• Proceedings of the Korean Society For Composite Materials Conference
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• 2005.04a
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• pp.1-4
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• 2005

A higher order zig-zag shell theory is developed to refine accurately predict deformation and stress of smart shell structures under the mechanical, thermal, and electric loading. The displacement fields through the thickness are constructed by superimposing linear zig-zag field to the smooth globally cubic varying field. Smooth parabolic distribution through the thickness is assumed in the transverse deflection in order to consider transverse normal deformation. The mechanical, thermal, and electric loading is applied in the sinusoidal distribution function in the in-surface direction. Thermal and electric loading is given in the linear variation through the thickness. Especially, in electric loading case, voltage is only applied in piezo-layer. The layer-dependent degrees of freedom of displacement fields are expressed in terms of reference primary degrees of freedom by applying interface continuity conditions as well as bounding surface conditions of transverse shear stresses. In order to obtain accurate transverse shear and normal stresses, integration of equilibrium equation approach is used. The numerical examples of present theory demonstrate the accuracy and efficiency of the proposed theory. The present theory is suitable for the predictions of behaviors of thick smart composite shell under mechanical, thermal, and electric loadings combined.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.12 no.10
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• pp.4642-4647
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• 2011

Solution for elastic foundation of plane strain state was derived by the application of variational method. Functions of the transverse distribution of the displacements for the analysis were chosen as linear functions. Loading conditions considered for the analysis were concentrated load and distributed load. Under the loading condition of the concentrated load, surface displacement was decreased drastically as the distance from the point of the loading increased. Under the loading condition of the distributed load, surface displacements were more uniformly distributed beneath the loading area when the ratio of the half of the loading width to the depth(B/H) of the compressible layer was greater. The surface displacement was more quickly converged from the edge of the loading area as the ratio(B/H) increased.

• Advances in aircraft and spacecraft science
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• v.10 no.3
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• pp.281-302
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• 2023

In this paper, bending analysis of exponentially varying functionally graded (FG) plate is presented using trigonometric shear deformation theory (TSDT) considering both transverse shear and normal deformation effects. The in-plane displacement field consists of sinusoidal functions in thickness direction to include transverse shear strains and transverse displacement include the effect of transverse normal strain using the cosine function in thickness coordinate. The governing equations and boundary conditions of the theory are derived using the virtual work principle. System of governing equations, for simply supported conditions, Navier's solution technique is used to obtain results. Plate material properties vary across thickness direction according to exponential distribution law. In the current theory, transverse shear stresses are distributed accurately through the plate thickness, hence obviates the need for a shear correction factor. TSDT results are compared with those from other theories to ensure the accuracy and effectiveness of the present theory. The current theory is in excellent agreement with the semi-analytical theory.

• Structural Engineering and Mechanics
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• v.84 no.6
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• pp.707-722
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• 2022

In this study, a new refined hyperbolic shear deformation theory (RHSDT) is developed using an equivalent single-layer shell displacement model for the static bending and free vibration response of cross-ply laminated composite spherical shells. It is based on a new kinematic in which the transverse displacement is approximated as a sum of the bending and shear components, leading to a reduction of the number of unknown functions and governing equations. The proposed theory uses the hyperbolic shape function to account for an appropriate distribution of the transverse shear strains through the thickness and satisfies the boundary conditions on the shell surfaces without requiring any shear correction factors. The shell governing equations for this study are derived in terms of displacement from Hamilton's principle and solved via a Navier-type analytical procedure. The validity and high accuracy of the present theory are ascertained by comparing the obtained numerical results of displacements, stresses, and natural frequencies with their counterparts generated by some higher-order shear deformation theories. Further, a parametric study examines in detail the effect of both geometrical parameters (i.e., side-to-thickness ratio and curvature-radius-to-side ratio), on the bending and free vibration response of simply supported laminated spherical shells, which can be very useful for many modern engineering applications and their optimization design.

• Smart Structures and Systems
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• v.9 no.2
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• pp.127-143
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• 2012

The present paper deals with the nonlinear analysis of the functionally graded piezoelectric (FGP) annular plate with two smart layers as sensor and actuator. The normal pressure is applied on the plate. The geometric nonlinearity is considered in the strain-displacement equations based on Von-Karman assumption. The problem is symmetric due to symmetric loading, boundary conditions and material properties. The radial and transverse displacements are supposed as two dominant components of displacement. The constitutive equations are derived for two sections of the plate, individually. Total energy of the system is evaluated for elastic solid and piezoelectric sections in terms of two components of displacement and electric potential. The response of the system can be obtained using minimization of the energy of system with respect to amplitude of displacements and electric potential. The distribution of all material properties is considered as power function along the thickness direction. Displacement-load and electric potential-load curves verify the nonlinearity nature of the problem. The response of the linear analysis is investigated and compared with those results obtained using the nonlinear analysis. This comparison justifies the necessity of a nonlinear analysis. The distribution of the displacements and electric potential in terms of non homogenous index indicates that these curves converge for small value of piezoelectric thickness with respect to elastic solid thickness.

