• Structural Engineering and Mechanics
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• 제68권6호
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• pp.661-675
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• 2018

In this paper, buckling analysis of hybrid functionally graded plates using a novel four variable refined plate theory is presented. In this theory the distribution of transverse shear deformation is parabolic across the thickness of the plate by satisfying the surface conditions. Therefore, it is unnecessary to use a shear correction factor. The variations of properties of the plate through the thickness are according to a symmetric sigmoid law (symmetric S-FGM). The principle virtual works is used herein to extract equilibrium equations. The analytical solution is determined using the Navier method for a simply supported rectangular plate subjected to axial forces. The precision of this theory is verified by comparing it with the various solutions available in the literature.

• Structural Engineering and Mechanics
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• 제68권4호
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• pp.409-421
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• 2018

In the present paper, functionally graded (FG) materials are presented to investigate the bending analysis of simply supported plates. It is assumed that the material properties of the plate vary through their length according to the power-law form. The displacement field of the present model is selected based on quasi-3D hyperbolic shear deformation theory. By splitting the deflection into bending, shear and stretching parts, the number of unknowns and equations of motion of the present formulation is reduced and hence makes them simple to use. Governing equations are derived from the principle of virtual displacements. Numerical results for deflections and stresses of powerly graded plates under simply supported boundary conditions are presented. The accuracy of the present formulation is demonstrated by comparing the computed results with those available in the literature. As conclusion, this theory is as accurate as other shear deformation theories and so it becomes more attractive due to smaller number of unknowns. Some numerical results are provided to examine the effects of the material gradation, shear deformation on the static behavior of FG plates with variation of material stiffness through their length.

• Structural Engineering and Mechanics
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• 제66권5호
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• pp.665-676
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• 2018

In this study, a four-node quadrilateral partial mixed plate element with low degrees of freedom (dofs) is developed for static and free vibration analysis of functionally graded material (FGM) plates rested on Winkler-Pasternak elastic foundations. The formulation of the presented finite element model is based on a parametrized mixed variational principle which is developed recently by the first author. The presented finite element model considers the effects of shear deformations and normal flexibility of the FGM plates without using any shear correction factor. It also fulfills the boundary conditions of the transverse shear and normal stresses on the top and bottom surfaces of the plate. Beside these capabilities, the number of unknown field variables of the plate is only six. The presented partial mixed finite element model has been validated through comparison with the results of the three-dimensional (3D) theory of elasticity and the results obtained from the classical and high-order plate theories available in the open literature.

• Steel and Composite Structures
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• 제34권6호
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• pp.795-802
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• 2020

The subject of the paper is a circular plate with symmetrically thickness-wise varying mechanical properties. The plate is simply supported and carries a concentrated force located in its centre. The axisymmetric bending problem of the plate with consideration of the shear effect is analytically and numerically studied. A nonlinear function of deformation of the straight line normal to the plate neutral surface is assumed. Two differential equations of equilibrium based on the principle of stationary potential energy are obtained. The system of equations is analytically solved and the maximum deflections and shear coefficients for example plates are derived. Moreover, the maximum deflections of the plates are calculated numerically (FEM), for comparison with the analytical results.

• Smart Structures and Systems
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• 제26권2호
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• pp.185-193
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• 2020

Nonlinear vibration of sandwich plate with functionally graded material (FGM) core and carbon nano tubes reinforced (CNTs) nano-composite layers by considering temperature-dependent material properties are studied in this paper. Base on Classical plate theory (CPT), the governing partial differential equations of motion for sandwich plate are derived using Hamilton principle. The Galerkin procedure and multiple scales perturbation method are used to find relation between nonlinear frequency and amplitude of vibration response. The dynamic responses of the sandwich plate are also investigated in both time and frequency domains. Then, the effects of nonlinearity, excitation, power law index of FG core, volume fraction of carbon nanotube, the function of material variations of FG core, temperature changes, scale transformation parameter and damping factor on the frequency responses are investigated.

