Approximate Solutions for Impulsively Loaded Elastic-Plastic Beams

1968 ◽  
Vol 35 (4) ◽  
pp. 803-809 ◽  
Author(s):  
J. B. Martin ◽  
L. S.-S. Lee
Keyword(s):  
Approximate Solutions ◽  
Impulsive Loading ◽  
Rigid Plastic ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Uniqueness Proof ◽  
Unified Method

A unified method of approximating the response of rigid-plastic and elastic, perfectly plastic beams subjected to impulsive loading is described. The method is based on the uniqueness proof for such problems. A simply supported beam subjected to a uniform impulse is given as an illustrative example.

The Elastic, Plastic Bending of a Simply Supported Plate

1961 ◽  
Vol 28 (3) ◽  
pp. 395-401 ◽  
Author(s):  
G. Eason
Keyword(s):  
Yield Condition ◽  
Constant Load ◽  
Flow Rule ◽  
Plastic Bending ◽  
Simply Supported ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises

In this paper the problem of the elastic, plastic bending of a circular plate which is simply supported at its edge and carries a constant load over a central circular area is considered. The von Mises yield condition and the associated flow rule are assumed and the material of the plate is assumed to be nonhardening, elastic, perfectly plastic, and compressible. Stress fields are obtained in all cases and a velocity field is presented for the case of point loading. Some numerical results are given comparing the results obtained here with those obtained when the Tresca yield condition is assumed.

Impulsive Loading of Elastic-Plastic Beams

1956 ◽  
Vol 23 (4) ◽  
pp. 515-521
Author(s):  
J. A. Seiler ◽  
B. A. Cotter ◽  
P. S. Symonds
Keyword(s):  
Cross Section ◽  
Initial Velocity ◽  
Sine Wave ◽  
Impulsive Loading ◽  
Ductile Material ◽  
Rigid Plastic ◽  
Elastic Deformations ◽  
Simply Supported ◽  
Elastic Plastic ◽  
Plastic Type

Abstract A simply supported uniform beam of ductile material, subjected to impulsive loading such that the initial velocity is a half-sine wave, is considered in this paper. The elastic and elastic-plastic motions are discussed under the assumption that plastic flow is confined to one cross section, and the final deformations are compared with those computed from an analysis which neglects all elastic deformations. The purpose of the work is to provide further information which may help in estimating the range of validity of the latter (“rigid-plastic”) type of analysis.

Combined Viscous and Plastic Deformations in Two-Dimensional Large Strain Finite Element Analysis

1985 ◽  
Vol 107 (1) ◽  
pp. 13-18 ◽  
Author(s):  
B. V. Kiefer ◽  
P. D. Hilton
Keyword(s):  
Finite Element ◽  
Input Parameter ◽  
Time Integration ◽  
Strain Increment ◽  
Total Strain ◽  
Two Dimensional ◽  
Elastic Plastic ◽  
Time Stepping ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Capabilities for the analysis of combined viscous and plastic behavior have been added to an existing finite element computer program for two-dimensional elastic-plastic calculations. This program (PAPSTB) has been formulated for elastic-plastic stress and deformation analyses of two-dimensional and axisymmetric structures. It has the ability to model large strains and large deformations of elastic-perfectly plastic, multi-linear hardening, or power-hardening materials. The program is based on incremental plasticity theory with a von Mises yield criterion. Time dependent behavior has been introduced into the PAPSTB program by adding a viscous strain increment to the elastic and plastic strain increment to form the total strain increment. The viscous calculations presently employ a power-law relationship between the viscous strain rate and the effective stress. The finite element code can be easily modified to handle more complex viscous models. The Newmark method for time integration is used, i.e., an input parameter is included which enables the user to vary the time domain approximation between forward (explicit) and backward (implicit) difference. Automatic time stepping is used to provide for stability in the viscous calculations. It is controlled by an input parameter related to the ratio of the current viscous strain increment to the total strain. The viscoplastic capabilities of the PAPSTB program are verified using the axisymmetric problem of an internally pressurized, thick-walled cylinder. The transient viscoplastic case is analyzed to demonstrate that the elastic-perfectly plastic solution is obtained as a steady-state condition is approached. The influence of varying the time integration parameter for transient viscoplastic calculations is demonstrated. In addition, the effects of time step on solution accuracy are investigated by means of the automatic time stepping algorithm in the program. The approach is then applied to a simple forging problem of cylinder upsetting.

An Elastic-Plastic Finite Element Model of Rolling Contact, Part 2: Analysis of Repeated Contacts

1985 ◽  
Vol 52 (1) ◽  
pp. 75-82 ◽  
Author(s):  
V. Bhargava ◽  
G. T. Hahn ◽  
C. A. Rubin
Keyword(s):  
Finite Element ◽  
Shear Strain ◽  
Element Model ◽  
Rolling Contact ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Rolling Contacts ◽  
Elastic Perfectly Plastic ◽  
Multiple Translations ◽  
Contact Part

This paper presents finite element analyses of two-dimensional (plane strain), elastic-plastic, repeated, frictionless rolling contact. The analysis employs the elastic-perfectly plastic, cycle and strain-amplitude-independent material used in the Merwin and Johnson analysis but avoids several assumptions made by these workers. Repeated rolling contacts are simulated by multiple translations of a semielliptical Hertzian pressure distribution. Results at p0/k = 3.5, 4.35, and 5.0 are compared to the Merwin and Johnson prediction. Shakedown is observed at p0/k = 3.5, but the comparisons reveal significant differences in the amount and distribution of residual shear strain and forward flow at p0/k = 4.35 and p0/k = 5.0. The peak incremental, shear strain per cycle for steady state is five times the value calculated by Merwin and Johnson, and the plastic strain cycle is highly nonsymmetric.

