• Title/Summary/Keyword: minimum potential energy

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Plasma control by tuning network modification in 4MHz ionized-physical vapor deposition (4MHz I-PVD장치에서 정합회로를 이용한 플라즈마 제어)

  • 주정훈
    • Journal of the Korean Vacuum Society
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    • v.8 no.1
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    • pp.75-82
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    • 1999
  • Ion energy is one of the crucial property in thin film deposition by internal ICP assisted I-PVD. As ion energy is determined by the difference between the plasma potential and the substrate bias potential, ICP excitation frequency was tested with medium frequency of 4 MHz and two types of tuning circuits, alternate and floating LC network with a biasing resistor, were tested. The results showed that plasma potential was less than 5 V in a range of Ar pressures, 5mTorr to 30 mTorr, at 4 MHz RF 600 W and 60 V of maximum RF antenna voltage was maintained either at RF input or output terminal. By proper control of RLC circuit installed after after RF antenna, 50V of RF induced voltage on RF antenna was obtained at 500W input power. The total impedance of RF antenna and plasma was around 10$\Omega$, and minimum RF voltage was obtained with a condition of lowest reactance at most 0.05$\Omega$.

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Study on bi-stable behaviors of un-stressed thin cylindrical shells based on the extremal principle

  • Wu, Yaopeng;Lu, Erle;Zhang, Shuai
    • Structural Engineering and Mechanics
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    • v.68 no.3
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    • pp.377-384
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    • 2018
  • Bi-stable structure can be stable in both its extended and coiled forms. For the un-stressed thin cylindrical shell, the strain energy expressions are deduced by using a theoretical model in terms of only two parameters. Based on the principle of minimum potential energy, the bi-stable behaviors of the cylindrical shells are investigated. The results indicate that the isotropic cylindrical shell does not have the second stable configuration and laminated cylindrical shells with symmetric or antisymmetric layup of fibers have the second stable state under some confined conditions. In the case of antisymmetric laminated cylindrical shell, the analytical expressions of the stability are derived based on the extremal principle, and the shell can achieve a compact coiled configuration without twist deformation in its second stable state. In the case of symmetric laminated cylindrical shell, the explicit solutions for the stability conditions cannot be deduced. Numerical results show that stable configuration of symmetric shell is difficult to achieve and symmetric shell has twist deformation in its second stable form. In addition, the roll-up radii of the antisymmetric laminated cylindrical shells are calculated using the finite element package ABAQUS. The results show that the value of the roll-up radii is larger from FE simulation than from theoretical analysis. By and large, the predicted roll-up radii of the cylindrical shells using ABAQUS agree well with the theoretical results.

Buckling analysis of FGM Euler-Bernoulli nano-beams with 3D-varying properties based on consistent couple-stress theory

  • Hadi, Amin;Nejad, Mohammad Zamani;Rastgoo, Abbas;Hosseini, Mohammad
    • Steel and Composite Structures
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    • v.26 no.6
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    • pp.663-672
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    • 2018
  • This paper contains a consistent couple-stress theory to capture size effects in Euler-Bernoulli nano-beams made of three-directional functionally graded materials (TDFGMs). These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in all three axial, thickness and width directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of minimum potential energy. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of TDFG nano-beam. At the end, some numerical results are performed to investigate some effective parameter on buckling load. In this theory the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor.

A Study on the Geometric Nonlinear Behaviour of Ship Plate by Energy Method (에너지법에 의한 선체판의 기하학적 비선형거동에 관한 연구)

  • Jae-Yong Ko
    • Journal of the Society of Naval Architects of Korea
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    • v.36 no.2
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    • pp.94-104
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    • 1999
  • Plate buckling is very important design criteria when the ship is composed of high tensile steel plates. In general, the plate element contributes to inplane stiffness against the action of inplane load. If the inplane stiffness of the plating decreases due to buckling including the secondary buckling, the flexural rigidity of the cross section of a ship's hull also decreases. In these cases, the precise estimation of plate's behaviour after buckling is necessary, and geometric nonlinear behaviour of isolated plates is required for structural system analysis. In this connection, the author investigated the geometric nonlinear behaviour of simply supported rectangular plates under uniaxial compression in the longitudinal direction in which the principle of minimum potential energy method is employed. Based on the energy method, elastic large deflection analysis of isolated palate is performed and simple expression are derived to discuss the bifurcation paint type buckling and limit point type buckling.

