A method for numerical solution of the dynamics equations of elastic media and structures

Abdukadyrov, S. A.; Pinchukova, N. I.; Stepanenko, M. V.

doi:10.1007/bf02498199

Cited by 11 publications

(14 citation statements)

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“…Comparing the numerical with known analytical [1-5] results and exact numerical [7,9] solutions for single obstacles showed that the greatest error in computing the pressure on an obstacle 1-3 in Fig. ib is realized in the case of a circular contour.…”

Section: Fz(t)--~(o~ C~ Z)dsmentioning

confidence: 82%

“…The features of its realization in probl~mg similar to those examined here are described in [7,9], where recommendations are presented on the utilization of different kinds of finite-difference approximations of the equations, the boundary conditions, and the selection of the parameter t o to minimize the numerical dispersion.…”

mentioning

confidence: 98%

“…The analytical solutions obtained here have a sufficiently complex structure and the possibility of investigating nonstationary processes by using the sununation of stationary components, as is done, say, in [5] for the comparatively simple problem of longitudinal step wave diffraction by the endface of a semiinfinite cylinder is problematical.There are a large number of investigations in which problems of nonstationary diffraction are solved by using numerical methods.The interaction of plane and spherical pressure waves with single obstacles of cylindrical shape is computed by the method of finite differences in [7][8][9].The mesh parameters and the difference approximation method for the equations were here selected in conformity with the method of minimizing the numerical dispersion [i0]. Plane nonstationary wave diffraction by a system of fixed cylinders and the motion of elastically coupled rigid cylinders in an acoustic medium were computed by an analogous method in [Ii,12].…”

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confidence: 99%

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Plane nonstationary wave diffraction by a system of rigid inclusions

Kurmanaliev¹

1985

Soviet Mining Science

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In estimating the action of explosive and seismic waves on underground workings, structure foundations, and other fixed or deformable obstacles, it is necessary to compute the perturbations from which the integral parameters of the action are formed, the force in the direction of wave motions and its impulse.For a number of problems of nonstationary wave interaction with single obstacles of simple geometric shape there are analytical solutions [1-6] which can be utilizedin practical computations.Problems of plane longitudinal and shear wave diffraction by systems of circular cavities and inclusions are considered only in a stationary formulation [4,5]. The analytical solutions obtained here have a sufficiently complex structure and the possibility of investigating nonstationary processes by using the sununation of stationary components, as is done, say, in [5] for the comparatively simple problem of longitudinal step wave diffraction by the endface of a semiinfinite cylinder is problematical.There are a large number of investigations in which problems of nonstationary diffraction are solved by using numerical methods.The interaction of plane and spherical pressure waves with single obstacles of cylindrical shape is computed by the method of finite differences in [7][8][9].The mesh parameters and the difference approximation method for the equations were here selected in conformity with the method of minimizing the numerical dispersion [i0]. Plane nonstationary wave diffraction by a system of fixed cylinders and the motion of elastically coupled rigid cylinders in an acoustic medium were computed by an analogous method in [Ii,12].Problems of the nonstationary interaction of a plane longitudinal wave with a system of fixed inclusions of distinct geometry are investigated below. On the boundary of an inhomogeneous half-plane z ~ 0 let there be given a normal pressure whose amplitude increases linearly from zero to o 0 in the time t = to, and then remains constant.The inhomogeneity is determined by the presence of a regular system of fixed inclusion with peripheral shape symmetric with respect to the z axis and with centers of gravity on the line z = s Let us use the notation:

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Section: Fz(t)--~(o~ C~ Z)dsmentioning

confidence: 82%

mentioning

confidence: 98%

mentioning

confidence: 99%

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Plane nonstationary wave diffraction by a system of rigid inclusions

Kurmanaliev¹

1985

Soviet Mining Science

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“…Ya. Sagomoyan [2] is devoted to problems of solid bodies penetrating into liquid and soil. An original method, based on the construction of kinematically possible fields for strain rates, in order to determine the forces of resistance to penetration while introducing hammers into plastic media, is presented in [3].…”

Section: Penetration Of An Axlsymmetric Conical Hammer Into Frozen Somentioning

confidence: 99%

“…The irreversibility of soil deformations during the introduction of hammers was considered in [2,5], in which a close approximation was adopted...it was assumed that a plastic medium behind the shock wave front is deformed to some density which is a constant value, independent of the amplitude of the shock wave. Such an approximation permits an analytic solution to the problem to be derived, but for comparatively small initial hammer speeds, when the bulk deformation of the soll is highly dependent upon load application, this is a rather rough estimate.…”

Section: Penetration Of An Axlsymmetric Conical Hammer Into Frozen Somentioning

confidence: 99%

Evolution of a shock pulse during its propagation over composite elastic systems

Stepanenko¹,

Tsareva²

1987

Soviet Mining Science

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Utilization of idealized homogeneous models in the analysis of dynamic processes of impact-actlon machines or in studying wave propagatlon in laminar media and composite material results in rough estimates whose limits of applicability are constrained substantially in the case of rigid effects (and for rigid systems).If problems of nonstationary wave processes in homogeneous elastic media and structures have an ancient history and have been studied ~aell enough (see [i, 2], say), then solutions for structural models are based on numerical methods and have been obtained for specific structures, which does not permit analysis of the general laws inherent to wave processes in systems of similar construction.In the partlchlar case when a real structure can be modeled by a periodic system, an analytic solution has successfully been obtained for the longwave component which is fundamental in the sense of impact energy transfer.The purpose of this paper is to clarify the nature of the change in the initial perturbation during its propagation over composite elastic systems of periodic structure and to estimate the applicability of the results obtained to describe longwave perturbations in systems with spoiled structure.The model of a one-dlmenslonal wavegulde ordinarily used in the analysis of impulse propagation over extended structural elements can be made complicated by imparting to it a structure with characteristic parameters (length, mass, stiffness). The number of such parameters in models of regular configuration can be small, which simplifies the analysis of the mechanical effects.The simplest such model is a rod with stiffly or elastically attached masses [3], a pln-polnt system with local stiffnesses [4], a pin-joint system with transverse connections [5], a cylindrical shell with stringers [6] (this latter model is carried out in the dynamics of structures from the theory of deformation of a unidirectional composite material [7][8][9]). The listed systems combine the fact that the element comprising the period is itself homogeneous but the inhomogeneity (mass, stiffness) is contained at the junctures.Periodic systems containing plecewise-homogeneous elements along both the length and in the transverse direction are considered below. Examples of such systems are represented in Figs. i and 2: a cylindrical shell with stringers and frames (Fig. la), and a laminar medium (Fig. 2a). This latter was used extensively in seismological problems, where mainly the dispersion properties of such systems and the dynamics of composites were investigated. Under a longitudinal impulse action and relatively large radial stiffness of the frames, the radial shell vibrations can be neglected as compared with the longitudinal and the deformation of a doubly periodic plate with a longitudinal-transverse set (Fig. ib) can be considered. The model of a laminar medium with identical acoustic resistances (0,c, : 02c=) corresponds to a rod of plecewlse-homogeneous construction (Fig. 2b).In this paper by using integral transforms with su...

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Nonsteady oscillations of a thin rod in an elastic half space

Yungerman

1991

J Appl Mech Tech Phys

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A method for numerical solution of the dynamics equations of elastic media and structures

Cited by 11 publications

References 1 publication

Plane nonstationary wave diffraction by a system of rigid inclusions

Plane nonstationary wave diffraction by a system of rigid inclusions

Evolution of a shock pulse during its propagation over composite elastic systems

Nonsteady oscillations of a thin rod in an elastic half space

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