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.

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.

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.

Impact With Finite Acceleration Time of Elastic and Elastic-Plastic Beams

1956 ◽  
Vol 23 (3) ◽  
pp. 411-415
Author(s):  
R. C. Alverson
Keyword(s):  
Plastic Deformation ◽  
Cross Section ◽  
Plastic Hinge ◽  
Small Time ◽  
Steel Beams ◽  
Time Interval ◽  
Transverse Impact ◽  
Rigid Plastic ◽  
Elastic Plastic ◽  
Small Time Interval

Abstract The purpose of the work described in this paper was to provide information on the elastic and plastic deformation of steel beams subjected to transverse impact. The particular impact problem treated was chosen to correspond to conditions in tests in which a beam initially at rest is struck by a massive hammer, so that a specified change of velocity is imposed at a certain cross section in a small time interval. In the present analysis the initial elastic and subsequent elastic-plastic motions were obtained by methods similar to those used by Bleich and Salvadori (3). As in (3), it is assumed that plastic deformation occurs only at a single stationary plastic hinge (in this case at the struck cross section). Results obtained are compared with those of a “rigid-plastic” solution of the same problem, in which plasticity conditions are correctly taken into account but elastic vibrations are not included.

scholarly journals Modelling of elastic-plastic behavior of cables

2018 ◽  
Vol 174 ◽  
pp. 03001
Author(s):  
Oleksandr Shimanovsky
Keyword(s):  
Cross Section ◽  
Material Behavior ◽  
Structural Systems ◽  
Plastic Behavior ◽  
Rigid Plastic ◽  
Limit Values ◽  
Plastic Deformations ◽  
Linear Hardening ◽  
Elastic Plastic ◽  
Deflected Mode

The paper describes general calculation theory and elasticplastic behavior of cables - bearing elements of suspension structural systems. It is mentioned that this theory is based almost on the same assumptions as the theory of cable calculation at behavior of material in elastic range, excluding additional supposition in the part of idealization of real dependence between stresses and deformations on account of difficulties with using the latter in actual structures design. For that reason, this dependence is replaced with a model in the form of analytic curve or, as it is accepted to say in this case, a diagram, which is built according to some simple mathematic rule, reflecting element behavior conditions and characteristics of its material. It is stated that four main models of material behavior are used in practice: elastic-plastic, elastic-plastic with linear hardening, rigid-plastic and rigid-plastic with linear hardening. Conditions of occurrence of plastic deformations in all behavior stages of cable cross section are determined. Interrelations for geometrically and physically nonlinear task of the cable at active loading are provided. Methods are given and limit values of loads acting on the cable are determined. Equations defining parameters of cable deflected mode in all deformation phases and conditions of changing phases of cable behavior are given.

scholarly journals The Power Losses in Cable Lines Supplying Nonlinear Loads

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1374
Author(s):  
Bartosz Rozegnał ◽  
Paweł Albrechtowicz ◽  
Dominik Mamcarz ◽  
Monika Rerak ◽  
Maciej Skaza
Keyword(s):  
Bessel Function ◽  
Cross Section ◽  
Power Loss ◽  
Sine Wave ◽  
Active Power ◽  
New Method ◽  
Power Losses ◽  
Nonlinear Loads ◽  
Current Harmonics ◽  
Cable Lines

This paper presents the skin effect impact on the active power losses in the sheathless single-core cables/wires supplying nonlinear loads. There are significant conductor losses when the current has a distorted waveform (e.g., the current supplying diode rectifiers). The authors present a new method for active power loss calculation. The obtained results have been compared to the IEC-60287-1-1:2006 + A1:2014 standard method and the method based on the Bessel function. For all methods, the active power loss results were convergent for small-cable cross-section areas. The proposed method gives smaller power loss values for these cable sizes than the IEC and Bessel function methods. For cable cross-section areas greater than 185 mm2, the obtained results were better than those for the other methods. There were also analyses of extra power losses for distorted currents compared to an ideal 50 Hz sine wave for all methods. The new method is based on the current penetration depth factor calculated for every considered current harmonics, which allows us to calculate the precise equivalent resistance for any cable size. This research is part of our work on a cable thermal analysis method that has been developed.

scholarly journals Finite Pure Plane Strain Bending of Inhomogeneous Anisotropic Sheets

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 145
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Yeong-Maw Hwang
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
Large Strains ◽  
Rigid Plastic ◽  
Plastic Properties ◽  
Elastic Plastic ◽  
Starting Point ◽  
The Difference ◽  
Inside Radius ◽  
Elastic Unloading

The present paper concerns the general solution for finite plane strain pure bending of incompressible, orthotropic sheets. In contrast to available solutions, the new solution is valid for inhomogeneous distributions of plastic properties. The solution is semi-analytic. A numerical treatment is only necessary for solving transcendent equations and evaluating ordinary integrals. The solution’s starting point is a transformation between Eulerian and Lagrangian coordinates that is valid for a wide class of constitutive equations. The symmetric distribution relative to the center line of the sheet is separately treated where it is advantageous. It is shown that this type of symmetry simplifies the solution. Hill’s quadratic yield criterion is adopted. Both elastic/plastic and rigid/plastic solutions are derived. Elastic unloading is also considered, and it is shown that reverse plastic yielding occurs at a relatively large inside radius. An illustrative example uses real experimental data. The distribution of plastic properties is symmetric in this example. It is shown that the difference between the elastic/plastic and rigid/plastic solutions is negligible, except at the very beginning of the process. However, the rigid/plastic solution is much simpler and, therefore, can be recommended for practical use at large strains, including calculating the residual stresses.

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