• Title/Summary/Keyword: stiffness problem

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Resonance Analysis According to Initial Tower Design for Floating Offshore Wind Turbine (부유식 해상풍력발전기 타워의 초기 형상에 따른 공진 해석)

  • Kim, Junbae;Shin, Hyunkyoung
    • Journal of Wind Energy
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    • v.9 no.4
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    • pp.57-64
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    • 2018
  • To maximize power generation and reduce the construction cost of a commercial utility-grade wind turbine, the size of the wind turbine should be large. The initial design of the 12 MW University of Ulsan(UOU) Floating Offshore Wind Turbine(FOWT) was carried out based on the 5 MW National Renewable Energy Laboratory(NREL) offshore wind turbine model. The existing 5 MW NREL offshore wind turbines have been expanded to 12 MW UOU FOWT using the geometric law of similarity and then redesigned for each factor. The resonance of the tower is the most important dynamic responses of a wind turbine, and it should be designed by avoiding resonance due to cyclic load during turbine operations. The natural frequency of the tower needs to avoid being within the frequency range corresponding to the rotational speed of the blades, 1P, and the blade passing frequency, 3P. To avoid resonance, vibration can be reduced by modifying the stiffness or mass. The direct expansion of the 5 MW wind turbine support structure caused a resonance problem with the tower of the 12 MW FOWT and the tower length and diameter was adjusted to avoid a match of the first natural frequency and 3P excitation of the tower.

Vibration analysis of functionally graded graphene platelet-reinforced composite doubly-curved shallow shells on elastic foundations

  • Sobhy, Mohammed;Zenkour, Ashraf M.
    • Steel and Composite Structures
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    • v.33 no.2
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    • pp.195-208
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    • 2019
  • Based on a four-variable shear deformation shell theory, the free vibration analysis of functionally graded graphene platelet-reinforced composite (FGGPRC) doubly-curved shallow shells with different boundary conditions is investigated in this work. The doubly-curved shells are composed of multi nanocomposite layers that are reinforced with graphene platelets. The graphene platelets are uniformly distributed in each individual layer. While, the volume faction of the graphene is graded from layer to other in accordance with a novel distribution law. Based on the suggested distribution law, four types of FGGPRC doubly-curved shells are studied. The present shells are assumed to be rested on elastic foundations. The material properties of each layer are calculated using a micromechanical model. Four equations of motion are deduced utilizing Hamilton's principle and then converted to an eigenvalue problem employing an analytical method. The obtained results are checked by introducing some comparison examples. A detailed parametric investigation is performed to illustrate the influences of the distribution type of volume fraction, shell curvatures, elastic foundation stiffness and boundary conditions on the vibration of FGGPRC doubly-curved shells.

Nonlinear formulation and free vibration of a large-sag extensible catenary riser

  • Punjarat, Ong-art;Chucheepsakul, Somchai
    • Ocean Systems Engineering
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    • v.11 no.1
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    • pp.59-81
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    • 2021
  • The nonlinear formulation using the principle of virtual work-energy for free vibration of a large-sag extensible catenary riser in two dimensions is presented in this paper. A support at one end is hinged and the other is a free-sliding roller in the horizontal direction. The catenary riser has a large-sag configuration in the static equilibrium state and is assumed to displace with large amplitude to the motion state. The total virtual work of the catenary riser system involves the virtual strain energy due to bending, the virtual strain energy due to axial deformation, the virtual work done by the effective weight, and the inertia forces. The nonlinear equations of motion for two-dimensional free vibration in the Cartesian coordinate system is developed based on the difference between the Euler's equations in the static state and the displaced state. The linear and nonlinear stiffness matrices of the catenary riser are obtained and the eigenvalue problem is solved using the Galerkin finite element procedure. The natural frequencies and mode shapes are obtained. The results are validated with regard to the reference research addressing the accuracy and efficiency of the proposed nonlinear formulation. The numerical results for free vibration and the effect of the nonlinear behavior for catenary riser are presented.

