Boundary Element Method Analysis of Boundary Value Problems With Periodic Boundary Conditions

Modern equipment elements in the energy, chemical industry, transport, aviation, and space engineering work under conditions of increased technological loads, at high temperatures and pressure levels. At the same time, the equipment is usually exposed to external loads of various natures. Hydroelastic phenomena must also be taken into account in designing and modernizing tanks and storage facilities for flammable and combustible substances. Flammable and combustible liquid accumulation leads to the increased environmental and fire hazard of such objects. The possible dangerous liquid leakage and tank depressurization negatively affect the surrounding area environment state. A fire in the tank is one of the most dangerous emergencies that could lead both to significant material and environmental damage and to human casualties. The paper treats the environmental hazards reducing problem from liquid hydrocarbon spills from storage tanks, which lead to destructive effects on all environment components especially during emergency situations. It has been established for sufficiently thin tank elastic walls, the fundamental frequency during coupled oscillations could be much lower than the frequency of the fluid in the shell with rigid walls. As the thickness of the tank wall increases, this effect becomes insignificant, and the lower oscillation frequency of the shell with liquid approaches the oscillation frequency of the liquid in a rigid tank. Parametric resonance and sub-resonance effects have been treated.

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“…where 𝑛𝑛 is the harmonic number. The possibility of representation use (9) has been proved in the work, [26], [27].…”

Section: Becausementioning

confidence: 99%

The Mutual Effect Study of Horizontal and Vertical Loads on the Elastic Tank Partially Filled with Liquid

et al. 2023

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“…Thus, the boundary value problem is formulated for evaluating the pressure as solution of eqn (6) under boundary conditions (10), (20). Note that the initial conditions are needed to be added.…”

Section: Unilateral Contact Of the Structural Element With The Liquidmentioning

confidence: 99%

“…Sloshing modes are the same for conical, spherical and cylindrical shells and have the Bessel-like behaviour. Generalization of the developed method for non-axisymmetric vibrations can be carried out using the approach from Gnitko et al [20].…”

Section: Singular Integral Equations In Evaluating Frequencies and Mo...mentioning

confidence: 99%

Singular and Hypersingular Integral Equations in Fluid–structure Interaction Analysis

Gnitko

KARAIEV

Degtyariov

et al. 2022

WIT Transactions on Engineering Sciences

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The paper presents new computational techniques based on coupled boundary and finite element methods to study fluid-structure interaction problems. Thin shells and plates are considered as structure elements interacting with an ideal and incompressible liquid. To describe the motion of both structural elements and the fluid, the basic relations of the continuous mechanics are incorporated. The liquid pressure is determined by applying the Laplace equation. Two kinds of boundary value problems are considered corresponding to one-sided and two-sided contact of structural elements with the liquid. Integral equations for numerical simulation of pressure are obtained. For a two-sided contact of the structural element with the liquid, hypersingular integral equations are received, whereas singular integral equations with logarithmic singularities describe the problems of one-sided contact. Considering the structure axial symmetry, the integral equations are reduced to one-dimensional ones. The finite element method for determining modes and frequencies of the elastic structure coupled with boundary element method for the hypersingular integral equation is implemented to find the fluid pressure on the structure element with two-sided contact with the liquid. The liquid pressure evaluation in axisymmetric problems is reduced to one-dimensional integral equations with kernels in the form of elliptic integrals. The effective technique is developed for numerical simulation of obtained singular integrals. The same technique is extended to hypersingular integral equations. The frequencies and modes of structure vibrations taking into account the added masses of the liquid are obtained. Thin circular plates and shells of revolution are considered as structure elements in numerical simulations. The accuracy and reliability of the proposed method are ascertained.

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Boundary Element Method Analysis of Boundary Value Problems With Periodic Boundary Conditions

Cited by 2 publications

References 17 publications

The Mutual Effect Study of Horizontal and Vertical Loads on the Elastic Tank Partially Filled with Liquid

The Mutual Effect Study of Horizontal and Vertical Loads on the Elastic Tank Partially Filled with Liquid

Singular and Hypersingular Integral Equations in Fluid–structure Interaction Analysis

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