• Journal of computational fluids engineering
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• v.12 no.4
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• pp.20-27
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• 2007

Two-dimensional stagnation flow toward a plane wall coated with magnetic fluid of uniform thickness is investigated. The flow field is represented as a similarity solution of the Navier-Stokes equation for this incompressible laminar flow. The resulting third order ordinary differential equation is solved numerically by using the shooting method and by determining two shooting parameters so as to satisfy the boundary and interface conditions. Features of the flow including streamline patterns are investigated for the varying values of density ratio, viscosity ratio, and Reynolds number. An adverse flow with double eddy pair in magnetic fluid region is found to emerge as the Reynolds number becomes higher than a threshold value. The results for the interface velocity, interface and wall shear stress, and boundary layer and displacement thickness are also presented.

• Journal of Aerospace System Engineering
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• v.15 no.2
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• pp.1-9
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• 2021

In this paper, a thickness compensation function is introduced to consider the shear deformation and warping effect resulting from increased thickness in the composite multi-cell wing box. The thickness compensation function is used to perform the structure optimization of the multi-cell. It is determined by minimizing the error of an analytical formula using solid mechanics and the Ritz method. It is used to define a structural performance prediction expression due to the increase in thickness. The parameter is defined by the number of spars and analyzed by the critical buckling load and the limited failure index as a response. Constraints in structural optimization are composed of displacements, torsional angles, the critical buckling load, and the failure index. The objective function is the mass, and its optimization is performed using a genetic algorithm.

• Steel and Composite Structures
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• v.35 no.1
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• pp.129-145
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• 2020

In typical, structural topology optimization plays a significant role to both increase stiffness and save mass of structures in the resulting design. This study contributes to a new numerical approach of topologically optimal design of Mindlin-Reissner plates considering Winkler foundation and mathematical formulations of multi-directional variable thickness of the plate by using multi-materials. While achieving optimal multi-material topologies of the plate with multi-directional variable thickness, the weight information of structures in terms of effective utilization of the material at the appropriate thickness location may be provided for engineers and designers of structures. Besides, numerical techniques of the well-established mixed interpolation of tensorial components 4 element (MITC4) is utilized to overcome a well-known shear locking problem occurring to thin plate models. The well-founded mathematical formulation of topology optimization problem with variable thickness Mindlin-Reissner plate structures by using multiple materials is derived in detail as one of main achievements of this article. Numerical examples verify that variable thickness Mindlin-Reissner plates on Winkler foundation have a significant effect on topologically optimal multi-material design results.

• Journal of Welding and Joining
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• v.28 no.2
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• pp.74-78
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• 2010

In this paper, a non-contact method of evaluating the thickness reduction in an aluminum sheet caused by corrosion and friction using SH-EMAT (shear horizontal, electromagnetic acoustic transducer) is described. Since this method is based on the measurement of the time-of-flight and amplitude change of guided waves caused from the thickness reduction, it provides information on the thinning defects. Information was obtained on the changes of the various wave features, such as their time-of-flight and amplitude, and their correlations with the thickness reduction were investigated. The interesting features in the dispersive behavior of selected guided modes were used for the detection of thinning defects. The measurements of these features using SH waves were performed on aluminum specimens with regions thinned by 7.2% to 29.5% of the total thickness. It is shown that the time-of-flight measurement provides an estimation of the thickness reduction and length of the thinning defects.

• Journal of the Korean Society of Safety
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• v.29 no.3
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• pp.72-78
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• 2014

The minimum thickness of long-span deck slab is proposed by checking the limit state according to the Korean highway bridge design code(limit state design). Both minimizing thickness and ensuring safety of deck slab are important design factors to increase a competitive price of the long span deck slabs. The required thicknesses for satisfying flexural capacity, preventing punching shear failure and limiting deflection were calculated by considering KL-510 load model which has increased total load compared to DB 24 from 432 kN to 510 kN. The results of the required thickness for various limit states were compared to propose the minimum thickness as a function of span length of deck slabs. The proposed minimum thickness is influenced by satisfying flexural capacity and limiting deflection. It turns out to be similar compared to the results of the previous study by ultimate strength design method even if the live load model was increased in total weights.

• Steel and Composite Structures
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• v.17 no.1
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• pp.21-46
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• 2014

This paper presents a simple n-order four variable refined theory for the bending and vibration analyses of functionally graded plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The present theory is variationally consistent, uses the n-order polynomial term to represent the displacement field, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The governing equations are derived by employing the Hamilton's principle and the physical neutral surface concept. The accuracy of the present solutions is verified by comparing the obtained results with available published ones.

