• Title/Summary/Keyword: numerical formulation

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Use of Adaptive Meshes in Simulation of Combustion Phenomena

  • Yi, Sang-Chul;Koo, Sang-Man
    • Proceedings of the Korea Association of Crystal Growth Conference
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    • 1996.06b
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    • pp.285-309
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    • 1996
  • Non oxide ceramics such as nitrides of transition metals have shown significant potential for future economic impact, in diverse applications in ceramic, aerospace and electronic industries, as refractory products, abrasives and cutting tools, aircraft components, and semi-conductor substrates amid others. Combustion synthesis has become an attractive alternative to the conventional furnace technology to produce these materials cheaply, faster and at a higher level of purity. However he process os highly exothermic and manifests complex dynamics due to its strongly non-linear nature. In order to develop an understanding of this process and to study the effect of operational parameters on the final outcome, numerical modeling is necessary, which would generated essential knowledge to help scale-up the process. the model is based on a system of parabolic-hyperbolic partial differential equations representing the heat, mass and momentum conservation relations. The model also takes into account structural change due to sintering and volumetric expansion, and their effect on the transport properties of the system. The solutions of these equations exhibit steep moving spatial gradients in the form of reaction fronts, propagating in space with variable velocity, which gives rise to varying time scales. To cope with the possibility of extremely abrupt changes in the values of the solution over very short distances, adaptive mesh techniques can be applied to resolve the high activity regions by ordering grid points in appropriate places. To avoid a control volume formulation of the solution of partial differential equations, a simple orthogonal, adaptive-mesh technique is employed. This involves separate adaptation in the x and y directions. Through simple analysis and numerical examples, the adaptive mesh is shown to give significant increase in accuracy in the computations.

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A Four-node General Shell Element with Drilling DOFs (면내회전자유도를 갖는 4절점 곡면 쉘요소)

  • Chung, Keun-Young;Kim, Jae-Min;Lee, Eun-Haeng
    • Journal of the Earthquake Engineering Society of Korea
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    • v.16 no.4
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    • pp.37-52
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    • 2012
  • In this study, a new 4-node general shell element with 6 DOFs per node is presented. Drilling rotational degrees of freedom are introduced by the variational principle with an independent rotation field. In formulation of the element, substitute transverse shear strain fields are used to avoid shear locking, while four nonconforming modes are applied in the in-plane displacement fields as a remedy for membrane locking. In addition, a direct modification method for nonconforming modes is employed in the numerical implementation of nonconforming modes to represent constant strain states. A 9-points integration rule is adopted for volume integration in the computation of the element stiffness matrix. With the combined use of these techniques, the developed shell element has no spurious zero energy modes, and can represent a constant strain state. Several numerical tests are carried out to evaluate the performance of the new element developed. The test results show that the behavior of the elements is satisfactory.

Bending of steel fibers on partly supported elastic foundation

  • Hu, Xiao Dong;Day, Robert;Dux, Peter
    • Structural Engineering and Mechanics
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    • v.12 no.6
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    • pp.657-668
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    • 2001
  • Fiber reinforced cementitious composites are nowadays widely applied in civil engineering. The postcracking performance of this material depends on the interaction between a steel fiber, which is obliquely across a crack, and its surrounding matrix. While the partly debonded steel fiber is subjected to pulling out from the matrix and simultaneously subjected to transverse force, it may be modelled as a Bernoulli-Euler beam partly supported on an elastic foundation with non-linearly varying modulus. The fiber bridging the crack may be cut into two parts to simplify the problem (Leung and Li 1992). To obtain the transverse displacement at the cut end of the fiber (Fig. 1), it is convenient to directly solve the corresponding differential equation. At the first glance, it is a classical beam on foundation problem. However, the differential equation is not analytically solvable due to the non-linear distribution of the foundation stiffness. Moreover, since the second order deformation effect is included, the boundary conditions become complex and hence conventional numerical tools such as the spline or difference methods may not be sufficient. In this study, moment equilibrium is the basis for formulation of the fundamental differential equation for the beam (Timoshenko 1956). For the cantilever part of the beam, direct integration is performed. For the non-linearly supported part, a transformation is carried out to reduce the higher order differential equation into one order simultaneous equations. The Runge-Kutta technique is employed for the solution within the boundary domain. Finally, multi-dimensional optimization approaches are carefully tested and applied to find the boundary values that are of interest. The numerical solution procedure is demonstrated to be stable and convergent.

