• Earthquakes and Structures
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• v.14 no.2
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• pp.103-115
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• 2018

In this work, a simple but accurate hyperbolic plate theory for the free vibration analysis of functionally graded material (FGM) sandwich plates is developed. The significant feature of this formulation is that, in addition to including the shear deformation effect, it deals with only 3 unknowns as the classical plate theory (CPT), instead of 5 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. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM face sheet and the homogeneous core and the sandwich with the homogeneous face sheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. Numerical results of the present theory are compared with the CPT, FSDT, order shear deformation theories (HSDTs), and 3D solutions. Verification studies show that the proposed theory is not only accurate and simple in solving the free vibration behaviour of FGM sandwich plates, but also comparable with the higher-order shear deformation theories which contain more number of unknowns.

• Computers and Concrete
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• v.18 no.6
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• pp.1213-1234
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• 2016

This paper describes a deformation-based strut-and-tie model for the flexural members at post-yield state. Boundary deformation conditions by flexural post-yield response are chosen in terms of the flexural bar strains as the main factor influenced on the shear strength. The main purpose of the proposed model is to predict the shear capacities of the flexural members associated with the given flexural deformation conditions. To verify the proposed strut-and-tie model, the estimated shear strengths depending on the flexural deformation are compared with the experimental results. The experimental data are in good agreement with the values obtained by the proposed model.

• The Journal of the Petrological Society of Korea
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• v.3 no.1
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• pp.20-33
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• 1994

Some of the seven types of subgrain boundaries (Means and Ree, 1988) in octachloropropane samples show distinctive deformation patterns during their development. Type II subgrain boundaries migrate to accommodate the deformation difference between adjacent grains. The formation of Type III requires a rigid-body roation of grains to reduce misorientation of adjacent grains. Type I, IV, V and VI develop either in static or dynamic condition. Type VII form only in static environments after deformation. Ribbon grains can develop via Type III or Type IV process. The orientation pattern and density of subgrain boundaries are more or less stable through a post-deformation heating. Subgrain boundary orientations are symmetric with respect to the grain-shape foliation in pure shear. In simple shear, their maximum inclines toward the direction of shear.

• Structural Engineering and Mechanics
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• v.57 no.1
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• pp.127-140
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• 2016

In this paper, a new first shear deformation plate theory based on neutral surface position is developed for the static and the free vibration analysis of functionally graded plates (FGPs). Moreover, the number of unknowns of this theory is the least one comparing with the traditional first-order and the other higher order shear deformation theories. The neutral surface position for a functionally graded plate which its material properties vary in the thickness direction is determined. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Based on the present shear deformation plate theory and the neutral surface concept, the governing equations are derived from the principle of Hamilton. There is no stretching-bending coupling effect in the neutral surface based formulation. Numerical illustrations concern flexural and dynamic behavior of FG plates with Metal-Ceramic composition. Parametric studies are performed for varying ceramic volume fraction, length to thickness ratios. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

• Geomechanics and Engineering
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• v.13 no.3
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• pp.385-410
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• 2017

This work presents a simple and refined nth-order shear deformation theory for mechanical and thermal buckling behaviors of functionally graded (FG) plates resting on elastic foundation. The proposed refined nth-order shear deformation theory has a new displacement field which includes undetermined integral terms and contains only four unknowns. Governing equations are obtained from the principle of minimum total potential energy. A Navier type analytical solution methodology is also presented for simply supported FG plates resting on elastic foundation which predicts accurate solution. The accuracy of the present model is checked by comparing the computed results with those obtained by classical plate theory (CPT), first-order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Moreover, results demonstrate that the proposed theory can achieve the same accuracy of the existing HSDTs which have more number of variables.

• Steel and Composite Structures
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• v.39 no.5
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• pp.493-509
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• 2021

There is not enough mixed finite element method (MFEM) model developed for static and dynamic analysis of functionally graded material (FGM) beams in the literature. The main purpose of this study is to develop a reliable and efficient computational modeling using an efficient functional in MFEM for free vibration and static analysis of FGM composite beams subject to high order shear deformation effects. The modeling of material properties was performed using mixture rule and Mori-Tanaka scheme which are more realistic determination techniques. This method based on the assumption that a two phase composite material consisting of matrix reinforced by spherical particles, randomly distributed in the beam. To explain the displacement components of the shear deformation effects, it was accepted that the shear deformation effects change sinusoidal. Partial differential field equations were obtained with the help of variational methods and then these equations were transformed into a novel functional for FGM beams with the help of Gateaux differential derivative operator. Thanks to the Gateaux differential method, the compatibility of the field equations was checked, and the field equations and boundary conditions were reflected to the function. A MFEM model was developed with a total of 10 degrees of freedom to apply the obtained functional. In the numerical applications section, free vibration and flexure problems solutions of FGM composite beams were compared with those predicted by other theories to show the effects of shear deformation, thickness changing and boundary conditions.

• Tunnel and Underground Space
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• v.3 no.2
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• pp.142-151
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• 1993

In this study, the deformation characteristics of atrtificially fractured joints of granite under normal and shear loading were investigated. To obtain the characteristics of joint deformation, compression and shear tests were performed in the laboratory on three different sizes of rock specimens. The rock used in the experimens was Iksan granite. Joints were produced artificially by fracturing using the apparatus for generating extension-joint. Joint normal deformability was studied by conducting cyclic loading tests on the joints. Joint closure varied non-linearly with normal stress through cyclic loadings. As normal stress increased, the joints gradually reached a state of maximum joint closure. The relation between normal stress and joint closure for mated and unmated joints was well described by the hyperbolic and exponential function, respectively. Joint shear deformability was studied by performing direct shear tests under normal stresses on the joints. it was shown that the behaviour in the prepeak range was non-linear and joint shear stiffness depended on the size of specimen and the normal stress.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.04a
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• pp.45-52
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• 1997

The elastic deflection of thin ice sheets due In bending and shear deformation is considered. The in-plane Young's modulus and the transverse shear modulus are calculated by least squres fit of transverse plate deflection data. Results show that thin ice plates behave predominantly in shear. Previously, the Young's moduli were calaulated based on bending theory alone. The Young's moduli of thin model ice sheets, estimated using the bending and shear theory, are more than an order of magnitude greater than calculated previously, and hence are more realistic. Further, the previous ambiguity in the Young's modulus, arising from fitting the data at various distances from the point of loading, is removed by considering shear and bending deformation.

• 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.

• Proceedings of the Korea Concrete Institute Conference
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• 1997.10a
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• pp.481-486
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• 1997

In the paper, a simplified method for nonlinear analysis of reinforced concrete structures is presented, which is based on timeoshenko beam theory and constitutive equations that are given by the relation of average stress and average strain for concrete and reinforcing bars. Especially, this method consider shear deformation and determine the failure mode. In this paper, 1-D beam element model and program considering shear deformation are suggested. In addition, program procedure is presented briefly and the results are plotted with test examples.