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Static analysis of cutout microstructures incorporating the microstructure and surface effects

  • Alazwari, Mashhour A.;Abdelrahman, Alaa A.;Wagih, Ahmed;Eltaher, Mohamed A.;Abd-El-Mottaleb, Hanaa E.
    • Steel and Composite Structures
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    • v.38 no.5
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    • pp.583-597
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    • 2021
  • This article develops a nonclassical model to analyze bending response of squared perforated microbeams considering the coupled effect of microstructure and surface stress under different loading and boundary conditions, those are not be studied before. The corresponding material and geometrical characteristics of regularly squared perforated beams relative to fully filled beam are obtained analytically. The modified couple stress and the modified Gurtin-Murdoch surface elasticity models are adopted to incorporate the microstructure as well as the surface energy effects. The differential equations of equilibrium including the Poisson's effect are derived based on minimum potential energy. Exact closed form solution is obtained for bending behavior of the proposed model considering the classical and nonclassical boundary conditions for both uniformly distributed and concentrated loads. The proposed model is verified with results available in the literature. Influences of the microstructure length scale parameter, surface energy, beam thickness, boundary and loading conditions on the bending behavior of perforated microbeams are investigated. It is observed that microstructure and surface parameters are vital in investigation of the bending behavior of perforated microbeams. The obtained results are supportive for the design, analysis and manufacturing of perforated nanobeams that commonly used in nanoactuators, nanoswitches, MEMS and NEMS systems.

An energy-based vibration model for beam bridges with multiple constraints

  • Huang, Shiping;Zhang, Huijian;Chen, Piaohua;Zhu, Yazhi;Zuazua, Enrique
    • Structural Engineering and Mechanics
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    • v.82 no.1
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    • pp.41-53
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    • 2022
  • We developed an accurate and simple vibration model to calculate the natural frequencies and their corresponding vibration modes for multi-span beam bridges with non-uniform cross-sections. A closed set of characteristic functions of a single-span beam was used to construct the vibration modes of the multi-span bridges, which were considered single-span beams with multiple constraints. To simplify the boundary conditions, the restraints were converted into spring constraints. Then the functional of the total energy has the same form as the penalty method. Compared to the conventional penalty method, the penalty coefficients in the proposed approach can be calculated directly, which can avoid the iteration process and convergence problem. The natural frequencies and corresponding vibration modes were obtained via the minimum total potential energy principle. By using the symmetry of the eigenfunctions or structure, the matrix size can be further reduced, which increases the computational efficiency of the proposed model. The accuracy and efficiency of the proposed approach were validated by the finite element method.

A Study on Development Potential of Shallow Geothermal Energy as Space Heating and Cooling Sources in Mongolia (몽골의 천부 지열에너지(냉난방 에너지)개발 가능성에 관한 연구)

  • Hahn, Jeong-Sang;Yoon, Yun-Sang;Yoon, Kern-Sin;Lee, Tae-Yul;Kim, Hyong-Soo
    • Journal of the Korean Society for Geothermal and Hydrothermal Energy
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    • v.8 no.2
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    • pp.36-47
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    • 2012
  • Time-series variation of groundwater temperature in Mongolia shows that maximum temperature is occured from end of October to the first of February(winter time) and minimum temperature is observed from end of April to the first of May(summer time). Therefore ground temperature is s a good source for space heating in winter and cooling in summer. Groundwater temperatures monitored from 3 alluvial wells in Ulaabaatar at depth between 20 and 24 m are $(4.43{\pm}0.8)^{\circ}C$ with average of $4.21^{\circ}C$ but mean annual ground temperature(MAGT) at the depth of 100 m in Ulaanbaatar was about $3.5{\sim}6.0^{\circ}C$. Bore hole length required to extract 1 RT's heat energy from ground in heating time and to reject 1 RT's heat energy to ground in summer time are estimated about 130 m and 98 m respectively. But in case that thermally enhanced backfill and U tube pipe placement along the wall are used, the length can be reduced about 25%. Due to low MAGT of Ulaabaatar such as $6^{\circ}C$, the required length of GHX in summer cooling time is less than the one of winter heating time. Mongolia has enough available property, therefore the most cost effective option for supplying a heating energy in winter will be horizontal GHX which absorbs solar energy during summer time. It can supply 1 RT's ground heat energy by 570 m long horizontally installed GHX.