Time dependent finite element analysis of steel-concrete composite beams considering partial interaction

  • Dias, Maiga M.;Tamayo, Jorge L.P.;Morsch, Inacio B.;Awruch, Armando M.
    • Computers and Concrete
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    • v.15 no.4
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    • pp.687-707
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    • 2015
  • A finite element computer code for short-term analysis of steel-concrete composite structures is extended to study long-term effects under service loads, in the present work. Long-term effects are important in engineering design because they influence stress and strain distribution of the structural system and therefore contribute to the increment of deflections in these structures. For creep analysis, a rheological model based on a Kelvin chain, with elements placed in series, was employed. The parameters of the Kelvin chain were obtained using Dirichlet series. Creep and shrinkage models, proposed by the CEB FIP 90, were used. The shear-lag phenomenon that takes place at the concrete slab is usually neglected or not properly taken into account in the formulation of beam-column finite elements. Therefore, in this work, a three-dimensional numerical model based on the assemblage of shell finite elements for representing the steel beam and the concrete slab is used. Stud shear connectors are represented for special beam-column elements to simulate the partial interaction at the slab-beam interface. The two-dimensional representation of the concrete slab permits to capture the non-uniform shear stress distribution in the horizontal plane of the slab due to shear-lag phenomenon. The model is validated with experimental results of two full-scale continuous composite beams previously studied by other authors. Results are given in terms of displacements, bending moments and cracking patterns in order to shown the influence of long-term effects in the structural response and also the potentiality of the present numerical code.

Mixed Convection in Channels of an Electronic Cabinet (전자장비 채널에서의 혼합대류에 관한 연구)

  • 이재헌;남평우;박상동;조성환
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.13 no.4
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    • pp.771-779
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    • 1989
  • Numerical analysis by SIMPLE algorithm has been performed to predict the characteristics of flow and heat transfer in channels between the printed circuit boards of an electronic cabinet. It is assumed that the electronic parts release uniform heat flux per unit axial length to the cooling air. The air flow between channels is assumed fully developed laminar, incompressible, and mixed convective. In this study, the electronic parts are mounted on both sides of the prinked circuit boards by two kinds of configuration such as the zig-zag and the symmetric one. The Rayleigh numbers ranging from 0 to 10$^{6}$ are considered to predict the characteristics of the main flow and the secondary flow occurred by natural convection, the temperature distribution in channel, the heat transfer rate from heated electronic parts and the increase of friction factor by natural convection. As the results of numerical calculation, several conclusions are drawn as follows. The influence of natural convection on the flow characteristics appears strong when the Rayleigh number is above 10$^{4}$. The main axial flow rate decreases by a half or more at the Rayleigh number of 10$^{6}$ . Although the friction factor increases as Rayleigh number increases, the increasing rate of heat transfer is higher than that of the friction factor. The cooling efficiency of the zig-zig-configuration is superior to that of the symmetric configuration at same Rayleigh number.

Predictive model of fatigue crack detection in thick bridge steel structures with piezoelectric wafer active sensors

  • Gresil, M.;Yu, L.;Shen, Y.;Giurgiutiu, V.
    • Smart Structures and Systems
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    • v.12 no.2
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    • pp.97-119
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    • 2013
  • This paper presents numerical and experimental results on the use of guided waves for structural health monitoring (SHM) of crack growth during a fatigue test in a thick steel plate used for civil engineering application. Numerical simulation, analytical modeling, and experimental tests are used to prove that piezoelectric wafer active sensor (PWAS) can perform active SHM using guided wave pitch-catch method and passive SHM using acoustic emission (AE). AE simulation was performed with the multi-physic FEM (MP-FEM) approach. The MP-FEM approach permits that the output variables to be expressed directly in electric terms while the two-ways electromechanical conversion is done internally in the MP-FEM formulation. The AE event was simulated as a pulse of defined duration and amplitude. The electrical signal measured at a PWAS receiver was simulated. Experimental tests were performed with PWAS transducers acting as passive receivers of AE signals. An AE source was simulated using 0.5-mm pencil lead breaks. The PWAS transducers were able to pick up AE signal with good strength. Subsequently, PWAS transducers and traditional AE transducer were applied to a 12.7-mm CT specimen subjected to accelerated fatigue testing. Active sensing in pitch catch mode on the CT specimen was applied between the PWAS transducers pairs. Damage indexes were calculated and correlated with actual crack growth. The paper finishes with conclusions and suggestions for further work.

