• Structural Engineering and Mechanics
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• v.72 no.5
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• pp.653-673
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• 2019

This work investigates a novel quasi-3D hyperbolic shear deformation theory is presented to discuss the buckling of new type of sandwich plates. This theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of all displacements through the thickness. The enhancement of this formulation is due to the use of only five unknowns by including undetermined integral terms, contrary to other theories where we find six or more unknowns. It does not require shear correction factors and transverse shear stresses vary parabolically across the thickness. A new type of FGM sandwich plates, namely, both FGM face sheets and FGM hard core are considered. The governing equations and boundary conditions are derived using the principle of virtual displacements. Analytical solutions are obtained for a simply supported plate. The accuracy of the present theory is verified by comparing the obtained results with quasi-3D solutions and those predicted by higher-order shear deformation theories. The comparison studies show that the obtained results are not only more accurate than those obtained by higher-order shear deformation theories, but also comparable with those predicted by quasi-3D theories with a greater number of unknowns.

• Structural Engineering and Mechanics
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• v.26 no.1
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• pp.1-14
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• 2007

Because of complexity, the literature regarding the free vibration analysis of a Timoshenko beam carrying "multiple" spring-mass systems is rare, particular that regarding the "exact" solutions. As to the "exact" solutions by further considering the joint terms of shear deformation and rotary inertia in the differential equation of motion of a Timoshenko beam carrying multiple concentrated attachments, the information concerned is not found yet. This is the reason why this paper aims at studying the natural frequencies and mode shapes of a uniform Timoshenko beam carrying multiple intermediate spring-mass systems using an exact as well as a numerical assembly method. Since the shear deformation and rotary inertia terms are dependent on the slenderness ratio of the beam, the shear coefficient of the cross-section, the total number of attachments and the support conditions of the beam, the individual and/or combined effects of these factors on the result are investigated in details. Numerical results reveal that the effect of the shear deformation and rotary inertia joint terms on the lowest five natural frequencies of the combined vibrating system is somehow complicated.

• Smart Structures and Systems
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• v.21 no.4
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• pp.397-405
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• 2018

In this paper, a novel simple shear deformation theory for buckling analysis of single layer graphene sheet is formulated using the nonlocal differential constitutive relations of Eringen. The present theory involves only three unknown and three governing equation as in the classical plate theory, but it is capable of accurately capturing shear deformation effects, instead of five as in the well-known first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Nonlocal elasticity theory is employed to investigate effects of small scale on buckling of the rectangular nano-plate. The equations of motion of the nonlocal theories are derived and solved via Navier's procedure for all edges simply supported boundary conditions. The results are verified with the known results in the literature. The influences played by Effects of nonlocal parameter, length, thickness of the graphene sheets and shear deformation effect on the critical buckling load are studied. Verification studies show that the proposed theory is not only accurate and simple in solving the buckling nanoplates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns.

• Proceeding of KASS Symposium
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• 2008.05a
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• pp.95-100
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• 2008

A 4-node assumed strain finite element based on higher order shear deformation theory is developed to investigate the behaviours of symmetric and unsymmetric laminated composite plates. The present element is based on Reddy's higher order shear deformation theory so that it can consider the parabolic distribution of shear deformation through plate thickness direction. In particular, assumed strain method is adopted to alleviate the shear locking phenomena inherited plate elements based on higher order shear deformation theory. The present finite element has seven degrees of freedom per node and denoted as HSA4. Numerical examples are carried out for symmetric and unsymmetric laminated composite plate with various thickness values. Numerical results are compared with reference solutions produced by other higher order shear deformation theories.