A Compressible Elastic, Perfectly Plastic Wedge

1958 ◽  
Vol 25 (2) ◽  
pp. 239-242
Author(s):  
D. R. Bland ◽  
P. M. Naghdi
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
The State ◽  
Hardening Material ◽  
Included Angle ◽  
Elastic Plastic ◽  
Numerical Example ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Abstract This paper is concerned with a compressible elastic-plastic wedge of an included angle β < π/2 in the state of plane strain. The solution, deduced for an isotropic nonwork-hardening material, employs Tresca’s yield criterion and the associated flow rules. By means of a numerical example the solution is compared with that of an incompressible elastic-plastic wedge in one case (β = π/4) for various positions of the elastic-plastic boundary.

Stresses and Displacements in an Elastic-Plastic Wedge

1957 ◽  
Vol 24 (1) ◽  
pp. 98-104
Author(s):  
P. M. Naghdi
Keyword(s):  
Plane Strain ◽  
Isotropic Material ◽  
Complete Solution ◽  
Normal Pressure ◽  
Stress Strain ◽  
Included Angle ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Domain ◽  
Elastic Perfectly Plastic

Abstract An elastic, perfectly plastic wedge of an incompressible isotropic material in the state of plane strain is considered, where the stress-strain relations of Prandtl-Reuss are employed in the plastic domain. For a wedge (with an included angle β) subjected to a uniform normal pressure on one boundary, the complete solution is obtained which is valid in the range 0 < β < π/2; this latter limitation is due to the character of the initial yield which depends on the magnitude of β. Numerical results for stresses and displacements are given in one case (β = π/4) for various positions of the elastic-plastic boundary.

Scaling of Solutions for the Lateral Buckling of Elastic-Plastic Pipelines

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Ralf Peek ◽  
Heedo Yun
Keyword(s):  
Finite Element ◽  
Analytical Solutions ◽  
Finite Element Solution ◽  
Reference Solution ◽  
Element Solution ◽  
Lateral Buckling ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
The Moment

Analytical solutions for the lateral buckling of pipelines exist for the case when the pipe material remains in the linearly elastic range. However for truly high temperatures and/or heavier flowlines, plastic deformation cannot be excluded. One then has to resort to finite element analyses, as no analytical solutions are available. This paper does not provide such an analytical solution, but it does show that if the finite element solution has been calculated once, then that solution can be scaled so that it applies for any other values of the design parameters. Thus the finite element solution need only be calculated once and for all. Thereafter, other solutions can be calculated by scaling the finite element solution using simple analytical formulas. However, the shape of the moment-curvature relation must not change. That is, the moment-curvature relation must be a scaled version of the moment-curvature relation for the reference problem, where different scale factors may be applied to the moment and curvature. This paper goes beyond standard dimensional analysis (as justified by the Bucklingham Π theorem), to establish a stronger scalability result, and uses it to develop simple formulas for the lateral buckling of any pipeline made of elastic-plastic material. The paper includes the derivation of the scaling result, the application procedure, the reference solution for an elastic-perfectly plastic pipe, and an example to illustrate how this reference solution can be used to calculate the lateral buckling response for any elastic-perfectly plastic pipe.

scholarly journals Eigenvibrations of a simply supported beam with elastically attached load

2018 ◽  
Vol 224 ◽  
pp. 04012 ◽  
Author(s):  
Anton A. Samsonov ◽  
Sergey I. Solov’ev ◽  
Pavel S. Solov’ev
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Eigenvalue Problem ◽  
Approximate Solutions ◽  
Uniform Grid ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Plates And Shells ◽  
The Finite Difference Method ◽  
Theoretical Results

The nonlinear differential eigenvalue problem describing eigenvibrations of a simply supported beam with elastically attached load is investigated. The existence of an increasing sequence of positive simple eigenvalues with limit point at infinity is established. To the sequence of eigenvalues, there corresponds a system of normalized eigenfunctions. To illustrate the obtained theoretical results, the initial problem is approximated by the finite difference method on a uniform grid. The accuracy of approximate solutions is studied. Investigations of the present paper can be generalized for the cases of more complicated and important problems on eigenvibrations of plates and shells with elastically attached loads.

Impulsive Loading of a Simply Supported Circular Rigid Plastic Plate

1968 ◽  
Vol 35 (1) ◽  
pp. 59-65 ◽  
Author(s):  
Norman Jones
Keyword(s):  
Yield Condition ◽  
Impulsive Loading ◽  
Bending Moments ◽  
Circular Plates ◽  
Governing Equations ◽  
Rigid Plastic ◽  
Static Loads ◽  
Simply Supported ◽  
Experimental Values ◽  
Theoretical Procedure

It is clear from a survey of literature on the dynamic deformation of rigid-plastic plates that most work has been focused on plates in which either membrane forces or bending moments alone are considered important, while the combined effect of membrane forces and bending moments on the behavior of plates under static loads and beams under dynamic loads is fairly well established. This paper, therefore, is concerned with the behavior of circular plates loaded dynamically and with deflections in the range where both bending moments and membrane forces are important. A general theoretical procedure is developed from the equations for large deflections of plates and a simplified yield condition due to Hodge. The results obtained when solving the governing equations for the particular case of a simply supported circular plate loaded with a uniform impulsive velocity are found to compare favorably with the corresponding experimental values recorded by Florence.

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