• Coupled systems mechanics
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• v.4 no.1
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• pp.99-114
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• 2015

In this paper, a refined exponential shear deformation beam theory is developed for bending analysis of functionally graded beams. The theory account for parabolic variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Contrary to the others refined theories elaborated, where the stretching effect is neglected, in the current investigation this so-called "stretching effect" is taken into consideration. The material properties of the functionally graded beam are assumed to vary according to power law distribution of the volume fraction of the constituents. Based on the present shear deformation beam theory, the equations of motion are derived from Hamilton's principle. Analytical solutions for static are obtained. Numerical examples are presented to verify the accuracy of the present theory.

• 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.

• Textile Coloration and Finishing
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• v.12 no.2
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• pp.121-128
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• 2000

This study discussed the mechanical properties such as bending and shear of polyester fabric treated with a several weight reduction machine. With the increase in the rate of weight loss, the bending rigidity of the warp and weft of treated fabric decreased regardless of the weight reduction machine. At 6.5% weight loss, the bending rigidity of warp and weft yarn decreased to $0.035\;gfcm^2/cm$ and $0.017\;gfcm^2/cm$, respectively, and these values show 54% and 94% of their untreated warp and weft. At same rate of the weight loss, the bending rigidity of polyester fabric treated with C.D.R slightly higher than that of the tank type or liquor-flow type. On the other hand, below 6.5% weight loss, the shear rigidity of the warp and weft of the treated fabric rapidly decreased. But with the increase in the above 6.5% rate of weight loss, the decreasing tendency of the shear rigidity declined. At same rate of the weight loss, the shear rigidity of fabric treated with tank type nearly equal to the that of the liquor flow type. But at same rate of the weight loss, the shear rigidity of the fabric treated with C.D.R type higher than that of the tank or liquor-flow type.

• Journal of the Korean Society for Advanced Composite Structures
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• v.3 no.4
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• pp.17-26
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• 2012

This study presents a governing equations of bending behavior of anisotropic sandwich plates with multi-layered laminated composite faces. Based on zig-zag models for through thickness deformations, the shear deformation of composite faces is included. All edges of plate are assumed to be simply supported. Results of the bending analysis under lateral loads are presented for the influence of various lay up sequences of antisymmetric angle-ply laminated faces. The accuracy of the approach is ascertained by comparing solutions from the sandwich plates theory with composite faces to the laminated plates theory. Since the present analysis considers the bending stiffness of the core and also the transverse shear deformations of the laminated faces, the proposed method showed higher than that calculated according to the general laminated plates theory. The information presented might be useful to design sandwich plates structure with polymer matrix composite faces.

• Journal of Korean Society of Steel Construction
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• v.20 no.4
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• pp.539-548
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• 2008

This study aims to determine the applicability of the previously published T-type modular profile beam in the manner of producing specimens designed specially for the said purpose, determining their bending and shear behaviors depending on the presence of shear reinforcement, and analyzing the results in comparison with the theoretical equation of plastic deformation. The modular profile beam contributes to bending and shear resistance with the addition of the profile to the form function, and enhances the molding performance through the modular concept. The experimental results showed that the TS series specimens with shear reinforcement have bending behaviors superior to those of the T series specimens without shear reinforcement, which suggests that the used shear reinforcement appropriately bears the shear force. However, it was considered that all the specimens except for the T1-1 specimen failed to have adequate bending performance because of the intermodular slipping caused by the shear failure of the bolts. It is expected that further studies on the T-type modular profile beam, in which shear connectors will be considered as a variable,be performed to develop optimal intermodular connection methods.

• Journal of the Earthquake Engineering Society of Korea
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• v.26 no.6
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• pp.227-235
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• 2022

For a member model in nonlinear structural analysis, a lumped plastic model that idealizes its flexural bending, shear, and axial behaviors by springs with the nonlinear hysteretic model is widely adopted because of its simplicity and transparency compared to the other rigorous finite element methods. On the other hand, a challenging task in its numerical solution is to satisfy the equilibrium condition between nonlinear flexural bending and shear springs connected in series. Since the local forces between flexural and shear springs are not balanced when one or both springs experience stiffness changes (e.g., cracking, yielding, and unloading), the additional unbalanced force due to overshooting or undershooting each spring force is also generated. This paper introduces an iterative scheme for numerical solutions satisfying the equilibrium conditions between flexural bending and shear springs. The effect of equilibrium iteration on analysis results is shown by comparing the results obtained from the proposed method to those from the conventional scheme, where the equilibrium condition is not perfectly satisfied.

• Steel and Composite Structures
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• v.14 no.1
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• pp.85-104
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• 2013

The present work deals with the thermomechanical bending response of functionally graded plates resting on Winkler-Pasternak elastic foundations. Theoretical formulations are based on a recently developed refined trigonometric shear deformation theory (RTSDT). The theory accounts for trigonometric distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional trigonometric shear deformation theory, the present refined trigonometric shear deformation theory contains only four unknowns as against five in case of other shear deformation theories. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. The elastic foundation is modelled as two-parameter Pasternak foundation. The results of the shear deformation theories are compared together. Numerical examples cover the effects of the gradient index, plate aspect ratio, side-to-thickness ratio and elastic foundation parameters on the thermomechanical behavior of functionally graded plates. It can be concluded that the proposed theory is accurate and efficient in predicting the thermomechanical bending response of functionally graded plates.

• Journal of the Korea Concrete Institute
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• v.14 no.6
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• pp.910-921
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• 2002

For the prediction of shear behavior of reinforced concrete beams, this paper proposed Transformation Angle Truss Model (TATM) considered bending moment effect. Shear stress-strain relationship obtained from the TATM was agreed well with test results conducted by this study Further, shear strength obtained from the TATM was compared to the experimentally observed results of 170 reinforced concrete beams which had various shear span ratios shapes of support and shapes of cross section. The shear strength of reinforced concrete beams obtained from test was better predicted by the TATM with 0.96 in average and 11.9％ in coefficient of variation than by other truss models. And the ratio of experimental results to theoretical results obtained from the TATM was almost constant regardless of the η and a/d.

• Advances in materials Research
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• v.5 no.4
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• pp.223-244
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• 2016

In this paper, a higher order shear and normal deformation theory is presented for functionally graded material (FGM) plates. By dividing the transverse displacement into bending, shear and thickness stretching parts, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. Indeed, the number of unknown functions involved in the present theory is only five, as opposed to six or even greater numbers in the case of other shear and normal deformation theories. The present theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of ail displacements across the thickness and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The obtained results are compared with three-dimensional and quasi- three-dimensional solutions and those predicted by other plate theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of functionally graded plates.

• Structural Engineering and Mechanics
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• v.55 no.5
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• pp.1001-1014
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• 2015

Bending analysis of functionally graded (FG) nano-plates is investigated in the present work based on a new sinusoidal shear deformation theory. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. The material properties of nano-plate are assumed to vary according to power law distribution of the volume fraction of the constituents. The size effects are considered based on Eringen's nonlocal theory. Governing equations are derived using energy method and Hamilton's principle. The closed-form solutions of simply supported nano-plates are obtained and the results are compared with those of first-order shear deformation theory and higher-order shear deformation theory. The effects of different parameters such as nano-plate length and thickness, elastic foundation, orientation of foundation orthtotropy direction and nonlocal parameters are shown in dimensionless displacement of system. It can be found that with increasing nonlocal parameter, the dimensionless displacement of nano-plate increases.