A new finite element procedure for fatigue life prediction of AL6061 plates under multiaxial loadings

  • Tarar, Wasim;Herman Shen, M.H.;George, Tommy;Cross, Charles
    • Structural Engineering and Mechanics
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    • v.35 no.5
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    • pp.571-592
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    • 2010
  • An energy-based fatigue life prediction framework was previously developed by the authors for prediction of axial, bending and shear fatigue life at various stress ratios. The framework for the prediction of fatigue life via energy analysis was based on a new constitutive law, which states the following: the amount of energy required to fracture a material is constant. In the first part of this study, energy expressions that construct the constitutive law are equated in the form of total strain energy and the distortion energy dissipated in a fatigue cycle. The resulting equation is further evaluated to acquire the equivalent stress per cycle using energy based methodologies. The equivalent stress expressions are developed both for biaxial and multiaxial fatigue loads and are used to predict the number of cycles to failure based on previously developed prediction criterion. The equivalent stress expressions developed in this study are further used in a new finite element procedure to predict the fatigue life for two and three dimensional structures. In the second part of this study, a new Quadrilateral fatigue finite element is developed through integration of constitutive law into minimum potential energy formulation. This new QUAD-4 element is capable of simulating biaxial fatigue problems. The final output of this finite element analysis both using equivalent stress approach and using the new QUAD-4 fatigue element, is in the form of number of cycles to failure for each element on a scale in ascending or descending order. Therefore, the new finite element framework can provide the number of cycles to failure at each location in gas turbine engine structural components. In order to obtain experimental data for comparison, an Al6061-T6 plate is tested using a previously developed vibration based testing framework. The finite element analysis is performed for Al6061-T6 aluminum and the results are compared with experimental results.

Static displacement and elastic buckling characteristics of structural pipe-in-pipe cross-sections

  • Sato, M.;Patel, M.H.;Trarieux, F.
    • Structural Engineering and Mechanics
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    • v.30 no.3
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    • pp.263-278
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    • 2008
  • Structural pipe-in-pipe cross-sections have significant potential for application in offshore oil and gas production systems because of their property that combines insulation performance with structural strength in an integrated way. Such cross-sections comprise inner and outer thin walled pipes with the annulus between them fully filled by a selectable thick filler material to impart an appropriate combination of properties. Structural pipe-in-pipe cross-sections can exhibit several different collapse mechanisms and the basis of the preferential occurrence of one over others is of interest. This paper presents an elastic analyses of a structural pipe-in-pipe cross-section when subjected to external hydrostatic pressure. It formulates and solves the static and elastic buckling problem using the variational principle of minimum potential energy. The paper also investigates a simplified formulation of the problem where the outer pipe and its contact with the filler material is considered as a 'pipe on an elastic foundation'. Results are presented to show the variation of elastic buckling pressure with the relative elastic modulus of the filler and pipe materials, the filler thickness and the thicknesses of the inner and outer pipes. The range of applicability of the simplified 'pipe on an elastic foundation' analysis is also presented. A brief review of the types of materials that could be used as the filler is combined with the results of the analysis to draw conclusions about elastic buckling behaviour of structural pipe-in-pipe cross-sections.

FPGA integrated IEEE 802.15.4 ZigBee wireless sensor nodes performance for industrial plant monitoring and automation

  • Ompal, Ompal;Mishra, Vishnu Mohan;Kumar, Adesh
    • Nuclear Engineering and Technology
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    • v.54 no.7
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    • pp.2444-2452
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    • 2022
  • The field-programmable gate array (FPGA) is gaining popularity in industrial automation such as nuclear power plant instrumentation and control (I&C) systems due to the benefits of having non-existence of operating system, minimum software errors, and minimum common reason failures. Separate functions can be processed individually and in parallel on the same integrated circuit using FPGAs in comparison to the conventional microprocessor-based systems used in any plant operations. The use of FPGAs offers the potential to minimize complexity and the accompanying difficulty of securing regulatory approval, as well as provide superior protection against obsolescence. Wireless sensor networks (WSNs) are a new technology for acquiring and processing plant data wirelessly in which sensor nodes are configured for real-time signal processing, data acquisition, and monitoring. ZigBee (IEEE 802.15.4) is an open worldwide standard for minimum power, low-cost machine-to-machine (M2M), and internet of things (IoT) enabled wireless network communication. It is always a challenge to follow the specific topology when different Zigbee nodes are placed in a large network such as a plant. The research article focuses on the hardware chip design of different topological structures supported by ZigBee that can be used for monitoring and controlling the different operations of the plant and evaluates the performance in Vitex-5 FPGA hardware. The research work presents a strategy for configuring FPGA with ZigBee sensor nodes when communicating in a large area such as an industrial plant for real-time monitoring.