• Earthquakes and Structures
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• v.1 no.1
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• pp.1-19
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• 2010

It has been known that one-dimensional rod theory is very effective as a simplified analytical approach to large scale or complicated structures such as high-rise buildings, in preliminary design stages. It replaces an original structure by a one-dimensional rod which has an equivalent stiffness in terms of global properties. If the structure is composed of distinct constituents of different stiffness such as coupled walls with opening, structural behavior is significantly governed by the local variation of stiffness. This paper proposes an extended version of the rod theory which accounts for the two-dimensional local variation of structural stiffness; viz, variation in the transverse direction as well as longitudinal stiffness distribution. The governing equation for the two-dimensional rod theory is formulated from Hamilton's principle by making use of a displacement function which satisfies continuity conditions across the boundary between the distinct structural components in the transverse direction. Validity of the proposed theory is confirmed by comparison with numerical results of computational tools in the cases of static, free vibration and forced vibration problems for various structures.

• Advances in materials Research
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• v.8 no.3
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• pp.155-177
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• 2019

In this paper, a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded sandwich plate with new definition of porosity distribution taking into account composition and the scheme of the sandwich plate. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, 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. Material properties of FGM layers are assumed to vary continuously across the plate thickness according to either power-law or sigmoid function in terms of the volume fractions of the constituents. The face layers are considered to be FG across each face thickness while the core is made of a ceramic homogeneous layer. Governing equations are derived from the principle of virtual displacements. The closed-form solution of a simply supported rectangular plate subjected to sinusoidal loading has been obtained by using the Navier method. Numerical results are presented to show the effect of the material distribution, the sandwich plate geometry and the porosity on the deflections and stresses of FG sandwich plates. The validity of the present theory is investigated by comparing some of the present results with other published results.

• Geomechanics and Engineering
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• v.10 no.3
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• pp.357-386
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• 2016

In this research work, an exact analytical solution for thermal stability of solar functionally graded rectangular plates subjected to uniform, linear and non-linear temperature rises across the thickness direction is developed. It is assumed that the plate rests on two-parameter elastic foundation and its material properties vary through the thickness of the plate as a power function. The neutral surface position for such plate is determined, and the efficient hyperbolic plate theory based on exact neutral surface position is employed to derive the governing stability equations. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the quadratic distribution of transverse shear stress through the thickness in such a way that shear stresses vanish on the plate surfaces. Therefore, there is no need to use shear correction factor. Just four unknown displacement functions are used in the present theory against five unknown displacement functions used in the corresponding ones. The non-linear strain-displacement relations are also taken into consideration. The influences of many plate parameters on buckling temperature difference will be investigated. Numerical results are presented for the present theory, demonstrating its importance and accuracy in comparison to other theories.

• Structural Engineering and Mechanics
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• v.60 no.2
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• pp.271-299
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• 2016

In this article, based on the higher-order shear deformation plate theory, buckling analysis of a rectangular plate made of functionally graded piezoelectric materials and its effective parameters are investigated. Assuming the transverse distribution of electric potential to be a combination of a parabolic and a linear function of thickness coordinate, the equilibrium equations for the buckling analysis of an FGP rectangular plate are established. In addition to the Maxwell equation, all boundary conditions including the conditions on the top and bottom surfaces of the plate for closed and open circuited are satisfied. Considering double sine solution (Navier solution) for displacement field and electric potential, an analytical solution is obtained for full simply supported boundary conditions. The accurate buckling load of FGP plate is presented for both open and closed circuit conditions. It is found that the critical buckling load for open circuit is more than that of closed circuit in all loading conditions. Furthermore, it is observed that the influence of dielectric constants on the critical buckling load is more than those of others.

• Computers and Concrete
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• v.27 no.3
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• pp.269-282
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• 2021

A dynamic analytical solution for a simply supported, rectangular functionally graded plate with a porous middle layer under time-dependent load based on a refined third-order shear deformation theory with a cubic variation of in-plane displacements according to the thickness and linear/quadratic transverse displacement is presented. The solution achieved in the trigonometric series form and rests on the Green's function method. Two porosity types and their influence on material properties, and mechanical behavior are considered. The network of pores is assumed to be empty or filled with low-pressure air, and the material properties are calculated using the power-law distribution idealization. Numerical calculations have been carried out to demonstrate the accuracy of the kinematic model for the dynamic problem, the effect of porosity, thickness of porous layers, power-law index, and type of loading on the dynamic response of an imperfect functionally graded material plate.