Dynamic methods of spatial calculation of structures based on a plate model

Toshmatov, Elyor; Usarov, M. K.; Ayubov, G.; Usarov, D.

doi:10.1051/e3sconf/20199704072

Cited by 15 publications

(7 citation statements)

References 11 publications

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“…Along with this, the dynamic behavior and stress-strain state (SSS) of various structures, with account for features and operating conditions, were studied in [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

“…The material of protective shell (figure 1) is hypothetical, i.e. : K=1.45; =0.78,=1/150.The relaxation kernel is taken in the form[16,23,24]: α=0; A=0.008; β=0.003 (low viscosity); 2) α=0.1; A=0.040; β=0.003 (high viscosity).E3S Web of Conferences 164, 02009 (2020) TPACEE-2019 https://doi.org/10.1051/e3sconf /20201640 0 20 Geometrical dimensions of the shell (figure 2) in dimensionless form are taken as:H/R2=2.346;R1/R2=0.949; r1/R2=0.54; r2/R2=1.468; a/R2=1.662; b/R2=0.684; c/R2=0.827;  / R2=0.0506.…”

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confidence: 99%

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Spatial forced oscillations of axisymmetric inhomogeneous systems

2020

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The aim of this paper is to develop an adequate mathematical model, methods and algorithms for solving three-dimensional problems for axisymmetric spatial inhomogeneous viscoelastic systems (shells, foundations and bases) and to assess the dynamics of protective shell (containment) of a nuclear power plant (NPP) under resonant modes of vibration. The problem is solved using the semi-analytical finite element method. Firstly, the eigenmodes of vibration of the system are determined in an elastic three-dimensional statement, secondly, the solution to the problem of forced vibrations of viscoelastic systems is constructed using the expansion of these eigenmodes of vibration. Viscoelastic properties of the material are described using the hereditary Boltzmann-Volterra theory. The principle of virtual displacements is used to simulate dynamic processes in inhomogeneous viscoelastic systems. The convergence and accuracy of the solutions obtained are investigated by test problems. The frequency response characteristics (FRC) in various points of the NPP containment are estimated at various viscosity parameters of the material. It was revealed that the highest amplitude of vibrations in resonance modes occurs at close values of the frequency of external effect to the first eigen frequencies of the system; in the presence of dense spectra of eigen frequencies of the system, the highest amplitudes can occur at higher frequencies of external effect.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

Spatial forced oscillations of axisymmetric inhomogeneous systems

2020

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“…The equations of longitudinal oscillations of a thick plate [11][12][13], built with internal forces and bimoments within the framework of the spatial theory of elasticity, are taken as the equation of motion of a building under seismic action directed along the longitudinal direction, and are written in the following form , 12 1 using the method of displacements expansion into the Maclaurin infinite power series, are constructed in [12,13] in the form:…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…The studies in [10,11] are devoted to the development of the methods for dynamic spatial calculation of a structure based on the finite difference method in the framework of the bimoment theory, which takes into account the spatial stress-strain state.…”

Section: Introductionmentioning

confidence: 99%

Continual model and dynamic calculation of buildings under seismic impacts

2020

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Continuum plate model in the form of a cantilever anisotropic plate developed in the framework of the bimoment theory of plates describing seismic oscillations of buildings is proposed in this paper as a dynamic model of a building. Formulas for the reduced moduli of elasticity, shear and density of the plate model of a building are given. Longitudinal oscillations of a building are studied using the continuum plate and box-like models of the building with Finite Element Model. Numerical results are obtained in the form of graphs, followed by their analysis.

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“…The studies in [11], [12] develop the methods for dynamic spatial calculation of the structure based on the finite difference method in the framework of the theory of bimoments, taking into account the spatial stress-strain state.…”

Section: Introductionmentioning

confidence: 99%

Calculation methods for plate and beam elements of box-type structure of building

2021

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The article is devoted to the dynamic calculation of the box-type structure of buildings for seismic resistance, taking into account the spatial work of the box elements under the influence of dynamic impact. The development of spatial calculations and the study of vibrations of elements of box-type structures, considering various factors, is an urgent problem of structural mechanics. In this article, a mathematical model and a numerical-analytical method were developed to solve the problem of dynamics using the finite difference method and expand the solution in terms of natural vibration modes in the spatial setting for the elements of box-type structures under the kinematic impact. The steady-state forced vibrations of box-type structures under stationary harmonic influences applied to the structure foundation are investigated, and the areas are identified where the greatest values of shearing forces and bending moments occur under harmonic influences.

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Dynamic methods of spatial calculation of structures based on a plate model

Cited by 15 publications

References 11 publications

Spatial forced oscillations of axisymmetric inhomogeneous systems

Spatial forced oscillations of axisymmetric inhomogeneous systems

Continual model and dynamic calculation of buildings under seismic impacts

Calculation methods for plate and beam elements of box-type structure of building

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