• Structural Engineering and Mechanics
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• v.86 no.1
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• pp.69-83
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• 2023

Analytical solutions to problems are crucial because they provide high-quality comparison data for assessing the accuracy of numerical solutions. Benchmark analytical solutions for the vibrations of cracked functionally graded material (FGM) plates are not available in the literature because of the high level of complexity of such solutions. On the basis of first-order shear deformation plate theory (FSDT), this study proposes analytical series solutions for the vibrations of FGM rectangular plates with side or internal cracks parallel to an edge of the plates by using Fourier cosine series and the domain decomposition technique. The distributions of FGM properties along the thickness direction are assumed to follow a simple power law. The proposed analytical series solutions are validated by performing comprehensive convergence studies on the vibration frequencies of cracked square plates with various crack lengths and under various boundary condition combinations and by performing comparisons with published results based on various plate theories and the theory of three-dimensional elasticity. The results reveal that the proposed solutions are in excellent agreement with literature results obtained using the Ritz method on the basis of FSDT. The paper also presents tabulations of the first six nondimensional frequencies of cracked rectangular Al/Al2O3 FGM plates with various aspect ratios, thickness-to-width ratios, crack lengths, and FGM power law indices under six boundary condition combinations, the tabulated frequencies can serve as benchmark data for assessing the accuracy of numerical approaches based on FSDT.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.10 no.10
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• pp.2615-2618
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• 2009

Double rectangular patch with 4-bridges is investigated for solution of IEEE 802.11b/g (2.4 GHz) and 802.11a (5.5 GHz). Rectangular patch for 5.5 GHz frequency band is printed on the PCB substrate and connected to another rectangular patch for 2.4 GHz frequency band with 4-bridges to obtain dual band operation in an antenna element. 4-bridges can modify the desired frequency band from its original frequency band by changing its width. Gain of 2.4 GHz patch is 5 dBi and 5.5 GHz patch is 3.7 dBi at ${\theta}=0^{\circ}$.

• Journal of Advanced Marine Engineering and Technology
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• v.25 no.3
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• pp.552-562
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• 2001

Measurement of average of heat transfer and friction coefficients were obtained with air flowing through electrically heated ducts having square, rectangular(aspect ration, 5), and triangular cross section for range of surface temperature from $540^{\circ}$to $1780^{\circ}$ R and Reynolds number from 1000 to 330,000. The results indicates that the effect of heat flux on correlations of the average heat transfer and friction coefficients is similar to that obtained for circular tubes in previous investigation and was nearly eliminated by evaluating the physical properties and density of the air a film temperature halfway between the average surface and fluid bulk temperatures, With the Nusselt and Reynolds numbers on the hydraulic diameter of the ducts, the data for the noncircular ducts could be represented by the same equations obtained in the previous investigation for circular tubes. Correlation of the average difference between the surface corner and midwall temperatures for the square duct was in agreement with predicted values from a previous analysis. However, for the rectangular and triangular ducts, the measured corner temperature was greater by approximately 20 and 35 percent, respectively, than the values predicted by analysis.

• Steel and Composite Structures
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• v.11 no.2
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• pp.131-147
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• 2011

The aim of this work is to provide some insights into the elasto-plastic behaviour of plate girder web square and rectangular panels with centred and eccentric holes under both compression and in-plane bending moment. The numerical study was validated comparing the numerical results obtained for one simple steel plate configuration with the corresponding experimental results, obtained at the University of Padova, observing the influence of the initial out-of-plane imperfections on the force vs. displacement relationship and ultimate strength. Once validated the numerical approach, the effect of bending moment on the stability of the plate is studied and some differences with respect to the uniform compression load case are shown. The influence of dimension and position of the hole, the plate aspect ratio and the steel grade on elasto-plastic behaviour is observed. Some indications regarding the critical slenderness (at which transition from elastic to plastic collapse occurs) are given for square and rectangular plates with symmetric and eccentric holes having small, medium and large diameter.

• Steel and Composite Structures
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• v.46 no.3
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• pp.353-366
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• 2023

This paper presents a finite-element analysis (FEA) of aluminum alloy rectangular hollow sections (RHSs) and square hollow sections (SHSs) with circular through-openings under three-point and four-point bending. First, a finite-element model (FEM) was developed and validated against the corresponding test results available in the literature. Next, using the validated FE models, a parametric study comprising 180 FE models was conducted. The cross-section width-to-thickness ratio (b/t) ranged from 2 to 5, the hole size ratio (d/h) ranged from 0.2 to 0.8 and the quantity of holes (n) ranged from 2 to 6, respectively. Third, results obtained from laboratory test and FEA were compared with current design strengths calculated in accordance with the North American Specifications (NAS), the modified direct strength method (DSM) and the modified Continuous strength method (CSM). The comparison shows that the modified CSM are conservative by 15% on average for aluminum alloy RHSs and SHSs with circular through-openings subject to bending. Finally, a new design equation is proposed based on the modified CSM after being validated with results obtained from laboratory test and FEA. The proposed design equation can provide accurate predictions of flexural capacities for aluminum alloy RHSs and SHSs with circular through-openings.

