• Geomechanics and Engineering
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• v.11 no.2
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• pp.289-307
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• 2016

A simple hyperbolic shear deformation theory taking into account transverse shear deformation effects is proposed for the free flexural vibration analysis of thick functionally graded plates resting on elastic foundations. By considering further supposition, the present formulation introduces only four unknowns and its governing equations are therefore reduced. Hamilton's principle is employed to obtain equations of motion and Navier-type analytical solutions for simply-supported plates are compared with the available solutions in literature to check the accuracy of the proposed theory. Numerical results are computed to examine the effects of the power-law index and side-to-thickness ratio on the natural frequencies.

• 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.

• Steel and Composite Structures
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• v.27 no.3
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• pp.311-325
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• 2018

This article presents the bending analysis of FGM rectangular plates resting on non-uniform elastic foundations in thermal environment. Theoretical formulations are based on a recently developed refined shear deformation theory. The displacement field of the present theory is chosen based on nonlinear variations in the in-plane displacements through the thickness of the plate. The present theory 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 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 modeled as non-uniform 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 thermo-mechanical behavior of functionally graded plates. Numerical results show that the present theory can archive accuracy comparable to the existing higher order shear deformation theories that contain more number of unknowns.

• Journal of the Korean Geotechnical Society
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• v.31 no.11
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• pp.15-23
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• 2015

An experimental study has been conducted to evaluate the effects of average and cyclic shear stresses on the undrained failure behaviors of dense marine silty sand by using the Cyclic Direct Simple Shear apparatus. The results show that when the average shear stress ratio is zero, symmetric cyclic shear deformation is the major component of deformation, and permanent shear deformation is relatively small. On the other hand, when the average shear stress ratio is larger than zero, asymmetric permanent shear deformation is the major component, and cyclic shear deformation does not change much as the number of cyclic loads increases. The average shear stress ratio has less effects on the number of cyclic loads needed to fail, as compared with the cyclic shear stress ratio. The proposed stress-dependent failure contour can effectively be used to assess the cyclic shear strength of soil beneath the foundation for the design of offshore structures.

• Structural Engineering and Mechanics
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• v.89 no.3
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• pp.225-238
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• 2024

In this paper, a quasi-3D hyperbolic shear deformation theory for the bending responses of a functionally graded (FG) porous micro-beam is based on a modified couple stress theory requiring only one material length scale parameter that can capture the size influence. The model proposed accounts for both shear and normal deformation effects through an illustrative variation of all displacements across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the micro-beam. The effective material properties of the functionally graded micro-beam are assumed to vary in the thickness direction and are estimated using the homogenization method of power law distribution, which is modified to approximate the porous material properties with even and uneven distributions of porosity phases. The equilibrium equations are obtained using the virtual work principle and solved using Navier's technique. The validity of the derived formulation is established by comparing it with the ones available in the literature. Numerical examples are presented to investigate the influences of the power law index, material length scale parameter, beam thickness, and shear and normal deformation effects on the mechanical characteristics of the FG micro-beam. The results demonstrate that the inclusion of the size effects increases the microbeams stiffness, which consequently leads to a reduction in deflections. In contrast, the shear and normal deformation effects are just the opposite.

• 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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.675-680
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• 2006

This paper deals with the flexural free vibrations of strip foundations. Based on dynamic equilibrium equations of a beam element resting on Winkler foundation, differential equations governing free vibration of strip foundation are derived, in which effects of rotatory inertia and shear deformation are included. For obtaining the natural frequencies, differential equations are solved by numerical methods. As the numerical results, relationships between natural frequencies and various strip parameters are obtained and presented in Tables and Figures.

• Structural Engineering and Mechanics
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• v.21 no.1
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• pp.19-33
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• 2005

An improved shear deformable thin-walled curved beam theory to overcome the drawback of currently available beam theories is newly proposed for the spatially coupled free vibration and elastic analysis. For this, the displacement field considering the shear deformation effects is presented by introducing displacement parameters defined at the centroid and shear center axes. Next the elastic strain and kinetic energies considering the shear effects due to the shear forces and the restrained warping torsion are rigorously derived. Then the equilibrium equations are consistently derived for curved beams with non-symmetric thin-walled sections. It should be noticed that this formulation can be easily reduced to the warping-free beam theory by simply putting the sectional properties associated with warping to zero for curved beams with L- or T-shaped sections. Finally in order to illustrate the validity and the accuracy of this study, finite element solutions using the isoparametric curved beam elements are presented and compared with those in available references and ABAQUS's shell elements.

• Proceedings of the Korea Concrete Institute Conference
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• 2005.11a
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• pp.53-56
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• 2005

This paper investigates the effect of ductile deformation behavior of high performance hybrid fiber-reinforced cement composites (HPHFRCCs) on the shear behavior of coupling beams to lateral load reversals. The matrix ductility and the reinforcement layout were the main variables of the tests. Three short coupling beams with two different reinforcement arrangements and matrixes were tested. They were subjected to cyclic loading by a suitable experimental setup. All specimens were characterized by a shear span-depth ratio of 1.0. The reinforcement layouts consisted of a classical scheme and diagonal scheme without confining ties. The effects of matrix ductility on deflections, strains, crack widths, crack patterns, failure modes, and ultimate shear load of coupling beams have been examined. The combination of a ductile cementitious matrix and steel reinforcement is found to result in improved energy dissipation capacity, simplification of reinforcement details, and damage-tolerant inelastic deformation behavior. Test results showed that the HPFRCC coupling beams behaved better than normal reinforced concrete control beams. These results were produced by HPHFRCC's tensile deformation capacity, damage tolerance and tensile strength.

• Proceedings of the Korean Geotechical Society Conference
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• 2000.11a
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• pp.3-14
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• 2000

Anisotropic consolidation, shear, a transportational component during or after deposition each may produce anisotropic fabrics, which result in the anisotropic properties of soils. Nevertheless, the isotropically consolidated compression triaxial tests are commonly used in practice to determine the strength of the anisotropically consolidated soils because of their practicality and simplicity. In this paper the effects of anisotropic consolidation on the strength properties of soils are discussed. For the sandy soils consolidated under a constant vertical consolidation pressure, the deformation modulus decreases with decreasing consolidation pressure ratio($\sigma$$\sub$3c/'/$\sigma$ sub 1c/'), but the liquefaction resistance increases. For the saturated cohesive soils, both the undrained shear strength and undrained creep strength decrese with decreasing the consolidation pressure ratio. When the in-situ strength properties of the anisotropically and normally consolidated soils are determined by the isotropically consolidated tests, the undrained shear strength and creep strength of saturated cohesive soils as well as the deformation modulus of sandy soils are measured to be higher than the rear in-situ values. This, therefore, could lead to a dangerous judgement in stability analysis