An efficient adaptive finite element method based on EBE-PCG iterative solver for LEFM analysis

  • Hearunyakij, Manat;Phongthanapanich, Sutthisak
    • Structural Engineering and Mechanics
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    • v.83 no.3
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    • pp.353-361
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    • 2022
  • Linear Elastic Fracture Mechanics (LEFM) has been developed by applying stress analysis to determine the stress intensity factor (SIF, K). The finite element method (FEM) is widely used as a standard tool for evaluating the SIF for various crack configurations. The prediction accuracy can be achieved by applying an adaptive Delaunay triangulation combined with a FEM. The solution can be solved using either direct or iterative solvers. This work adopts the element-by-element preconditioned conjugate gradient (EBE-PCG) iterative solver into an adaptive FEM to solve the solution to heal problem size constraints that exist when direct solution techniques are applied. It can avoid the formation of a global stiffness matrix of a finite element model. Several numerical experiments reveal that the present method is simple, fast, and efficient compared to conventional sparse direct solvers. The optimum convergence criterion for two-dimensional LEFM analysis is studied. In this paper, four sample problems of a two-edge cracked plate, a center cracked plate, a single-edge cracked plate, and a compact tension specimen is used to evaluate the accuracy of the prediction of the SIF values. Finally, the efficiency of the present iterative solver is summarized by comparing the computational time for all cases.

Enhancement of Steering Stability Considering Suspension Movement (현가장치 운동량을 고려한 조향 안정성 향상)

  • Yujin, Chae;Byeong Cheol, Shin;Sung Eun, Song;Hyoungwook, Lee
    • Journal of Institute of Convergence Technology
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    • v.12 no.1
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    • pp.31-35
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    • 2022
  • This study has been carried out in order to improve the rolling problem by enhancing steering stability compared to the 2021 Student Car of the KNUT_EV team for KSAE. Among the various factors affecting steering performances, it was focused on the height of the centroid of weight, the motion ratio, and the spring deflection. In the 2022 Car, a pull rod suspension was used to reduce the height of the centroid of weight and designed with a structure of the rod and rocker to satisfy the target motion ratio. The spring deflection was testified by ADAMS and ABAQUS analysis, and the spring stiffness was selected at 350lb/inch and 450lb/inch for the front and rear wheels, respectively. As a result, the rolling angle of the 2022 Car was reduced compared to the 2021 Car, and the rolling phenomenon was improved.

Laboratory analysis of loose sand mixed with construction waste material in deep soil mixing

  • Alnunu, Mahdi Z.;Nalbantoglu, Zalihe
    • Geomechanics and Engineering
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    • v.28 no.6
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    • pp.559-571
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    • 2022
  • Deep soil mixing, DSM technique has been widely used to improve the engineering properties of problematic soils. Due to growing urbanization and the industrial developments, disposal of brick dust poses a big problem and causes environmental problems. This study aims to use brick dust in DSM application in order to minimize the waste in brick industry and to evaluate its effect on the improvement of the geotechnical properties. Three different percentages of cement content: (10, 15 and 20%) were used in the formation of soil-cement mixture. Unlike the other studies in the literature, various percentages of waste brick dust: (10, 20 and 30%) were used as partial replacement of cement in soil-cement mixture. The results indicated that addition of waste brick dust into soil-cement mixture had positive effect on the inherent strength and stiffness of loose sand. Cement replaced by 20% of brick dust gave the best results and reduced the final setting time of cement and resulted in an increase in unconfined compressive strength, modulus of elasticity and resilient modulus of sand mixed with cement and brick dust. The findings were also supported by the microscopic images of the specimens with different percentages of waste brick dust and it was observed that waste brick dust caused an increase in the interlocking between the particles and resulted in an increase in soil strength. Using waste brick dust as a replacement material seems to be promising for improving the geotechnical properties of loose sand.

Nonlinear vibration of SSMFG cylindrical shells with internal resonances resting on the nonlinear viscoelastic foundation

  • Kamran, Foroutan;Habib, Ahmadi
    • Structural Engineering and Mechanics
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    • v.84 no.6
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    • pp.767-782
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    • 2022
  • In this paper, the nonlinear vibration behavior of the spiral stiffened multilayer functionally graded (SSMFG) cylindrical shells exposed to the thermal environment and a uniformly distributed harmonic loading using a semi-analytical method is investigated. The cylindrical shell is surrounded by a nonlinear viscoelastic foundation consisting of a two-parameter Winkler-Pasternak foundation augmented by a Kelvin-Voigt viscoelastic model with a nonlinear cubic stiffness. The distribution of temperature and material constitutive of the stiffeners are continuously changed through the thickness direction. The cylindrical shell has three layers consisting of metal, FGM, and ceramic. The interior layer of the cylindrical shell is rich in metal, while the exterior layer is rich in ceramic, and the FG material is located between two layers. The nonlinear vibration problem utilizing the smeared stiffeners technique, the von Kármán equations, and the Galerkin method has been solved. The multiple scales method is utilized to examine the nonlinear vibration behavior of SSMFG cylindrical shells. The considered resonant case is 1:3:9 internal resonance and subharmonic resonance of order 1/3. The influences of different material and geometrical parameters on the vibration behavior of SSMFG cylindrical shells are examined. The results show that the angles of stiffeners, temperature, and elastic foundation parameters have a strong effect on the vibration behaviors of the SSMFG cylindrical shells.

