• Title/Summary/Keyword: Free boundary conditions

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EFFECT OF THE BOUNDARY CONDITION OF REDISTANCE EQUATION ON THE LEVEL SET SOLUTION OF SLOSHING PROBLEM (Redistance 방정식의 경계조건이 슬로싱 문제의 level set 해석에 미치는 영향)

  • Choi, H.G.
    • 한국전산유체공학회:학술대회논문집
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    • 2009.04a
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    • pp.165-169
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    • 2009
  • The effect of the Dirichlet boundary condition for the redistance equation of level set method on the solutionof sloshing problem is investigated by adopting four Dirichlet boundary conditions. For the solution of the incompressible Navier-Stokes equations, P1P1 four-step fractional finite element method is employed and a least-square finite element method is used for the solutions of the two hyperbolic type equations of level set method; advection and redistance equation. ALE (Arbitrary Lagrangian Eulerian) method is used to deal with a moving computational domain. It has been shown that the free surface motion in a sloshing tank is strongly dependent on the type of the Dirichlet boundary condition and the results of broken dam and sloshing problems using various Dirichlet boundary conditions are discussed and compared with the existing experimental results.

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Exact Free Vibration Analysis of Straight Thin-walled Straight Beams (직선 박벽보에 대한 엄밀한 자유진동해석)

  • 김문영;윤희택;나성훈
    • Proceedings of the KSR Conference
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    • 2000.11a
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    • pp.358-365
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    • 2000
  • For the general case of loading conditions and boundary conditions, it is very difficult to obtain closed form solutions for buckling loads and natural frequencies of thin-walled structures because its behaviour is very complex due to the coupling effect of bending and torsional behaviour. In consequence, most of previous finite element formulations are introduce approximate displacement fields to use shape functions as Hermitian polynomials, and so on. The Purpose of this study is to presents a consistent derivation of exact dynamic stiffness matrices of thin-walled straight beams, to be used ill tile free vibration analysis, in which almost types of boundary conditions are exist An exact dynamic element stiffness matrix is established from governing equations for a uniform beam element of nonsymmetric thin-walled cross section. This numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. The natural frequency is evaluated for the thin-walled straight beam structure, and the results are compared with analytic solutions in order to verify the accuracy of this study.

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Numerical investigation of floating breakwater movement using SPH method

  • Najafi-Jilani, A.;Rezaie-Mazyak, A.
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.3 no.2
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    • pp.122-125
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    • 2011
  • In this work, the movement pattern of a floating breakwater is numerically analyzed using Smoothed Particle Hydrodynamic (SPH) method as a Lagrangian scheme. At the seaside, the regular incident waves with varying height and period were considered as the dynamic free surface boundary conditions. The smooth and impermeable beach slope was defined as the bottom boundary condition. The effects of various boundary conditions such as incident wave characteristics, beach slope, and water depth on the movement of the floating body were studied. The numerical results are in good agreement with the available experimental data in the literature The results of the movement of the floating body were used to determine the transmitted wave height at the corresponding boundary conditions.

Vibration Analysis of Composite Cylindrical Shells Subjected to Electromagnetic and Thermal Fields with Different Boundary Conditions (경계조건에 따른 자기장 및 열하중을 받는 복합재료 원통셸의 진동해석)

  • Park, Sang-Yun;Kim, Sung-Kyun;Choi, Jong-Woon;Song, Ohseop
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2012.10a
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    • pp.653-660
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    • 2012
  • In this paper free vibration analysis of symmetric and cross-ply elastic laminated shells based on FSDT with two different boundary conditions(C-C, S-S) was performed through discretization of equations of motion and boundary condition. Model of laminated composite cylindrical shells subjected to a combination of magnetic and thermal fields is developed via Hamilton's variational principle. These coupled equations of motion are based on the electromagnetic equations (Faraday, Ampere, Ohm, and Lorenz equations) and thermal equations which are involved in constitutive equations. Variations of dynamic characteristics of composite shells with applied magnetic field, temperature gradient, and stacking sequence for each boundary conditions are investigated and pertinent conclusions are derived.

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Free vibration of Levy-type rectangular laminated plates using efficient zig-zag theory

  • Behera, Susanta;Kumari, Poonam
    • Advances in Computational Design
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    • v.3 no.3
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    • pp.213-232
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    • 2018
  • First time, an exact solution for free vibration of the Levy-type rectangular laminated plate is developed considering the most efficient Zig-Zag theory (ZIGT) and third order theory (TOT). The plate is subjected to hard simply supported boundary condition (Levy-type) along x axis. Using the equilibrium equations and the plate constitutive relations, a set of 12 m first order differential homogenous equations are obtained, containing displacements and stress resultant as primary variables. The natural frequencies of a single-layer isotropic, multi-layer composites and sandwich plates are tabulated for three values of length-to-thickness ratio (S) and five set of boundary conditions and further assessed by comparing with existing literature and recently developed 3D EKM (extended Kantorovich method) solution. It is found that for the symmetric composite plate, TOT produces better results than ZIGT. For antisymmetric and sandwich plates, ZIGT predicts the frequency for different boundary conditions within 3% error with respect to 3D elasticity solution while TOT gives 10% error. But, ZIGT gives better predictions than the TOT concerning the displacement and stress variables.