• 한국산학기술학회논문지
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• 제14권11호
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• pp.5930-5938
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• 2013

Erigen의 비국소 탄성이론을 이용한 S형상 점진기능재료 나노-스케일 판의 전단변형이론을 정식화하여 평형방성식을 유도하였다. 비국소 탄성이론은 미소 규모 효과를 고려할 수 있고 S형상함수는 점진기능재료의 정확한 특성 변화를 고려할 수 있다. 4변이 단순지지된 나노-스케일 판의 지배방정식을 풀기 위해 Navier 방법을 사용하였다. 거듭 제곱 지수와 비국소 변수의 효과를 나타내기 위한 나노-스케일 판의 해석적 좌굴하중을 제시하였고, 국소 탄성이론과의 관계를 수치해석 결과를 통하여 고찰하였다. 또한 (i) 거듭제곱 지수, (ii) 나노-스케일 판의 크기, (iii) 비국소 계수, (iv) 형상비 그리고 (v) 모드 수 등이 나노-스케일 판의 이축 무차원 좌굴하중에 미치는 효과에 대하여 관찰하였다. 본 연구의 결과를 검증하기 위해 참고문헌의 결과들과 비교 분석하였다.

• Coupled systems mechanics
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• 제12권3호
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• pp.199-220
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• 2023

This article presents a new analytical model to study the effect of porosity on the shear correction factors (SCFs) of functionally graded porous beams (FGPB). For this analysis, uneven and logarithmic-uneven porosity functions are adopted to be distributed through the thickness of the FGP beams. Critical to the application of this theory is a determination of the correction factor, which appears as a coefficient in the expression for the transverse shear stress resultant; to compensate for the assumption that the shear strain is uniform through the depth of the cross-section. Using the energy equivalence principle, a general expression is derived from the static SCFs in FGPB. The resulting expression is consistent with the variationally derived results of Reissner's analysis when the latter are reduced from the two-dimensional case (plate) to the one-dimensional one (beam). A convenient algebraic form of the solution is presented and new study cases are given to illustrate the applicability of the present formulation. Numerical results are presented to illustrate the effect of the porosity distribution on the (SCFs) for various FGPBs. Further, the law of changing the mechanical properties of FG beams without porosity and the SCFare numerically validated by comparison with some available results.

• Computers and Concrete
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• 제20권2호
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• pp.229-246
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• 2017

The dynamic bending response of single walled carbon nanotube reinforced composite (SWCNTRC) plates subjected to hygro-thermo-mechanical loading are investigated in this paper. The mechanical load is considered as wind pressure for dynamic bending responses of SWCNTRC plate. The dynamic version of the High Order shear deformation Theory (HSDT) for a composite plate with Matrix and SWCNTRC plate is first formulated. Distribution of fibers through the thickness of the SWCNTRC plate could be uniform or functionally graded (FG). The dynamic displacement response is predicted by using Nemarck integration method. The effective material properties of SWCNTRC are estimated by using micromechanics based modeling approach. The effect of different environmental condition, volume fraction of SWCNT, Width-to-thickness ratio, wind pressure, different SWCNTRC-FG plates, boundary condition, E1/E2 ratio, different temperature on dynamic displacement response is investigated. The dynamic displacement response is compared with the available literature and it shows good agreement.

• Steel and Composite Structures
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• 제24권5호
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• pp.537-548
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• 2017

In this paper presents bending characteristic of single wall carbon nanotube reinforced functionally graded composite (SWCNTRC-FG) plates. The finite element implementation of bending analysis of laminated composite plate via well-established higher order shear deformation theory (HSDT). A seven degree of freedom and $C^0$ continuity finite element model using eight noded isoperimetric elements is developed for precise computation of deflection and stresses of SWCNTRC plate subjected to sinusoidal transverse load. The finite element implementation is carried out through a finite element code developed in MATLAB. The results obtained by present approach are compared with the results available in the literatures. The effective material properties of the laminated SWCNTRC plate are used by Mori-Tanaka method. Numerical results have been obtained with different parameters, width-to-thickness ratio (a/h), stress distribution profile along thickness direction, different SWCNTRC-FG plate, boundary condition, through the thickness (z/h) ratio, volume fraction of SWCNT.

• Coupled systems mechanics
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• 제9권6호
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• pp.575-597
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• 2020

Equilibrium equations of a porous FG plate resting on Winkler-Pasternak foundations with various boundary conditions are derived using a new refined shear deformation theory. Different types of porosity distribution rate are considered. Governing equations are obtained including the plate-foundation interaction. This new model meets the nullity of the transverse shear stress at the upper and lower surfaces of the plate. The novel rule of mixture is proposed to describe and approximate material properties of the FG plates with different distribution case of porosity. The validity of this theory is studied by comparing some of the present results with other higher-order theories reported in the literature. Effects of variation of porosity distribution rate, boundary conditions, foundation parameter, power law index, plate aspect ratio, side-to-thickness ratio on the deflections and stresses are all discussed.