• Geomechanics and Engineering
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• v.15 no.5
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• pp.1047-1059
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• 2018

This paper focuses on the cracking and fragmentation process in rock materials containing a pair of non-parallel flaws, which are through the specimen thickness, under vertical compression. Several numerical experiments are conducted with varying flaw arrangements that affect the initiation and tensile wing cracks, shear crack growth, and crack coalescing behaviors. To obtain realistic numerical results, a parallelized peridynamics formulation coupled with a finite element method, which is able to capture arbitrarily occurring cracks, is employed. From previous studies, crack initiation and propagation of tensile wing cracks, horsetail cracks, and anti-wing cracks are well understood along with the coalescence between two parallel flaws. In this study, the coalescence behaviors, their fragmentation sequences, and the role of an x-shaped shear band in rock material containing two non-parallel flaws are discussed in detail on the basis of simulation results strongly correlated with previous experimental results. Firstly, crack initiation and propagation of tensile wing cracks and shear cracks between non-parallel flaws are investigated in time-history and then sequential coalescing behavior is analyzed. Secondly, under the effect of varying inclination angles of two non-parallel flaws and overlapping ratios between a pair of non-parallel flaws, the cracking patterns including crack coalescence, fragmentation, and x-shaped shear band are investigated. These numerical results, which are in good agreement with reported physical test results, are expected to provide insightful information of the fracture mechanism of rock with non-parallel flaws.

• Steel and Composite Structures
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• v.29 no.3
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• pp.363-377
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• 2018

An efficient and free of shear locking finite element model is developed and employed to study free vibration of tapered bidirectional functionally graded material (BFGM) beams. The beam material is assumed to be formed from four distinct constituent materials whose volume fraction continuously varies along the longitudinal and thickness directions by power-law functions. The finite element formulation based on the first-order shear deformation theory is derived by using hierarchical functions to interpolate the displacement field. In order to improve efficiency and accuracy of the formulation, the shear strain is constrained to constant and the exact variation of the cross-sectional profile is employed to compute the element stiffness and mass matrices. A comprehensive parametric study is carried out to highlight the influence of the material distribution, the taper and aspect ratios as well as the boundary conditions on the vibration characteristics. Numerical investigation reveals that the proposed model is efficient, and it is capable to evaluate the natural frequencies of BFGM beams by using a small number of the elements. It is also shown that the effect of the taper ratio on the fundamental frequency of the BFGM beams is significantly influenced by the boundary conditions. The present results are of benefit to optimum design of tapered FGM beam structures.

• Journal of Welding and Joining
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• v.21 no.7
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• pp.59-64
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• 2003

Microstructure and shear strength of Sn-Zn lead-free solders and Au/Ni/Cu UBM joint under thermal aging conditions was investigated. The samples were aged isothermally at 10$0^{\circ}C$ and 15$0^{\circ}C$ for 300, 600, and 900 hours. The IMCs(Intermetallic Compound) at the interface between solder and UBM were examined by FESEM and TEM. The results showed that the shear strength was decreased with aging time and temperature. The solder ball with high activated RA flux had about 8.2% higher shear strength than that of RMA flux. Poor wetting and many voids were observed in the fractured solder joint with of RMA flux. The decreased shear strengths were caused by IMC growth and Zn grain coarsening. Zn reacted with Au and then was transformed to the $\beta$ -AuZn compound. Although AuZn grew first, $r-Ni_5Zn_{21}$ compounds were formed with aging time. The layers indicated by $Ni_5Zn_{21}(1)$, (2), and (3) were formed with the thickness of ∼0.7 ${\mu}{\textrm}{m}$, ∼4 ${\mu}{\textrm}{m}$, and ∼2 ${\mu}{\textrm}{m}$, respectively.

• Steel and Composite Structures
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• v.17 no.4
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• pp.453-470
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• 2014

This article is the result of an investigation on the influence of a Pasternak elastic foundation on the stability of exponentially graded (EG) cylindrical shells under hydrostatic pressure, based on the first-order shear deformation theory (FOSDT) considering the shear stresses. The shear stresses shape function is distributed parabolic manner through the shell thickness. The governing equations of EG orthotropic cylindrical shells resting on the Pasternak elastic foundation on the basis of FOSDT are derived in the framework of Donnell-type shell theory. The novelty of present work is to achieve closed-form solutions for critical hydrostatic pressures of EG orthotropic cylindrical shells resting on Pasternak elastic foundation based on FOSDT. The expressions for critical hydrostatic pressures of EG orthotropic cylindrical shells with and without an elastic foundation based on CST are obtained, in special cases. Finally, the effects of Pasternak foundation, shear stresses, orthotropy and heterogeneity on critical hydrostatic pressures, based on FOSDT are investigated.