Shear capacity of stud shear connectors with initial damage: Experiment, FEM model and theoretical formulation

  • Qi, Jianan;Wang, Jingquan;Li, Ming;Chen, Leilei
    • Steel and Composite Structures
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    • v.25 no.1
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    • pp.79-92
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    • 2017
  • Initial damage to a stud due to corrosion, fatigue, unexpected overloading, a weld defect or other factors could degrade the shear capacity of the stud. Based on typical push-out tests, a FEM model and theoretical formulations were proposed in this study. Six specimens with the same geometric dimensions were tested to investigate the effect of the damage degree and location on the static behavior and shear capacity of stud shear connectors. The test results indicated that a reduction of up to 36.6% and 62.9% of the section area of the shank could result in a dropping rate of 7.9% and 57.2%, respectively, compared to the standard specimen shear capacity. Numerical analysis was performed to simulate the push-out test and validated against test results. A parametrical study was performed to further investigate the damage degree and location on the shear capacity of studs based on the proposed numerical model. It was demonstrated that the shear capacity was not sensitive to the damage degree when the damage section was located at 0.5d, where d is the shank diameter, from the stud root, even if the stud had a significant reduction in area. Finally, a theoretical formula with a reduction factor K was proposed to consider the reduction of the shear capacity due to the presence of initial damage. Calculating K was accomplished in two ways: a linear relationship and a square relationship with the damage degree corresponding to the shear capacity dominated by the section area and the nominal diameter of the damaged stud. This coefficient was applied using Eurocode 4, AASHTO LRFD (2014) and GB50017-2003 (2003) and compared with the test results found in the literature. It was found that the proposed method produced good predictions of the shear capacity of stud shear connectors with initial damage.

Modified HAZUS Method for Seismic Fragility Assessment of Domestic PSC-I Girder Bridges (PSC-I 거더교의 지진취약도 평가를 위한 HAZUS 방법의 국내 적용성 연구)

  • Seo, Hyeong-Yeol;Yi, Jin-Hak;Kim, Doo-Kie;Song, Jong-Keol
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.14 no.2
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    • pp.161-170
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    • 2010
  • To reduce the amount of seismic damage, several design codes are being improved considering the earthquake resistant systems, and many researches are being conducted to develop the earthquake damage evaluation techniques. This study develops the Korean seismic fragility function using the modified HAZUS method applicable to PSC-I girder bridges in Korea. The major coefficients are modified considering the difference between the seismic design levels of America and Korea. Seismic fragility function of the PSC-I girder bridge (one of the standard bridge types in Korea) is evaluated using two methods: numerical analysis and modified HAZUS method. The main coefficients are obtained about 70% of the proposed values in HAZUS. It is found that the seismic fragility function obtained using the modified HAZUS method closes to the fragility function obtained by conventional numerical analysis method.

Numerical Modeling of Elastic Wave Scattering in an Isotropic Medium Containing an Orthotropic Inclusion (직교이방성 함유체를 포함하는 등방성 기지에서의 탄성파 산란 수치해석 모델)

  • Lee, Jung-Ki
    • Journal of the Korean Society for Nondestructive Testing
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    • v.21 no.1
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    • pp.69-79
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    • 2001
  • A volume integral equation method(VIEM) is applied for the effective analysis of elastic wave scattering problems in unbounded solids containing general anisotropic inclusions. It should be noted that this newly developed numerical method does not require the Green's function for anisotropic inclusions to solve this class of problems since only the Green's function for the unbounded isotropic matrix is Involved In their formulation for the analysis. nis new method can also be applied to general two-dimensional elastodynamic problems with arbitrary shapes and number of anisotropic inclusions. Through the analysis of plane elastodynamic problems in unbounded isotropic matrix with an orthotropic inclusion, it is established that this new method is very accurate and effective for solving plane elastic problems in unbounded solids containing general anisotropic inclusions.

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Ductile Fracture of a Marine Structural Steel based on HC-DSSE Combined Fracture Strain Formulation (HC-DSSE 조합 파단 변형률 정식화에 기반한 선박해양 구조물용 강재의 연성 파단 예측)

  • Park, Sung-Ju;Lee, Kangsu;Cerik, Burak Can;Kim, Younghyn;Choung, Joonmo
    • Journal of the Society of Naval Architects of Korea
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    • v.56 no.1
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    • pp.82-93
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    • 2019
  • In this paper, the ductile fracture criteria for a marine structural steel (EH36) are presented and validated. The theoretical background of the recently developed Hosford-Coulomb (HC) fracture strain model and the DSSE fracture strain model which was developed to apply to the shell elements is described. In order to accurately estimate the flow stress in the large strain range up to the fracture, the material constants for the combined Swift-Voce constitutive equation were derived by the numerical analyses of the smooth and notched specimens made from the EH36 steel. As a result of applying the Swift-Voce flow stress to the other notched specimen model, a very accurate load - displacement curve could be derived. The material constants of the HC fracture strain and DSSE fracture strain models were independently calibrated based on the numerical analyses for the smooth and notch specimen tests. The user subroutine (VUMAT of Abaqus) was developed to verify the accuracy of the combined HC-DSSE fracture strain model. An asymmetric notch specimen was used as verification model. It was confirmed that the fracture of the asymmetric specimen can be accurately predicted when a very small solid elements are used together with the HC fracture strain model. On the other hand, the combined HC-DSSE fracture strain model can predict accurately the fracture of shell element model while the shell element size effect becomes less sensitive.