Plastic Deformation of Semi-Infinite Beams Subject to Transverse Impact Loading at the Free End

1956 ◽  
Vol 23 (2) ◽  
pp. 239-243
Author(s):  
M. F. Conroy
Keyword(s):  
Plastic Deformation ◽  
Impact Loading ◽  
Constant Velocity ◽  
Bending Moment ◽  
Transverse Force ◽  
Square Root ◽  
Transverse Loading ◽  
Transverse Impact ◽  
Velocity Impact ◽  
Time Part

Abstract The object of this paper is to consider the plastic deformation of semi-infinite beams subject to dynamic transverse loading at the free end. The type of loading considered is that of a constant bending moment, together with a transverse force the magnitude of which is inversely proportional to the square root of time. Part 1 of the paper consists of a plastic-rigid analysis of the problem, based on the plastic-rigid analysis of infinite beams under transverse, constant velocity, impact loading developed by the author. Part 2 of the paper consists of an elastic-plastic solution of the problem, based on a theoretical analysis of the plastic deformation of infinite beams subject to transverse, constant-velocity impact loading developed by H. F. Bohnenblust. Specific problems are considered for which the deflection solutions obtained by elastic ideally plastic and rigid ideally plastic analyses are compared.

The Behavior of Long Beams Under Impact Loading

1950 ◽  
Vol 17 (1) ◽  
pp. 27-34
Author(s):  
P. E. Duwez ◽  
D. S. Clark ◽  
H. F. Bohnenblust
Keyword(s):  
Plastic Deformation ◽  
Cross Sections ◽  
Constant Velocity ◽  
Bending Moment ◽  
Infinite Length ◽  
Longitudinal Impact ◽  
Deflection Curve ◽  
Transverse Impact ◽  
Cold Rolled ◽  
Annealed Copper

Abstract This paper presents the results of a theoretical and experimental investigation of the plastic deformation of long beams which are subjected to a concentrated transverse impact of constant velocity. In the theoretical analysis, the beam is supposed to be of infinite length, and plane cross sections are assumed to remain plane. The bending moment is assumed to depend on the curvature according to a function that is obtained from the stress-strain curve of the material. The theory neglects both the lateral displacement of the cross sections against each other due to the shearing force and the rotary kinetic energy of the motion of the beam. The theory shows that a strain is not propagated along a beam at constant velocity, as in the case of longitudinal impact. The strain depends on the ratio between the square of the distance from the point of impact and the time. This is correct regardless of the shape of the moment - curvature curve. If certain approximations are applied to the bending moment - curvature curve, the theory provides a method of computing the deflection curve of a beam at any instant during impact. An experimental study has been made in which the deflection curves of long simply supported beams have been obtained during impact. The deflection characteristics of a cold-rolled steel and an annealed-copper beam have been computed by approximating the bending moment - curvature curves. It is shown that for materials such as cold-rolled low-carbon steel, for which plastic deflection is localized at the point of impact, the observed deflection curve is closely approximated by computing a curve based on the assumption that the beam remains elastic. For a soft material like annealed copper, plastic deformation extends over a relatively large distance from the point of impact and, taking plastic deformation into account, a satisfactory agreement is obtained between theory and experimental results.

scholarly journals Analytical Solutions to Predict Impact Behaviour of Stringer Stiffened Composite Aircraft Panels

2021 ◽  
Author(s):  
A. Chao Correas ◽  
A. Casares Crespo ◽  
H. Ghasemnejad ◽  
G. Roshan
Keyword(s):  
Impact Loading ◽  
Variable Stiffness ◽  
Impact Response ◽  
Low Velocity Impact ◽  
Analytical Models ◽  
Transverse Impact ◽  
Low Velocity ◽  
Mass System ◽  
Stiffened Panels ◽  
Velocity Impact

AbstractThis paper aims to develop an analytical method to predict the low-velocity impact response of simply supported stringer stiffened panels. Since the combination of stringer and panel provides aircraft structure with variable thicknesses, significant mathematical modelling is required to predict the transverse impact response of this type of designs. Within this analysis, the effect of variable stiffness distribution due to the stringer presence has been included. The performance of various layups is investigated to find the most suitable combination for panel-stringer laminate under impact loading. Analytical models were developed based on a spring-mass system to predict the dynamic behaviour of the striker-plate domain and, finally, determine the contact force history, which shows the main novelty of this research. Compared with Finite Element results, the model developed proved to successfully predict stringer stiffened composite panels' response with a range of layups and geometry designs under low-velocity impact loading conditions. The analytical results agree with the available data in the literature, and the error is less than 5%.

Plastic-Rigid Analysis of Long Beams Under Transverse Impact Loading

1952 ◽  
Vol 19 (4) ◽  
pp. 465-470
Author(s):  
M. F. Conroy
Keyword(s):  
Impact Loading ◽  
Bending Moment ◽  
Large Strains ◽  
Transverse Impact ◽  
Plastic Bending ◽  
Elastic Plastic ◽  
Straight Line ◽  
Probable Form ◽  
Constant Yield ◽  
Elastic Strains

Abstract The object of this paper is to set forth the results of an investigation of the behavior of long beams under transverse, constant-velocity impact loading, when a plastic-rigid type of analysis is adopted. It was expected that such an analysis would be satisfactory for problems involving large strains, and easier to evaluate than the corresponding elastic-plastic solution. Consideration is first given to the case of ideal plasticity. Elastic strains are neglected and the material of the beam is assumed to flow plastically at a constant yield limit. In this case expressions for the bending moment, shear force, curvature and deflection distributions along the beam are obtained analytically for any given impact velocity. The manner in which the solution for a beam having an elastic-ideally plastic bending moment-curvature relationship converges to the plastic-rigid solution, as EI increases, is discussed. Consideration is next given to the case of work-hardening where the material is assumed to obey a plastic-rigid bending moment-curvature relationship consisting of a straight line with nonzero slope. Unfortunately, difficulty arises in finding a solution analytically in this case. However, by considering the solution for a beam having the corresponding elastic-plastic bending moment-curvature relationship and a large EI-value, some speculation as to the probable form of the solution may be made.

On the Effect of Shear on Plastic Deformation of Beams Under Transverse Impact Loading

1960 ◽  
Vol 27 (1) ◽  
pp. 107-110 ◽  
Author(s):  
B. Karunes ◽  
E. T. Onat
Keyword(s):  
Impact Loading ◽  
Pure Shear ◽  
Bending Moment ◽  
Transverse Impact ◽  
Rigid Plastic ◽  
Inertia Effects ◽  
Interaction Diagram ◽  
Shear Effects ◽  
The Impact ◽  
Special Case

The impact problem for a rigid-plastic beam is formulated by using an interaction curve relating shearing force and bending moment for fully plastic action, and allowing for shear and rotary inertia effects. Using a simplified interaction diagram, the problem of point-impact loading is solved for a special case. The analysis shows that the shear effects are of considerable importance when the parameter μ0 = 2Q0l/M0 is less than 20 where Q0 and M0 are plastic-carrying capacities of the cross section for pure shear and bending, respectively, and 21 is the length of the beam.

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