Stress-Strain State of a Composite Plate Under the Action of a Transient Movable Load

Serdyuk, A.O.; Сердюк, Д.О.; Fedotenkov, G. V.

doi:10.1007/s11029-021-09972-z

Cited by 3 publications

(6 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…where Considering the formula (32), the denominator of the function (30) can be represented as: then the expressions for X from (31) will take the form (30) G L nm = nm ( )…”

Section: Verificationmentioning

confidence: 99%

“…In this paper, Green function method and method of compensating load are used. In the literature [21][22][23][24][25][26][27][28][29][30][31][32], the use of Green function is studied for solving the transient problems of elasticity theory and shell theory. Papers of Tartakovsky [21][22][23][24][25] consider the investigation of transient contact problems for thin spherical cylindrical shells and elastic halfspace.…”

Section: Introductionmentioning

confidence: 99%

“…Okonechnikov investigated the cases of transient impact of rigid indenter on elastic half-space [29,30]. Papers of Serdyuk [31,32] include the formation of basic solution and investigation of stress-strain state of infinite anisotropic Kirchhoff shell.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Transient Deformation of an Anisotropic Cylindrical Shell with Structural Features

Lokteva

Сердюк

Скопинцев

2023

J. Inst. Eng. India Ser. C

View full text Add to dashboard Cite

In this work, a new transient function of normal displacements is obtained in a thin elastic anisotropic cylindrical shell of constant thickness with structural features. Structural features form of two sequences in angular direction of weld spots or rivets. Structural features are mathematically described by point boundary conditions of rigid pinching or point boundary conditions of hinge support, accordingly. A load with time variable amplitude and impact boundaries influences on the outer surface of the shell along the normal. Such movement of the shell is considered in the cylindrical coordinate system as connected with the shell axis. Kirchhoff-Love hypothesis are confirmed as a shell model. The solution of this problem can be formed with the help of Green function method and lift compensation method. The required function of transient normal displacements is represented as the sum of integral operators of Green convolution for an infinite shell with functions of current transient load and compensating loads out of point boundary conditions. Compensating loads satisfying to boundary conditions can be found based on the solution of Volterra integral equations of the first kind with the difference kernel. Green function is such kernel. The system solution can be executed including preliminary discretization of compensating time loads. The convolution integrals can be taken numerically with the help of quadrature formula by the method of rectangles. The verification of the method is represented by comparing the solution of specific case with the known solution for a hinged isotropic cylindrical shell.

show abstract

“…where Considering the formula (32), the denominator of the function (30) can be represented as: then the expressions for X from (31) will take the form (30) G L nm = nm ( )…”

Section: Verificationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Transient Deformation of an Anisotropic Cylindrical Shell with Structural Features

Lokteva

Сердюк

Скопинцев

2023

J. Inst. Eng. India Ser. C

View full text Add to dashboard Cite

show abstract

“…The formula for the analytical inversion of the two-dimensional integral Fourier transform for Equation ( 23) can be constructed using the connection of the integral Fourier transform with the Fourier series on a variable interval [40][41][42][43][44][45][46]:…”

Section: The Surface Spatial Transient Functionmentioning

confidence: 99%

Conductive Heat Transfer in Materials under Intense Heat Flows

2022

View full text Add to dashboard Cite

The paper presents the solution of the spatial transient problem of the impact of a moving heat flux source induced by the laser radiation on the surface of a half-space using the superposition principle and the method of transient functions. The hyperbolic equation of transient thermal conductivity accounting for the relaxation time is used to model the laser heating process. It is assumed that the heat flux is distributed symmetrically with respect to the center of the heating spot. The combined numerical and analytical algorithm has been developed and implemented, which allows one to determine the temperature distribution both on the surface and on the depth of the half-space. In this case, the principle of superposition is used with the use of a special symmetric Gaussian distribution to describe the model of a source of high-intensity heat flux. The use of such a symmetric distribution made it possible to calculate the integrals over the spatial variables analytically. The results of the work could be used to estimate the contribution of the conductive component in the overall heat transfer of materials exposed to intense heat flows (laser surface treatment, laser additive technologies, streamlining and heating of materials by high-enthalpy gases, etc.).

show abstract

“…Нестационарные контактные задачи с подвижными границами являются одной из наименее исследованных проблем механики контактного взаимодействия. Один из подходов к исследованию подобных задач, основанный на решении интегральных уравнений с ядрами в виде функций влияния, представлен в статьях [1][2][3]. Значительное количество публикаций посвящено численным методам решения, таким как метод граничных элементов (МГЭ), метод конечных элементов (МКЭ) и др.…”

Section: Introductionunclassified

Taking Account of Friction at the Initial Stage of Indentation of Convex Punch Into Elastic Half-Plane

Kazakov,

Tarlakovskii

2022

PSP

View full text Add to dashboard Cite

The initial stage of indentation of a convex rigid punch into isotropic elastic half-plane with friction is considered. A closed mathematical formulation in Cartesian coordinates is presented by equations of motion in the absence of a body force for homogeneous isotropic elastic medium in terms of displacement potentials, Cauchy equations for deformations, Hooke law and translational equation for the punch. Initial conditions are homogeneous. Outside of contact region surface is free from stresses. Inside contact region normal displacements of the surface of a half-space and the surface of a punch are taken to be equal and the relation between tangential and normal stresses in a form of Coulomb friction law is given. Due to the short duration of the supersonic stage and smallness of the contact region radius the tangential stress direction is considered to be point independent. Resolving functional equations are given in a form of convolutions with influence functions. The latter is the solution the original problem for half-plane with a special boundary condition in a form of the Dirac delta function. This solution is obtained in the domain of Laplace transform by time and Fourier transform by spatial coordinate. The original is constructed with the combined Fourier–Laplace inversion method. Solution is given with consideration to the initial stage characteristic property of supersonic velocity of contact region expansion (no smaller than propagation velocity of expansion-compression waves). It is shown that kinematic parameters of the punch, resulting force and discontinuities of the first kind on boundaries of the contact region are independent of friction unlike contact pressure. Calculation examples for different values of friction coefficient are presented.

show abstract

Stress-Strain State of a Composite Plate Under the Action of a Transient Movable Load

Cited by 3 publications

References 29 publications

Transient Deformation of an Anisotropic Cylindrical Shell with Structural Features

Transient Deformation of an Anisotropic Cylindrical Shell with Structural Features

Conductive Heat Transfer in Materials under Intense Heat Flows

Taking Account of Friction at the Initial Stage of Indentation of Convex Punch Into Elastic Half-Plane

Contact Info

Product

Resources

About