bars having a rectangular cross-section and the experimental results have been found to agree well with the theoretical results obtained numerically.

Springback analysis of channel cross-sectioned bar of work-hardening materials under torsional loading

2016 ◽  
Vol 33 (7) ◽  
pp. 1899-1928 ◽  
Author(s):  
Radha Krishna Lal ◽  
Vikas Kumar Choubey ◽  
J.P. Dwivedi ◽  
V.P. Singh
Keyword(s):  
Residual Stresses ◽  
Cross Section ◽  
Work Hardening ◽  
Finite Difference Approximation ◽  
Channel Cross Section ◽  
Difference Approximation ◽  
Plastic Behavior ◽  
Torsional Loading ◽  
Hardening Material ◽  
Content Type

Purpose The purpose of this paper is to deal with the springback problems of channel cross-section bars of linear and non-linear work-hardening materials under torsional loading. Using the deformation theory of plasticity, a numerical scheme based on the finite difference approximation has been proposed. The growth of the elastic-plastic boundary and the resulting stresses while loading, and the springback and the residual stresses after unloading are calculated. Design/methodology/approach The numerical method which has been described in this paper for obtaining the solution of elasto-plastic solution can also be used for other sections. The only care that needs to be taken is to decrease the mesh size near points of stress concentration. The advantage of this technique is that it automatically takes care of all plastic zones developing over the section at different loads and gives a solution satisfying the elastic and plastic torsion equations in their respective regions. Findings As expected, elastic recovery is found to be more with decreasing values of n and λ. The difference in springback becomes more and more with increasing values of angle of twist. The material will approach an elastic ideally plastic behavior with increasing values of λ and n. Originality/value It seems that no attempt has been made to study residual stresses in elasto-plastic torsion of a work-hardening material for a channel cross-section.

Residual Stress analysis of Triangular Sectioned bar of Non-Linear Work- Hardening Materials under Torsional Loading

2018 ◽  
Vol 5 (2) ◽  
pp. 6502-6508
Author(s):  
Radha Krishna Lal ◽  
Vikas Kumar Choubey ◽  
J.P. Dwivedi ◽  
S.K. Srivastava
Keyword(s):  
Residual Stress ◽  
Stress Analysis ◽  
Work Hardening ◽  
Torsional Loading ◽  
Non Linear ◽  
Residual Stress Analysis

Springback analysis of thin rectangular bars of non-linear work-hardening materials under torsional loading

2002 ◽  
Vol 44 (7) ◽  
pp. 1505-1519 ◽  
Author(s):  
J.P. Dwivedi ◽  
S.K. Shah ◽  
P.C. Upadhyay ◽  
N.K. Das Talukder
Keyword(s):  
Work Hardening ◽  
Torsional Loading ◽  
Non Linear

scholarly journals Finite difference approximation of eigenvibrations of a bar with oscillator

2020 ◽  
Vol 329 ◽  
pp. 03030
Author(s):  
D. M. Korosteleva ◽  
L. N. Koronova ◽  
K. O. Levinskaya ◽  
S. I. Solov’ev
Keyword(s):  
Finite Difference ◽  
Spectral Problem ◽  
Model Problem ◽  
Second Order ◽  
Harmonic Oscillators ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Eigenvalues And Eigenfunctions ◽  
Constant Coefficients ◽  
Theoretical Results

The second-order ordinary differential spectral problem governing eigenvibrations of a bar with attached harmonic oscillator is investigated. We study existence and properties of eigensolutions of formulated bar-oscillator spectral problem. The original second-order ordinary differential spectral problem is approximated by the finite difference mesh scheme. Theoretical error estimates for approximate eigenvalues and eigenfunctions of this mesh scheme are established. Obtained theoretical results are illustrated by computations for a model problem with constant coefficients. Theoretical and experimental results of this paper can be developed and generalized for the problems on eigenvibrations of complex mechanical constructions with systems of harmonic oscillators.

scholarly journals Displacement convexity for the entropy in semi-discrete non-linear Fokker–Planck equations

2018 ◽  
Vol 30 (6) ◽  
pp. 1103-1122 ◽  
Author(s):  
JOSÉ A. CARRILLO ◽  
ANSGAR JÜNGEL ◽  
MATHEUS C. SANTOS
Keyword(s):  
A Priori ◽  
Gradient Flow ◽  
Planck Equation ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Standard Entropy ◽  
Non Linear ◽  
Finite State ◽  
Mean Function ◽  
Fokker Planck

The displacement λ-convexity of a non-standard entropy with respect to a non-local transportation metric in finite state spaces is shown using a gradient flow approach. The constant λ is computed explicitly in terms ofa prioriestimates of the solution to a finite-difference approximation of a non-linear Fokker–Planck equation. The key idea is to employ a new mean function, which defines the Onsager operator in the gradient flow formulation.

Springback analysis of Triangular Cross-sectioned Bar of Non-Linear Work- Hardening Materials under Torsional Loading

2017 ◽  
Vol 4 (2) ◽  
pp. 2673-2681
Author(s):  
Radha Krishna Lala ◽  
Vikas Kumar Choubey ◽  
J.P. Dwivedi ◽  
V.P. Singh ◽  
S.K. Srivastava
Keyword(s):  
Work Hardening ◽  
Torsional Loading ◽  
Non Linear

scholarly journals A problem of non – linear deformation of five–layer conical shells with allowance for discrete ribs

2021 ◽  
Author(s):  
N. V. Arnauta ◽  
Keyword(s):  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Shells Of Revolution ◽  
Linear Deformation ◽  
Conical Shells ◽  
Non Linear ◽  
Stationary Loading ◽  
Discrete Ribs ◽  
Linear Differential ◽  
Wave Problems

A problem of non – linear deformation of multiplayer conical shells with allowance for discrete ribs under non – stationary loading is considered. The system of non – linear differential equations is based on the Timoshenko type theory of rods and shells. The Reissner’s variational principle is used for deductions of the motion equations. An efficient numerical method with using Richardson type finite difference approximation for solution of problems on nonstationary behaviour of multiplayer shells of revolution with allowance distcrete ribs which permit to realize solution of the investigated wave problems with the use of personal computers. As a numerical example, the problem of dynamic deformation of a five-layer conical shell with rigidly clamped ends under the action of an internal distributed load was considered.

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