A Study on Post-Tensioned Reinforced Concrete Slab by the Beam Theory (포스트텐션된 철근콘크리트 슬래브의 보 이론에 의한 연구)

  • Han, Bong-Koo;Kim, Duck-Hyun
    • Composites Research
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    • v.22 no.5
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    • pp.24-29
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    • 2009
  • In this paper, a post-tensioned reinforced concrete slab was analyzed by the specially orthotropic laminates theory. Both the geometrical and material property of the cross section of the slab was considered symmetrically with respect to the neutral surface so that the bending extension coupling stiffness, $B_{ij}=0$, and $D_{16}=D_{26}=0$. Reinforced concrete slab behave as specially orthotropic plates. In general, the analytical solution for such complex systems is very difficult to obtain. Thus, finite difference method was used for analysis of the problem. In this paper, the finite difference method and the beam theory were used for analysis. The result of beam analysis was modified to obtain the solution of the plate analysis.

A Study on the Finite Element Analysis of Tire under Rolling and Loading Conditions (회전 및 하중을 받는 타이어의 응력해석에 관한 연구)

  • Hwang, Joon;Namgung, Suk
    • Journal of the Korean Society for Precision Engineering
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    • v.12 no.3
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    • pp.101-109
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    • 1995
  • Axisymmetric and quasi-static finite element analysis of an inflated tire rotating with constant angular velocity and contact to road has been performed. Centrifugal force effect was added to load stiffness matrix and equation of effective material properties were calculated by the Halpin-Tsai formulation. In this report, radial truck/bus tire was analyzed. It was inflated and rotated at speeds up to 140 km/h. Then, contact problem was performed to calculate stress-strain field of tire wiht flat rigid road under the load due to the self-weight of a vehicle. Significant changes of stress-strain field of tire were observed in the finite element analysis. Shear stress, strain and strain energy density were rapidly increased at the dege of #2 belt at freely rotating state. This concentrated stress and strain made belt edge sparation. Under the condition of flat riged road contact, strain energy density of #2 belt, carcass turn-up part were concentrated and bigger values than only freely rotation state. Therefore, dynamic behaivor of tire has to considered as design factors which are affected to belt edge separation and bead breakage.

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A variational nodal formulation for multi-dimensional unstructured neutron diffusion problems

  • Qizheng Sun ;Wei Xiao;Xiangyue Li ;Han Yin;Tengfei Zhang ;Xiaojing Liu
    • Nuclear Engineering and Technology
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    • v.55 no.6
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    • pp.2172-2194
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    • 2023
  • A variational nodal method (VNM) with unstructured-mesh is presented for solving steady-state and dynamic neutron diffusion equations. Orthogonal polynomials are employed for spatial discretization, and the stiffness confinement method (SCM) is implemented for temporal discretization. Coordinate transformation relations are derived to map unstructured triangular nodes to a standard node. Methods for constructing triangular prism space trial functions and identifying unique nodes are elaborated. Additionally, the partitioned matrix (PM) and generalized partitioned matrix (GPM) methods are proposed to accelerate the within-group and power iterations. Neutron diffusion problems with different fuel assembly geometries validate the method. With less than 5 pcm eigenvalue (keff) error and 1% relative power error, the accuracy is comparable to reference methods. In addition, a test case based on the kilowatt heat pipe reactor, KRUSTY, is created, simulated, and evaluated to illustrate the method's precision and geometrical flexibility. The Dodds problem with a step transient perturbation proves that the SCM allows for sufficiently accurate power predictions even with a large time-step of approximately 0.1 s. In addition, combining the PM and GPM results in a speedup ratio of 2-3.