Rigid-plastic Cylindrical Shell Research Articles

Optimization of plastic cylindrical shells with stepwise varying thickness in the case of von Mises material

The problems of the optimization of rigid-plastic cylindrical shells are studied under the condition that the shell wall thickness is piece-wise constant. It is assumed that the deflections of the shell are moderately large and the material obeys the von Mises yield condition and the associated deformation law. The optimization problem is posed as an optimal control problem and necessary optimality conditions are derived with the aid of the variational methods of optimality theory. The set of equations obtained is solved numerically. An example regarding the minimization of the central deflection of the shell with two steps in the thickness is presented.

The impact torsional buckling for the rigid plastic cylindrical shell

By using the energy criterion in[3], the impact torsional buckling for the rigid plastic cylindrical shell is studied. The linear dynamic torsional buckling equations for the rigid plastic shell is drived, and the critical impact velocity is given.

Optimal design of rigid-plastic cylindrical shells in the post-yield range

An optimal design technique is developed for rigid-plastic cylindrical shells subjected to a distributed transverse pressure and a specified axial load. Moderately large deflections are taken into account and a deformation-type theory of plasticity is employed. The optimal design procedure results in a unified approach to optimization in the post-yield range. Necessary conditions for optimality are established by the aid of variational methods of the optimal control theory. Two examples are presented: (1) the optimal layout of rigid circular supports (stiffeners) is found which minimizes the mean deflection; (2) the optimal thickness distribution of a sandwich shell is established which corresponds to the minimum material consumption requiring the deflection of the design coinciding with that of the constant thickness shell.

Parametrical optimization of plastic cylindrical shells in the post-yield range

An optimal design technique is developed for rigid-plastic cylindrical shells accounting for the moderately large deflections. The study is confined to sandwich shells subjected to the axial dead-load and to the internal pressure loading. The optimization problem is posed in the parametrical form, the parameters being certain constant quantities which should specify the internal load distribution as well as cross-sectional dimensions of the shell or it support positions. Necessary optimality conditions are established using the variational methods of the optimal control theory. As an example the optimal layout for a set of the rigid circular supports (stiffeners) is stated.

Supporting power and optimal design of rigid plastic cylindrical shells

evident that ~.~=l. In the general case the ideal stiffly plastic material of each layer t=1 is characterized by a yield stress of oiunder tension and~is i under compression. In addition, the layers and the contact surfaces of the layers allow plastic shear if the tangential stresses in them reach the value T~ of the shear yield stress. The edges of the shell are hinged. The transverse load is unmformiy distributed over the perimeter of the annular cross section (Fig. I).

Optimal Design of Plastic Cylindrical Shells with Additional Supports

The problem of optimal location of an additional support for a rigid-plastic cylindrical shell is considered. The shell is subjected to the action of the uniform rectangular transverse impulse. Material of the shell is assumed to obey to the approximate square yield condition and the associated flow law. The problem is treated as a special distributed parameter problem, where bending moment, shear force, transverse deflection and deflection rate are considered as state variables. The state variables are assumed to be continuous in certain subregions but the discontinuities are allowed on the boundaries of these subregions.Necessary optimality conditions are derived with the aid of variational methods of the optimal control theory. It is shown that two different optimality criteria lead to the same location of the additional support.

The Directional Moment in the Buckling of Rigid-Plastic Cylindrical Shells

A change in direction of the plastic strain rate vector accompanies the growth of a perturbation in plate and shell buckling when a yield locus with a continuously turning tangent is used. A directional moment results which has been found to have a strong influence on the mode selection. A perturbation analysis of the axi-symmetric buckling of an axially compressed rigid-plastic cylindrical shell taking account of this effect is presented in a form particularly suited for quasi-static buckling. The approach leads to a simple analytic solution which illustrates directly features of plastic buckling noted previously only in numerical solutions. It is concluded that the change in direction of the plastic strain rate vector is an essential part of plastic buckling, especially in moderately thick plates and shells which show little buckling deformation until loaded well past the yield point.

Behavior of a rigid-plastic cylindrical shell under an external pressure pulse

1. A short shell under moderate load is deformed into a frustum of a cone. 2. A long shell under moderate load also has the shape of a frustum of a cone in the acceleration stage, but in the deceleration stage the shell is divided into two parts by a moving hinge region: the zone between the fixed and hinge regions gradually escapes from the deformation process and the other zone continues in motion in the form of a frustum of a cone. 3. A short shell under heavy load consists in the acceleration stage, of two frustums of a cone separated by a fixed hinge region; in the deceleration stage, the shape of the shell is maintained up to a definite time, but the hinge region, gradually decelerating, moves to the free end of the shell until it stops and the generator becomes straight; at the end of the process, the shell has the shape of a frustum of a cone. 4. A long shell under heavy load is deformed just like a short shell in the acceleration stage, but in the deceleration stage its shape is the same only for certain values of shell dimension and of deformation time.

The Influence of Large Deflections on the Behavior of Rigid-Plastic Cylindrical Shells Loaded Impulsively

A theoretical investigation is herein undertaken in order to examine the response of circular cylindrical shells subjected to dynamic loads of an intensity sufficient to cause large permanent deformations. The shell material is assumed to be rigid, perfectly plastic and the influence of finite deflections is retained in the governing equations. It emerges clearly from the study that geometry changes influence markedly the shell behavior even for quite small deflections and, therefore, they should be retained in any dynamic analyses of cylindrical shells with axial restraints.

How to design rigid-plastic cylindrical shells for combined loading

How to design rigid-plastic cylindrical shells for combined loading

Large deflections of rigid-plastic cylindrical shells under axial tension and external pressure

Using Tresca's yield condition and the associated flow rule, axis-symmetric modes of deformation for sandwich-type cylindrical shells with simply supported ends are studied. The shell under observation is loaded with external pressure and with a prescribed constant tensile end-load. Deflections may be of the same order as the thickness of the shell. Within the limits of the concept of a rigid-plastic body, exact and closed-form solutions are found. The applicability of the solutions obtained depending on the shell length and the end-load value is discussed. The elastic-plastic problem is resolved for shells without an end-load. It turned out that considerable plastic deformations developed in the shell already under a load corresponding to a transition from the pure elastic state to the elastic-plastic one. This fact is compared with some experimental data available.

Dynamic loading of rigid-plastic cylindrical shells

T he behaviour of an infinitely long, rigid-plastic cylindrical shell under impulsive loading by a ring of concentrated force and a band of uniform pressure is discussed. The loads are assumed to be greater than the statical collapse values and to act for a short period of time. Numerical results are obtained for rectangular and triangular pulse shapes for the ring of force and for a rectangular pulse shape for a band of uniform pressure. In the final section of the paper, the steady-state motion which would be produced by a constant load greater than the statical value moving along the shell with constant velocity is obtained for the particular cases of a ring of force and a band of uniform pressure.

Impact pressure loading of rigid-plastic cylindrical shells

The collapse load of a rigid-plastic body is defined as the smallest load at which deformations become possible. If a load greater than the collapse load is applied, the material of the body will undergo accelerated plastic flow. The present report considers a rigid-plastic cylindrical shell, loaded for a short time with a pressure greater than the collapse load. It is found that the shell is still specified by a single parameter depending on its dimensions, and that four different types of solution exist depending upon whether the load is “medium” of “high”, and the shell is “short” or “long”. Expressions for the stresses, velocities, and displacements are found in each case, and typical results are presented graphically.