Coupled BEM and FEM analysis of fluid-structure interaction in dual compartment tanks

Gnitko, V.; Degtyariov, Kyryl; Naumenko, V.; Strelnikova, Elena

doi:10.2495/cmem-v6-n6-976-988

Cited by 14 publications

(17 citation statements)

References 9 publications

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“…In the axisymmetric case, we can calculate surface integrals as curve integrals of Green's function integrated by the angle variable [15]. Green's function and its normal derivative, integrated by the angle variable, are expressed in terms of complete elliptic integrals of the first and second kind [15], [16] using the following formulae [17]…”

Section: Origin Intensity Factorsmentioning

confidence: 99%

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Singular Boundary Method in a Free Vibration Analysis of Compound Liquid-Filled Shells

Gnitko

Degtyariov

Karaiev

et al. 2019

Boundary Elements and Other Mesh Reduction Methods XLII

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A new numerical approach is proposed to address problems of free liquid vibrations in axisymmetric compound rigid shells using a singular boundary method. The liquid is supposed to be perfect and incompressible, and its flow is irrotational so the liquid velocity can be presented as a potential gradient. The approximation of a small fluid surface elevation is used, and the free surface function is presented as a sum of the fluid-filled shell height and the small elevation function. A series expansion of the potential function about stationary states is used. To find the stationary states, an eigenvalue problem is formulated. Eigenvalues and eigenvectors are obtained using the singular boundary method with the origin intensity factor as the singular integral over the singular boundary element. The numerical results for free vibration analysis of cylindrical shells, obtained by singular boundary method and direct boundary element methods, are compared. Different compound rigid shells are considered in numerical simulations of free liquid vibrations.

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Section: Origin Intensity Factorsmentioning

confidence: 99%

“…So, evaluating the original intensity factors is reduced to calculation of integrals with logarithmic singularity. To treat with this singularity, we use quadrature formulae with quadrature nodes in the roots of orthogonal polynomials with the logarithmic weight [1] and apply the technique described in Gnitko et al [17].…”

Section: Origin Intensity Factorsmentioning

confidence: 99%

Singular Boundary Method in a Free Vibration Analysis of Compound Liquid-Filled Shells

Gnitko

Degtyariov

Karaiev

et al. 2019

Boundary Elements and Other Mesh Reduction Methods XLII

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“…Проте досить складно безпосередньо застосовувати обчислювальну тривимірну гідродинамічну модель при проектуванні резервуарів, оскільки проведення такого аналізу потребує значних витрат часу та зусиль. Тому актуальним є розроблення ефективних методів на основі числових алгоритмів, що використовують теорію потенціалу [11,12].…”

Section: аналіз останніх досліджень та публікаційunclassified

Method of discrete singularities in problems of filler vibrations in fuel tanks under overloads and at low gravity

2019

Bulletin of V.N. Karazin Kharkiv National University, Series «Mathematical Modeling. Information Technology. Automated Control

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The paper is about free vibration problems in fuel tanks with different levels of fillers both under overloads and low gravity. The fuel tanks are considered as rigid shells of revolution. The liquid, contained in the tanks, is supposed to be an ideal and incompressible one, and its flow, induced by external excitations, is irrotational. The problem of free axisymmetric harmonic oscillations of the fluid-filled rigid compound shell is considered. The mixed boundary value problem is formulated, and boundary conditions are received on the boundaries of the fluid domain. The non-penetration conditions is formulated on the rigid shell boundaries, and on the free liquid surface there are kinematic and dynamic boundary conditions. The flow fluctuations are described by using the velocity potential that for ideal and incompressible liquids satisfies the Laplace equation. For its solution, the integral representation is in use. But there are two unknown functions, the velocity potential and the function describing the shape and position of the free surface during time. The transformation of the boundary conditions leads to eliminating one of these unknown functions. So, the system of boundary singular integral equations is obtained to determine the velocity potential. The discrete singularity method and the boundary element method are applied for its numerical solution. The problem of determining own modes and frequencies is solved by using the techniques, where the surface tension effects are neglected. Then these modes are considered as basic functions to determine the modes and frequencies of the liquid taking into account the surface tension. Thus, in this work the method is developed which takes into account the surface tension effect on the frequency of fluid fluctuations in the rigid tank under low gravity conditions. The surface of the interaction between liquid media and gas is considered as a thin membrane, whose thickness is neglected. The fluid pressure on this surface is determined by the Laplace-Young equation. The developed method is useful for the investigation of free and forced fluid oscillations in rigid compound shells with arbitrary meridians.

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“…The values of fluxes (tractions) are Y i (i=1,2,3). By using the multi-domain approach [13] to determine unknown X values the next system of integral equations in the operator form is obtained:…”

Section: Axisymmetric Elasticity Problems For An Isotropic Body With mentioning

confidence: 99%

“…Receiving X 2 from the second and third equations in (13) and substituting it into first and fourth equations respectively, one can obtain the next expressions:…”

Section: Axisymmetric Elasticity Problems For An Isotropic Body With mentioning

confidence: 99%

Multi-Domain Boundary Element Method for Axisymmetric Problems in Potential Theory and Linear Isotropic Elasticity

Gnitko

Degtyariov

Karaiev

et al. 2018

WIT Transactions on Engineering Sciences

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The paper presents an approach based on reduced boundary element methods to resolve axisymmetric problems in potential and linear isotropic elasticity theories. The singular integral equations for these problems are received using fundamental solutions. Initially three-dimensional problems expressed in Cartesian coordinates are transformed to cylindrical ones and integrated with respect to the circumference coordinate. So the three-dimensional axisymmetric problems are reduced to systems of singular integral equations requiring the evaluation of linear integrals only. The fundamental solutions and their derivatives are expressed in terms of complete elliptic integrals. The effective algorithm for treatment of the singular integrals is proposed. The multi-domain boundary element method is applied for the numerical simulation. As examples, the following problems are considered: fluid induced vibrations of a compound cylindrical-spherical elastic shell partially filled with an ideal incompressible liquid, and axisymmetric elasticity problems for an isotropic body with rigid or elastic circular cylindrical inclusions.

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Coupled BEM and FEM analysis of fluid-structure interaction in dual compartment tanks

Cited by 14 publications

References 9 publications

Singular Boundary Method in a Free Vibration Analysis of Compound Liquid-Filled Shells

Singular Boundary Method in a Free Vibration Analysis of Compound Liquid-Filled Shells

Method of discrete singularities in problems of filler vibrations in fuel tanks under overloads and at low gravity

Multi-Domain Boundary Element Method for Axisymmetric Problems in Potential Theory and Linear Isotropic Elasticity

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