Free vibration analysis of trapezoidal Double Layered plates embedded with viscoelastic medium for general boundary conditions using differential quadrature method

  • S. Abdul Ameer;Abbas Hameed Abdul Hussein;Mohammed H. Mahdi;Fahmy Gad Elsaid;V. Tahouneh
    • Steel and Composite Structures
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    • v.50 no.4
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    • pp.429-441
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    • 2024
  • This paper studies the free vibration behavior of trapezoidal shaped coupled double-layered graphene sheets (DLGS) system using first-order shear deformation theory (FSDT) and incorporating nonlocal elasticity theory. Two nanoplates are assumed to be bonded by an interlayer van der walls force and surrounded by an external kelvin-voight viscoelastic medium. The governing equations together with related boundary condition are discretized using a mapping-differential quadrature method (DQM) in the spatial domain. Then the natural frequency of the system is obtained by solving the eigen value matrix equation. The validity of the current study is evaluated by comparing its numerical results with those available in the literature and then a parametric study is thoroughly performed, concentrating on the series effects of angles and aspect ratio of GS, viscoelastic medium, and nonlocal parameter. The model is used to study the vibration of DLGS for two typical deformation modes, the in-phase and out-of-phase vibrations, which are investigated. Numerical results indicate that due to Increasing the damping parameter of the viscoelastic medium has reduced the frequency of both modes and this medium has been able to overdamped the oscillations and by increasing stiffness parameters both in-phase and out-of-phase vibration frequencies increased.

Shape Function Modification for the Imposition of EFGM Essential Boundary Conditions (EFGM에서 필수경계조건 처리를 위한 형상함수 수정법)

  • Seok, Byeong-Ho;Song, Tae-Han;Im, Jang-Geun
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.3 s.174
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    • pp.803-809
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    • 2000
  • For the effective analysis of an engineering problem, meshless methods which require only positioning finite points without the element meshing recently have been proposed and being studied extensively. Meshless methods have difficulty in imposing essential boundary conditions directly, because non-interpolate shape functions originated from an approximation process are used. So some techniques, which are Lagrange multiplier method, modified variational principles and coupling with finite elements and so on, were introduced in order to impose essential boundary conditions. In spite of these methods, imposition of essential boundary conditions have still many problems like as non-positive definiteness, inaccuracy and negation of meshless characteristics. In this paper, we propose a new method which modifies shape function. Through numerical tests, convergence, accuracy and validity of this method are compared with the standard EFGM which uses Lagrange multiplier method or modified variational principles. According to this study, the proposed method shows the comparable accuracy and efficiency.

Meshless Method Based on Wave-type Function for Accurate Eigenvalue Analysis of Arbitrarily Shaped, Clamped Plates (임의 형상 고정단 평판의 고정밀도 고유치 해석을 위한 파동 함수 기반 무요소법)

  • Kang, Sang-wook
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.26 no.5
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    • pp.602-608
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    • 2016
  • The paper proposes a practical meshless method for the free vibration analysis of clamped plates having arbitrary shapes by extending the non-dimensional dynamic influence function (NDIF) method, which was developed by the author in 1999. In the proposed method, the domain and boundary of the plate of interest are discretized using only nodes without elements unlike FEM and the system matrices are obtained by making domain nodes and boundary nodes satisfy the governing differential equation and boundary conditions, respectively. However, since the above system matrices are not square ones, the problem of free vibrations of clamped plates is not reduced to an algebraic eigenvalue problem. An additional theoretical treatment is considered to produce an algebraic eigenvalue problem. It is revealed from case studies that the proposed method is valid and accurate.

A Study on the Free Vibration Responses of Various Buried Pipelines (각종 매설관의 자유진동거동에 관한 연구)

  • Jeong, Jin-Ho;Park, Byung-Ho;Kim, Sung-Ban;Kim, Chun-Jin
    • Proceedings of the Korean Geotechical Society Conference
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    • 2006.03a
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    • pp.1340-1347
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    • 2006
  • Dynamic response of buried pipelines both in the axial and the transverse directions on concrete pipe and steel pipe, FRP pipe were investigated through a free vibration analysis. End boundary conditions considered herein consist of free ends, fixed ends, and fixed-free ends in the axial and the transverse direction. Guided ends, simply supported ends, and supported-guided ends were added to the transverse direction. The buried pipeline was regarded as a beam on an elastic foundation and the ground displacement of sinusoidal wave was applied to it. Natural frequencies and mode shapes were determined according to end boundary conditions. In addition, the effects of parameters on the natural frequency were evaluated. The natural frequency is affected most significantly by the soil stiffness and the length of the buried pipelines. The natural frequency increases as the soil stiffness increases while it decreases as the length of the buried pipeline increases. Such behavior appears to be dominant in the axial direction rather than in the transverse direction of the buried pipelines.

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