Dynamic Plastic Response Research Articles

Suggestion of a new dimensionless number for dynamic plastic response of beams and plates

A dimensionless number, termed response number in the present paper, is suggested for the dynamic plastic response of beams and plates made of rigid-perfectly plastic materials subjected to dynamic loading. It is obtained at dimensional reduction of the basic governing equations of beams and plates. The number is defined as the product of the Johnson's damage number and the square of the half of the slenderness ratio for a beam; the product of the damage number and the square of the half of the aspect ratio for a plate or membrane loaded dynamically. Response number can also be considered as the ratio of the inertia force at the impulsive loading to the plastic limit load of the structure. Three aspects are reflected in this dimensionless number: the inertia of the applied dynamic loading, the resistance ability of the material to the deformation caused by the loading and the geometrical influence of the structure on the dynamic response. For an impulsively loaded beam or plate, the final dimensionless deflection is solely dependent upon the response number. When the secondary effects of finite deflections, strain-rate sensitivity or transverse shear are taken into account, the response number is as useful as in the case of simple bending theory. Finally, the number is not only suitable to idealized dynamic loads but also applicable to dynamic loads of general shape.

Response and Failure of Ductile Circular Plates Struck by a Mass

A theoretical analysis is presented in this paper to predict the dynamic plastic response of aluminium alloy and mild steel circular plates when struck normally by blunt solid cylindrical masses at the center. Reasonable agreement is obtained with experimental results for the permanent transverse displacements. Different failure mechanisms, which have been found in previous experimental studies on aluminium alloy and mild steel plates, are also illustrated by the proposed theory.

Recent Studies on the Dynamic Plastic Behavior of Structures - An Update

This article contains a brief review of the literature, published since the previous Applied Mechanics Reviews article in 1989 [1], on the dynamic plastic response of basic structural members made from ductile metallic type materials. The external dynamic loads cause large inelastic strains in the structural members which dominate material elastic effects. Thus, the external dynamic energy is absorbed plastically and, generally speaking, produces large permanent deformations. This field of research is of interest for the structural crashworthiness and collision protection of land, sea and air transportation systems, as well as the design of energy absorbing systems, and provides vital input into safety calculations and hazard assessments throughout industry.

Dynamic plastic response of thin circular plates struck transversely by nonblunt masses

A theoretical analysis is presented which examines the dynamic plastic response of thin circular plates struck transversely by a mass with a conical head and a spherical nose at the centre of the plates. The analysis employs an interaction yield surface which combines the bending moment and membrane force required for plastic flow. Material strain rate sensitive effects are considered with the aid of the Cowper-Symonds equation and Perrone and Bhadra's approximation. Good agreement between the theoretical predictions and the experimental results has been obtained on the maximum permanent deflections and the maximum forces between striker and plates for various impact energies.

Deformation and failure of clamped beams under low speed impact loading

A quasi-static procedure is proposed herein for estimating the dynamic plastic response and failure of clamped metal beams subjected to low velocity impact at any point on the span by a heavy mass. Based on the principle of virtual work, load-displacement relationships are obtained. Failure maps are constructed by assuming that axial tensile and shear strains are independent parameters. To combine the influence of the axial and shear strains, an effective strain criterion is suggested for the rupture of the beams. It is found that the present theoretical predictions are in good agreement with experimental observations.

Failure Maps of Clamped Beams Under Impulsive Loading*

A previously proposed quasi-static procedure is adopted in this paper to estimate the dynamic plastic response and failure of clamped beams under uniformly distributed impulsive loading. Based on the principle of energy conservation and the assumption of equivalent work done, the problem of a beam under impulsive loading is analyzed through the solution of an identical beam subjected to an equivalent static load. It transpires that the present theoretical predictions are in good agreement with the experimental observations in terms of maximum permanent transverse displacements, failure modes, and the critical input impulses causing beam failure due to either tensile tearing or transverse shear.