• Steel and Composite Structures
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• v.25 no.6
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• pp.717-726
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• 2017

In this paper, a new simple shear deformation theory for bending analysis of functionally graded plates is developed. The present theory involves only three unknown and three governing equation as in the classical plate theory, but it is capable of accurately capturing shear deformation effects, instead of five as in the well-known first shear deformation theory and higher-order shear deformation theory. A shear correction factor is, therefore, not required. 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. Equations of motion are obtained by utilizing the principle of virtual displacements and solved via Navier's procedure. The elastic foundation is modeled as two parameter elastic foundation. The results are verified with the known results in the literature. The influences played by transversal shear deformation, plate aspect ratio, side-to-thickness ratio, elastic foundation, and volume fraction distributions are studied. Verification studies show that the proposed theory is not only accurate and simple in solving the bending behaviour of functionally graded plates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns.

• Journal of the Korean Geotechnical Society
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• v.34 no.4
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• pp.13-25
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• 2018

When deformation occurs on slope reinforced with anchor, shear stress and bending stress are applied on the shear surface along the slip surface and increase of the shear deformation causes the tension force variation of the anchor. In this study, shear test was performed by measuring the tension force of the anchor by inducing shear deformation in vertical direction of the anchor using a large-scale direct shear test equipment in order to confirm the tension force variation of the anchor induced by shear deformation. The shear test was performed for 8 conditions which were classified according to the anchor reinforcement, separation distance (1D, 2D, 4D) from the shear surface to bonded part and the lateral-pressure condition (0.1 MPa, 0.2 MPa) of adjacent ground. As a result of the shear test, it was found that the separation distance and the lateral-pressure condition affect the shear force of the ground reinforced by anchor and the tension force of the anchor, and experimentally verified that the shear force variation is related to axial force variation of the anchor head and tip. Therefore, it was confirmed that the behavior of the bonded part induced by the shear deformation can be indirectly predicted by analyzing the tendency of the tension force variation of the anchor head.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.361-368
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• 2001

This paper deals with the buckling load of antisymmetric angle-ply and cross-ply laminated rectangular plates. Buckling analysis is preformed for a simply supported, shear deformable laminated plate subjected to uniaxial compression and biaxial compression combined with uniform lateral pression. The shear deformation theory is considered to figure out a more exact behavior of laminated plates exactly. The purposes of this study are to formulate anisotropic laminated plates with shear deformation and to investigate the buckling load according to the various variables of laminated plates by using the exact solutions for anisotropic laminated plates having simply supported boundary.

• Steel and Composite Structures
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• v.21 no.6
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• pp.1347-1368
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• 2016

In this article, an exact analytical solution for mechanical buckling analysis of symmetrically cross-ply laminated plates including curvature effects is presented. The equilibrium equations are derived according to the refined nth-order shear deformation theory. The present refined nth-order shear deformation theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components, in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments The most interesting feature of this theory is that it accounts for a parabolic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Buckling of orthotropic laminates subjected to biaxial inplane is investigated. Using the Navier solution method, the differential equations have been solved analytically and the critical buckling loads presented in closed-form solutions. The sensitivity of critical buckling loads to the effects of curvature terms and other factors has been examined. The analysis is validated by comparing results with those in the literature.

• Steel and Composite Structures
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• v.20 no.5
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• pp.1023-1042
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• 2016

Based on Hamilton's principle, the flexural vibration differential equations and boundary conditions of the steel-concrete composite beam (SCCB) with comprehensive consideration of the influences of the shear deformation, interface slip and longitudinal inertia of motion were derived. The analytical natural frequencies of flexural vibration were compared with available results previously observed by the experiments, the results calculated by the FE model and the other similar beam theories available in the open literatures. The comparison results showed that, the calculation results of the analytical and Timoshenko models had a good agreement with the results of the experimental test and FE model. Finally, the influences of shear deformation and interface slip on the flexural natural frequencies of the SCCB were discussed. The shear deformation effect increases with the increase of the mode orders of flexural natural vibration, and the flexural natural frequencies of the higher mode orders ignoring the influence of shear deformations effect would be overestimated. The interface slip effect decrease with the increase of the mode orders of flexural natural vibration, and the influence of the interface slip effect on flexural natural frequencies of the low mode orders is significant. The influence of the degree of shear connection on shear deformation effect is insignificant, and the low order modes of flexural natural vibration are mainly composed of the rotational displacement of cross sections.

• 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.