Reaction of a three-layer hydroelastic cylindrical shell to an axisymmetric internal explosion

Belov, A. I.; Kornilo, V. A.; Pinchukova, N. I.; Stepanenko, M. V.

doi:10.1007/bf00911137

Cited by 3 publications

(5 citation statements)

References 5 publications

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“…Our aim is to construct such a difference scheme for the discrete analog of eqn ( 5) so that its dispersion relation would be as close as possible to relation (6). The MDM approach" helps to achieve this goal.…”

Section: Dispersive Waveguidesmentioning

confidence: 99%

“…The studies of the MD in initial-boundary problems have a long-standing history and extensive literature beginning with classical works [1]- [4]. The present study is the further development of the so-called Mesh Dispersion Minimization (MDM) procedure in the explicit finite difference algorithms originally presented in [5] and then used in calculations of diverse range of practical engineering problems in [6]- [11].…”

Section: Introductionmentioning

confidence: 99%

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Mesh Dispersion Minimization Algorithms Within Explicit Finite-Difference Schemes to Calculate Transient Wave Processes in Elastic Media and Composite Structures

Abdukadirov

2021

Computational Methods and Experimental Measurements XX

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Precise calculation of wave fronts and high-gradient components is always of utmost importance for problems of numerical simulation of wave processes in media and composite structures. The usage mesh algorithms come across specific obstacles, which do not allow to accurately calculate such disturbances localized at the loading area or propagated with time. One of such obstacles (notably in the problems with singularities) is the spurious effect caused by the mesh dispersion responsible for the emergence of high-frequency "parasite" oscillations damaged the computer solution. In this work, advanced numerical algorithms within the explicit finite-difference scheme are developed exactly for very purpose -to precisely calculate wave processes with singularities. The algorithms are constructed with the condition that dependence domains are the same (or maximally closed) in differential and difference equations corresponding to continual and discrete models, respectively. In the designed algorithms, the influence of spurious effects of numerical dispersion is suppressed (or essentially minimized) that allows discontinuities in fronts and high-gradient components to be accurately calculated. A set of examples of computer simulations of linear and nonlinear wave processes are presented. Among them are (a) impact propagation in a waveguide resting on an elastic foundation, (b) cylindrical and spherical waves, and (c) wave propagation and fracture pattern in a unidirectional composite. Comparison of results calculated by conventional and developed algorithms clearly shows the advantage of the latter. To this end, precise numerical solutions (in mesh points of the discrete space) are obtained for the problems listed above.

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Section: Dispersive Waveguidesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mesh Dispersion Minimization Algorithms Within Explicit Finite-Difference Schemes to Calculate Transient Wave Processes in Elastic Media and Composite Structures

Abdukadirov

2021

Computational Methods and Experimental Measurements XX

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“…We compare the results of the solution of non-stationary problems. For this purpose, as previously, we add zero initial conditions to equations (14), (16) and (20) for a semi-infinite system ) 0 ( ≥ x , and choose the effect of step-wise stress,…”

Section: Longitudinal Waves In a Thin Rod Embedded Into Elastic Mediummentioning

confidence: 99%

“…-dynamic fracture of media [10,11,25,28,30], -pulses and vibrations propagation over structural elements [12,[15][16][17][18][22][23][24], -non-stationary hydroelasticity of shells at an internal explosion [12,16,31], -vibrostability of components of impact machines [18], -seismic waves interaction with elastic and rigid obstacles [21,22], -impact pile driving into soil [23], -collisions of solids [26], -high-velocity penetration of a projectile into a target [24,27,29,34], -seismic waves propagation in blocked rocks [17,32,33]. Along with finite-difference algorithms, finite-element ones were also studied [35,36] as well as a hybrid circuit with spectral elements [37].…”

mentioning

confidence: 99%

“…The requirement of convergence of the domains of dependence (CDD) is formulated below as a condition allowing ND minimization. Note that the NDM principle was originally formulated as a requirement of coincidence of the solutions of dispersion equations of the continual and discrete models in [9] and in subsequent papers [10][11][12][13][15][16][17][18][19][20][21][22][23], where numerical simulation of various non-stationary problems (including geodynamic ones) was performed using NDM. In linear one-dimensional problems, NDM and CDD principles are equivalent, as shown below.…”

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confidence: 99%

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Numerical simulation of shock-wave processes in elastic media and structures. Part I: Solving method and algorithms

et al. 2012

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Finite-difference algorithms for solving non-stationary wave problems are presented, which allow to obtain the description of fronts and front zones with a minimal influence of spurious effects of numerical approximation. The principal condition of the construction of calculation algorithms is the convergence of domains of dependence of continual and difference equations. It is shown that the fulfillment of this condition provides a maximally exact wave fronts description. Numerical solutions of several one-dimensional and two-dimensional wave problems are presented. In the second part of the paper, we will give examples of numerical simulation of applied problems of structure dynamics and geodynamics -impact driving of piles into the soil, formation of pendulum waves in a block massif, stress state of a homogeneous massif in the zone of interaction with a punch, fracture of a layered solid under the action of a local pulse, and high-speed penetration of a layered target.Exact calculation of wave fronts and high-frequency disturbances is always of utmost importance for problems of numerical simulation of the dynamics of deformable media and structures. On the one hand, this is due to an attempt to expand the base of test problems formed by analytical solutions, which is an essential aspect of numerical simulation. On the other hand, it is important for the analysis of various applied problems having no analytical solutions, in which the parameters of wave fronts and disturbances in their vicinity may be criterial for the strength and shock resistance estimation. Examples of such problems in mining are shock pulses propagation in block media, dynamic strength of component parts of impact machines, stability of underground structures under explosions and rock bursts, etc. Adequate simulation of discontinuous and high-frequency components of the wave field acquires special importance due to multiple reflections of unit waves from inhomogeneities that are inevitably present in actual media and structures.Apart from scarce and relatively simple models of the dynamics of media and structures, wave processes in structured bodies cannot be described using analytical approaches.Undoubtedly, the idea of adequate numerical simulation of a wave field with discontinuities in inhomogeneous media and compound structures is attractive. Numerical solutions not only essentially supplement the known analytical ones, but also allow to obtain qualitative and quantitative evaluations of the process under study and to explain physical consequences. Besides, numerical

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Deformed solid mechanics at the Siberian Branch, Academy of Sciences of the USSR

Annin

Ревуженко

Shemyakin

1988

J Appl Mech Tech Phys

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Reaction of a three-layer hydroelastic cylindrical shell to an axisymmetric internal explosion

Cited by 3 publications

References 5 publications

Mesh Dispersion Minimization Algorithms Within Explicit Finite-Difference Schemes to Calculate Transient Wave Processes in Elastic Media and Composite Structures

Mesh Dispersion Minimization Algorithms Within Explicit Finite-Difference Schemes to Calculate Transient Wave Processes in Elastic Media and Composite Structures

Numerical simulation of shock-wave processes in elastic media and structures. Part I: Solving method and algorithms

Deformed solid mechanics at the Siberian Branch, Academy of Sciences of the USSR

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