Blast loading of fully clamped circular plates with transverse shear effects

The dynamic response of a fully clamped circular plate, which is made from a rigid, perfectly plastic material, is investigated with the aid of the extended Johansen yield criterion which retains the influence of the transverse shear force as well as the bending moments. Theoretical solutions are obtained for a general blast loading distributed uniformly over the entire area of a plate. The effects of different boundary conditions, pressure pulse loading shapes and the influence of the transverse shear force on the dynamic plastic response of circular plates are explored. It is found that Youngdahl's correlation parameters may be used to eliminate the effect of the pulse loading shape on the dynamic response of circular plates. The critical conditions are predicted for a transverse shear severance to occur at the supports of a circular plate (mode III failure) when transverse shear effects are retained in the yield condition. Theoretical predictions for the impulsive loading case are compared with the bound theorem predictions, which reveals that the lower bound results give good agreement with the corresponding theoretical results.

Experimental Investigation into the Dynamic Plastic Response and Perforation of a Clamped Circular Plate Struck Transversely by a Mass

An experimental investigation is reported on the dynamic response of a clamped circular plate struck transversely by a mass at any point along a radial line. A study is made of the variation of the failure mode with a change of striker diameter-plate thickness ratio, together with an assessment of transverse shear effects and the energy-absorbing capacity for impact velocities up to 12.2 m/s. The experimental results show that the steel and aluminium alloy targets fail by plugging with a plug having approximately the same diameter as the striker, which has a blunt end. The experimental results also show that the energy-absorbing capacity of a plate is reduced significantly when struck by a mass close to the supports compared to a strike at the centre and that the transverse shear force plays a more dominant role when a mass strikes close to the supports. A new criterion for the design of metal targets against projectile impact is proposed.

Analysis of Large Deflection Dynamic Response of Rigid‐Plastic Beams

This paper describes, how, by a new procedure called the membrane factor method, the dynamic response of rigid plastic impulsively loaded beams with deflection in the range in which bending moment and membrane force both are of importance, is analyzed. The analysis shows that the membrane factor method, which retains the effect of the membrane force induced by large deflection on energy dissipation, provides a simpler way to trace the large deflection dynamic plastic response of beams with end axial constraints, than the complicated conventional methods. The theoretical method can be applied to the large deformations of dynamically loaded rigid-plastic plates.

Dynamic plastic response and failure of a clamped beam struck transversely by a mass

A theoretical analysis is presented which examines the dynamic response of a rigid-perfectly plastic clamped beam struck transversely by a mass at any point on the span. The analysis employs an interaction yield surface which combines the bending moment, membrane force and transverse shear force required for plastic flow. Material strain rate sensitive effects are examined with the aid of the Cowper-Symonds equation. Good agreement is obtained between the theoretical predictions for the maximum permanent transverse displacements and the corresponding experimental results. An energy density failure criterion is used to predict the dynamic inelastic failure of this impact problem.

Dynamic response of a grillage under mass impact

An approximate theoretical analysis is presented in this paper for the dynamic plastic response of a clamped beam grillage when struck transversely by a mass at the centre which produces large transverse displacements. The theoretical rigid-plastic predictions are compared with some recent experimental results on grillages struck by large masses and the predictions of a quasi-static method of analysis. The influence of inertia is explored for the behaviour of a grillage when struck by a small striker travelling with a high velocity.

Dynamic response and failure of fully clamped circular plates under impulsive loading

An approximate theoretical analysis is presented which examines the dynamic plastic response and three failure modes of fully clamped circular plates subjected to uniformly distributed transverse impulsive loads. The rigid-plastic analysis employs an interaction yield surface which combines the bending moments, membrane force and the transverse shear force required for plastic flow and uses the Cowper-Symonds constitutive equation to cater for material strain rate effects. Good agreement is obtained between the theoretical predictions for permanent transverse deflections (failure mode 1) and the corresponding experimental results of Bodner and Symonds, and Teeling-Smith and Nurick recorded on strain rate sensitive plates. Correlation of a theoretical critical impulse to rupture with the corresponding experimental values of Teeling-Smith and Nurick was poor, possibly because the boundary conditions in the experiments were not ideally clamped, as assumed in the theory. Further experimental results are required which pay particular attention to the details of the clamped boundary conditions in the experimental tests when failure occurs due to tensile tearing (failure mode 2) or transverse shear (failure mode 3) at the supports.

