Dynamic deformation of rigid-plastic curvilinear plates of variable thickness

A general solution is obtained for the problem of dynamic bending of an ideal rigid-plastic plate of variable thickness with a simply supported or clamped curvilinear contour under the action of a short-time high-intensity explosive-type load uniformly distributed over the surface. Several mechanisms of plate deformation are demonstrated to exist. For each mechanism, equations of dynamic deformation are derived and conditions of mechanism implementation are analyzed. Examples of numerical solutions are given. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 108–120, September–October, 2007.     

Bending of a stretched plate containing an eccentrically plate reinforced hole of arbitrary shape

In this paper we consider the problem of a stretched plate containing a hole of arbitrary shape which is reinforced by thickening the plate, on one side only, in a region surrounding the hole. Due to the eccentricity of the reinforcement a bending boundary layer occurs in the neighbourhood of the junction between the plate and the reinforcement. The equations for the moments at the junction are found to be identical to those for the circular hole in Ref. [1]. The boundary layer occurring at a clamped edge of arbitrary shape is also discussed.     

Vibro-acoustic behavior of an isotropic plate with arbitrarily varying thickness

This paper presents numerical simulation studies on the vibro-acoustic characteristics of an isotropic square plate with six different types of unidirectionally, arbitrarily varying thickness. Finite Element Method (FEM) is used to predict the free and forced vibration characteristics while Boundary Element Method (BEM) is used to predict the sound radiation characteristics. It is found that influence of taper ratio on mode shapes are significant. The resonant amplitude is influenced by changes in mode shapes along with excitation location. The influence of taper ratio and excitation location is significant on overall sound power level except for increasing-decreasing thickness variation. It is found that resonant amplitude and overall sound power level behavior is same for both linear and parabolic variation.     

Stress intensity factors of a plate with two cracks emanating from an arbitrary hole

In this paper, Muskhelishvili complex function theory and boundary collocation method are used to calculate the stress intensity factors (SIF) of a plate with two cracks emanating from an arbitrary hole. The calculated examples include a circular, elliptical, rectangular, or rhombic hole in a plate. The principle and procedure by the method is not only rather simple, but also has good accuracy. The SIF values calculated compare very favorably with the existing solutions. At the same time,the method can be used for different finite plate with two cracks emanating from a hole with more complex geometrical and loading conditions. It is an effective unified approach for this kind of fracture problems.     

Modeling of dynamic deformation of rigid-plastic doubly connected plates with arbitrary fixed curvilinear contours on a viscoelastic foundation

A general solution is obtained for the problem of dynamic bending of an ideal rigid-plastic doubly connected plate with arbitrary simply supported or clamped curvilinear contours subjected to short-time high-intensity explosive dynamic loading uniformly distributed over the surface. The plate rests on a viscoelastic foundation. It is demonstrated that there are several mechanisms of plate deformation. Equations of dynamic deformation are derived for each mechanism, and implementation conditions are analyzed. Numerical examples are given.     

Pressing a rigid-plastic strip through a curvilinear matrix channel

We develop a model that describes pressing a rigid-plastic strip through a curvilinear matrix channel; this model takes into account the material strengthening, the gap between the strip and the matrix channel, and the contact friction. We present examples of computations of the strip pressing through channels of various shapes. The model imitates the technological processes of a thin strip bending by pressing it through a curvilinear matrix channel.     

Finite expansion of a hole in an elastic-plastic thin plate of finite thickness

A finite deformation theory for axially symmetric thin elastic-plastic plates is obtained by a consistent approximation from the corresponding three-dimensional theory. This theory can be applied to plates of finite thickness, and is different from the usual plane stress theory. The problem of the expansion of a circular hole in an infinite plate is investigated and the effect of the transversely variable stress components is studied.     

Free vibrations of an isotropic nonhomogeneous infinite plate of linearly varying thickness

Summary The free transverse vibrations of an isotropic nonhomogeneous infinite plate of variable thickness have been studied on the basis of classical plate theory. The governing differential equation of motion has been solved by Frobenius method by expressing the transverse displacement as an infinite series. The frequencies corresponding to the first two modes of vibration are computed for different values of thickness variation constant, nonhomogeneity parameter, and different combinations of boundary conditions.

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Sommario Viene considerato il problema delle vibrazioni flessionali libere di una lastra infinita, isotropa, non omogenea, di spessore variabile. L'equazione del moto è stata risolta col metodo di Frobenius, esprimendo lo spostamento mediante sviluppo in serie. Sono state calcolate le prime due au to frequenze per varie combinazioni delle condizioni ai limiti e per differenti valori dei parametri caratteristici della variazione di spessore e della disomogeneità.

     

On the stress distribution in a spherical shell with an off-center curvilinear hole

A numerical analysis is made of the joint effect of two factors of asymmetry—ellipticity and eccentricity—on the stress distribution near a free hole in a spherical shell. The nature of deformation is determined by the predominant factor. Whether there are “fixed” points on the graphs of stress distribution around a small hole at which they intersect depends on how rigidly the outer edge is fixed. As the rigidity of fixation is increased, the points smear __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 113–118, January 2006.     

Wave field in a rectangular plate with an off-center hole

Kazakh Institute of Chemical Technology, Chimkent. Translated from Prikladnaya Mekhanika, Vol. 26, No. 5, pp. 76–81, May, 1990.