• Journal of the Korea Concrete Institute
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• v.11 no.4
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• pp.55-62
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• 1999

When stress is beyond elastic limit or cracks occur in a reinforced concrete member subjected to axial force and biaxial bending, curvature about each principal axis of uncracked section is influenced by axial force and bending moments about both major and minor principal axes. It is mainly due to the translation and rotation of principal axes of the cross section after cracking. Recently, by considering these effects, a numerical method predicting the behavior of concrete columns subjected to axial force and biaxial bending was proposed. In this study, in order to verify the proposed numerical method and investigate the effects of cracking on the behavior of reinforced concrete columns, a series of tests were carried out for 16 tied reinforced concrete columns with 100×100 mm square and 200×100 mm rectangular sections under various loading conditions. The angle between the direction of eccentricity and the major principal axis of uncracked section were 0, 30, 40° for the square section and 0, 30, 45, 60, 90° for the rectangular section, respectively. A comparison between numerical predictions and test results shows good agreements in ultimate loads, axial force-lateral deflection relations, and lateral deflection trajectories. It is also found, in this limited investigation, that the ACI's moment magnifier method is conservative in both uniaxial and biaxial loading conditions.

• Structural Engineering and Mechanics
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• v.34 no.2
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• pp.175-188
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• 2010

This paper deals with the buckling and postbuckling responses, and the progressive failure of square laminates of symmetric lay-up with a central rectangular cutout under in-plane shear load. A detailed investigation is made to show the effects of cutout size and cutout aspect ratio on the buckling and postbuckling responses, failure loads and failure characteristics of $(+45/-45/0/90)_{2s}$, $(+45/-45)_{4s}$ and $(0/90)_{4s}$ laminates. The 3-D Tsai-Hill criterion is used to predict the failure of a lamina while the onset of delamination is predicted by the interlaminar failure criterion. In addition, the effects of boundary conditions on buckling loads, failure loads, failure modes, and maximum transverse deflection for a $(+45/-45/0/90)_{2s}$ laminate with and without a square cutout have been presented. It is concluded that because of early onset of delamination at the net section of cutouts before first-ply failure, total strength of the laminate with very small cutouts can not be utilized.

• Wind and Structures
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• v.29 no.1
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• pp.65-75
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• 2019

A heated square cylinder (with height $A^*$) is kept parallel to the cold wall at a fixed gap height $0.5A^*$ from the wall. Another adiabatic rectangular cylinder (of same height $A^*$ and width $0.5A^*$) is placed upstream in an inline tandem arrangement. The spacing between the two cylinders is fixed at $3.0A^*$. The inlet flow is taken as Couette-Poiseuille flow based non-linear velocity profile. The conventional fluid (also known as base fluid) is chosen as water (W) whereas the nanoparticle material is selected as $Al_2O_3$. Numerical simulations are performed by using SIMPLE algorithm based Finite Volume approach with staggered grid arrangement. The dependencies of hydrodynamic and heat transfer characteristics of the cylinder on non-dimensional parameters governing the nanofluids and the fluid flow are explored here. A critical discussion is made on the mechanism of improvement/reduction (due to the presence of the upstream cylinder) of heat transfer and drag coefficient, in comparison to those of an isolated cylinder. It is observed that the heat transfer increases with the increase in the non-linearity in the incident velocity profile at the inlet. For the present range studied, particle concentration has a negligible effect on heat transfer.

• Journal of the Korean Institute of Gas
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• v.12 no.1
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• pp.54-61
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• 2008

Experimental investigations were performed to assess the influences of different multiple obstacles on flame propagation in a rectangular confinement. Three different multiple obstacles were used: circular, triangular and square cross-sections with blockage ratios of 15% and 30%. The same method described in Park et al. [13] to investigate the interaction between the propagating flame and the obstacle was applied. Before the freely propagating flame impinged on the obstacle, the flame propagation speed remains close to the laminar burning velocity, regardless of the obstacles used. The reported data revealed that the trend in increase of the local flame propagation speed is a result of the interaction between the obstacle and the propagating flame front behind the obstacle. The local speed was found to increase from a circular to a triangular and a square obstacle. The mean flame speed was found to be less dependent on both the obstacle types and the different blockage ratios used.

• International Journal of High-Rise Buildings
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• v.7 no.4
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• pp.313-325
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• 2018

Concrete-filled steel tubular (CFST) members are commonly used as composite columns in modern construction. However, the current guidelines for members' fire design (EN1994-1-2) have been proved to be unsafe in case the relative slenderness is higher than 0.5. In addition, the simplified design methods of Eurocode 4 are limited to circular and square CFST columns, while in practice columns with rectangular and elliptical hollow sections are being increasingly used because of their architectural aesthetics. In the last years a large experimental research has been carried out at Coimbra University on the topic. They have been tested concrete filled circular, square, rectangular and elliptical hollow columns with restrained thermal elongation. Some parameters such as the slenderness, the type of cross-section geometry as well as the axial and rotational restraint of the surrounding structure to the column have been tested in order to evaluate their influence on the fire resistance of such columns. In this paper it is evaluated the influence of the boundary conditions (pin-ended and semi-rigid end-support conditions) on the behavior of the columns in case of fire. In these tests it could not be seen a marked effect of the tested boundary conditions but it is believed that the increasing of rotational stiffness increases the fire resistance of the columns.