The Optimal Mode and an Approximate Expression of Final Displacement in Dynamic Plastic Response of Structures

The paper is concerned with the dynamic response of impulsively loaded rigid-perfectly plastic structures. By combining the mode approximation technique with the upper and the lower bound theorems, we have derived a set of sequential inequalities on the final displacement of the structure. This can be applied to give a reasonable explanation for the criterion of choosing an optimal mode proposed by Symonds (1980). In addition, an approximate expression of the final displacement of the structure is suggested in cases where the “mode approximation” apparently works poorly. Finally, the suggested expression is also illustrated by examples.

The large deflection dynamic plastic response of rectangular plates

Summary By assuming a kinematically admissible, time-dependent velocity field and considering the global equilibrium of all the forces acting on each rigid segment during large deflection of a plate, a complete theoretical investigation is undertaken herein to trace the large deflection dynamic plastic response (including the transient phase) of simply-supported or fully-clamped rectangular plates. This procedure deduces two modifying factors ƒ1 and ƒ2 which reflect the effect of the membrane forces and are employed to formulate the governing equations in the case of large deflections. The present prediction of the final plate deflection coincides excellently with the corresponding experimental results for deflections up to 5–10 times the plate thickness. This theory greatly improves the estimates based on the bending-only theory and provides a new way to trace the transient phase of dynamically loaded plates when the effect of membrane forces is significant.

Impact response of a string-on-plastic foundation

Summary A complete analysis of the large deformation response of a plastic string resting on a plastic foundation and undergoing localized mass impact, is presented. The formulation is based on the conservation of linear momentum and the kinematic and dynamic continuity conditions on a moving wave front. A closed-form solution is obtained for the instantaneous velocity and deflection profiles as well as for the final permanent deformed shape of the string and the magnitude of the maximum central deflection. An approximate expression for the central deflection amplitude is also derived using the solution of the corresponding static problem. Finally, the string-on-foundation problem is related to the large deflection dynamic plastic response of a cylindrical shell subjected to mass impact. A parametric study is performed to assess the effect of the impacting mass, the impact velocity, and the shell parameters on the magnitude of the permanent displacements and deformed shape of the shell.

A Comment on the Low Speed Impact of a Clamped Beam by a Heavy Striker∗

ABSTRACT An approximate theoretical analysis is presented for a rigid, perfectly plastic clamped beam struck transversely at the mid-span by a mass which produces Finite transverse displacements. An alternative quasi-static procedure is proposed for estimating the dynamic plastic response of a beam when struck by a heavy mass that travels at a low speed. The theoretical basis of this method is explained and the accuracy is examined by an error analysis. Finally, it is suggested that this quasi-static procedure could be used for estimating the dynamic plastic response of other structures that are struck by a heavy mass traveling at a low speed,

Dynamic Plastic Response of Circular Plates With Transverse Shear

Dynamic Plastic Response of Circular Plates With Transverse Shear

Analysis of the large deflection dynamic plastic response of simply-supported circular plates by the “membrane factor method

Based on energy equilibrium, a new procedure called the Membrane Factor Method is developed to analyze the dynamic plastic response of plates with deflections in the range where both bending moments and membrane forces are important. The final deflection of a simply-supported circular rigid-plastic plate loaded by a uniformly distributed impulse is obtained. In comparison with other approximate solutions, the present results are found to be simpler and in better agreement with the corresponding experimental values reoorded by Florence.

The dynamic plastic response characteristics of circular beam

In this paper the problem of a circular beam subjected to radial impact by a rigid mass at its tip in its own plane is investigated on the basis of rigid-perfectly plastic assumption. The analytical solution of the particle velocities is obtained as the function of travelling plastic hinge location. By analysing the solution, some special properties of circular beam problem are found.

Dynamic plastic response of thin circular plates with transverse shear and rotatory inertia subjected to rectangular pulse loading

The dynamic response of a simply supported circular plate made of a rigid-perfectly plastic material is investigated when taking account of transverse shear, bending moments and rotatory inertia. Basic equations are established for an arbitrary loading case. Theoretical solutions are given for a rectangular shaped pressure pulse loading, and numerical results are presented which show the effects of transverse shear and rotatory inertia on the bending moment, transverse shear force and transverse displacement of circular plates.