• Advances in materials Research
• /
• v.4 no.1
• /
• pp.31-44
• /
• 2015

This paper presents a simple n-order four variable refined theory for buckling analysis of functionally graded plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The present theory is variationally consistent, uses the n-order polynomial term to represent the displacement field, does not require shear correction factor, and eliminates the shear stresses at the top and bottom surfaces. A power law distribution is used to describe the variation of volume fraction of material compositions. Equilibrium and stability equations are derived based on the present n-order refined theory. The non-linear governing equations are solved for plates subjected to simply supported boundary conditions. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. The effects of aspect and thickness ratios, gradient index, on the critical buckling are all discussed.

• Geomechanics and Engineering
• /
• v.9 no.3
• /
• pp.361-372
• /
• 2015

In this paper, a refined exponential shear deformation theory for free vibration analysis of functionally graded beam with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose, a new displacement field based on refined shear deformation theory is implemented. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Based on the present refined shear deformation beam theory, the equations of motion are derived from Hamilton's principle. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. Illustrative examples are given also to show the effects of varying gradients, porosity volume fraction, aspect ratios, and thickness to length ratios on the free vibration of the FG beams.

• Steel and Composite Structures
• /
• v.17 no.1
• /
• pp.21-46
• /
• 2014

This paper presents a simple n-order four variable refined theory for the bending and vibration analyses of functionally graded plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The present theory is variationally consistent, uses the n-order polynomial term to represent the displacement field, 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. The governing equations are derived by employing the Hamilton's principle and the physical neutral surface concept. The accuracy of the present solutions is verified by comparing the obtained results with available published ones.

• Structural Engineering and Mechanics
• /
• v.69 no.3
• /
• pp.335-345
• /
• 2019

In present study, a novel refined hyperbolic shear deformation theory is proposed for the buckling analysis of thick isotropic plates. The new displacement field is constructed with only two unknowns, as against three or more in other higher order shear deformation theories. However, the hyperbolic sine function is assigned according to the shearing stress distribution across the plate thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using any shear correction factors. The equations of motion associated with the present theory are obtained using the principle of virtual work. The analytical solution of the buckling of simply supported plates subjected to uniaxial and biaxial loading conditions was obtained using the Navier method. The critical buckling load results for thick isotropic square plates are compared with various available results in the literature given by other theories. From the present analysis, it can be concluded that the proposed theory is accurate and efficient in predicting the buckling response of isotropic plates.

• Steel and Composite Structures
• /
• v.22 no.4
• /
• pp.713-732
• /
• 2016

A novel four variable refined plate theory is proposed in this work for laminated composite plates. The theory considers a parabolic distribution of the transverse shear strains, and respects the zero traction boundary conditions on the surfaces of the plate without employing shear correction coefficient. The displacement field is based on a novel kinematic in which the undetermined integral terms are used, and only four unknowns are involved. The analytical solutions of antisymmetric cross-ply and angle-ply laminates are determined via Navier technique. The obtained results from the present model are compared with three-dimensional elasticity solutions and results of the first-order and the other higher-order theories reported in the literature. It can be concluded that the developed theory is accurate and simple in investigating the bending and buckling responses of laminated composite plates.

• Proceedings of the Korean Society For Composite Materials Conference
• /
• 2000.11a
• /
• pp.46-49
• /
• 2000

A decoupled thermo-~lezoelectric-mechanical model of composite laminates with surface bonded piezoelectric actuators, subjected to externally applied load, temperature change load, electric field load is developed. The governing differential equations are obtained by applying the principle of free energy and variational techniques. A higher order zigzag theory displacement field is employed to accurately capture the transverse shear and normal effects in laminated composite plates of arbitrary thickness.

• Steel and Composite Structures
• /
• v.18 no.4
• /
• pp.1063-1081
• /
• 2015

In this paper, a new nonlocal hyperbolic refined plate model is presented for free vibration properties of functionally graded (FG) plates. This nonlocal nano-plate model incorporates the length scale parameter which can capture the small scale effect. The displacement field of the present theory is chosen based on a hyperbolic variation in the in-plane displacements through the thickness of the nano-plate. By dividing the transverse displacement into the bending and shear parts, the number of unknowns and equations of motion of the present theory is reduced, significantly facilitating structural analysis. The material properties are assumed to vary only in the thickness direction and the effective properties for the FG nano-plate are computed using Mori-Tanaka homogenization scheme. The governing equations of motion are derived based on the nonlocal differential constitutive relations of Eringen in conjunction with the refined four variable plate theory via Hamilton's principle. Analytical solution for the simply supported FG nano-plates is obtained to verify the theory by comparing its results with other available solutions in the open literature. The effects of nonlocal parameter, the plate thickness, the plate aspect ratio, and various material compositions on the dynamic response of the FG nano-plate are discussed.

• Steel and Composite Structures
• /
• v.21 no.6
• /
• pp.1287-1306
• /
• 2016

The current research presents a buckling analysis of isotropic and orthotropic plates by proposing a new four variable refined plate theory. Contrary to the existing higher order shear deformation theories (HSDT) and the first shear deformation theory (FSDT), the proposed model uses a new displacement field which incorporates undetermined integral terms and involves only four variables. The governing equations for buckling analysis are deduced by utilizing the principle of virtual works. The analytical solution of a simply supported rectangular plate under the axial loading has been determined via the Navier method. Numerical investigations are performed by using the proposed model and the obtained results are compared with CPT solutions, FSDT solutions, and the existing exact solutions in the literature. It can be concluded that the developed four variable refined plate theory, which does not use shear correction coefficient, is not only simple but also comparable to the FSDT.

• Structural Engineering and Mechanics
• /
• v.82 no.6
• /
• pp.725-734
• /
• 2022

This work presents a simple exponential shear deformation theory for the flexural and free vibration responses of thick bridge deck. Contrary to the existing higher order shear deformation theories (HSDT) and the first shear deformation theory (FSDT), the proposed model uses a new displacement field which incorporates undetermined integral terms and involves only two variables. Governing equations and boundary conditions of the theory are derived by the principle of virtual work. The simply supported thick isotropic square and rectangular plates are considered for the detailed numerical studies. Results of displacements, stresses and frequencies are compared with those of other refined theories and exact theory to show the efficiency of the proposed theory. Good agreement is achieved of the present results with those of higher order shear deformation theory (HSDT) and elasticity theory. Moreover, results demonstrate that the developed two variable refined plate theory is simple for solving the flexural and free vibration responses of thick bridge deck and can achieve the same accuracy of the existing HSDTs which have more number of variables.

• Smart Structures and Systems
• /
• v.13 no.4
• /
• pp.659-683
• /
• 2014

The static analysis of structures with arbitrary cross-section geometry and material lamination via a refined one-dimensional (1D) approach is presented in this paper. Higher-order 1D models with a variable order of expansion for the displacement field are developed on the basis of Carrera Unified Formulation (CUF). Classical Euler-Bernoulli and Timoshenko beam theories are obtained as particular cases of the first-order model. Numerical results of displacement, strain and stress are provided by using the finite element method (FEM) along the longitudinal direction for different configurations in excellent agreement with three-dimensional (3D) finite element solutions. In particular, a layered thin-walled cylinder is considered as first assessment with a laminated conventional cross-section. An atherosclerotic plaque is introduced as a typical structure with arbitrary cross-section geometry and studied for both the homogeneous and nonhomogeneous material cases through the 1D variable kinematic models. The analyses highlight limitations of classical beam theories and the importance of higher-order terms in accurately detecting in-plane cross-section deformation without introducing additional numerical problems. Comparisons with 3D finite element solutions prove that 1D CUF provides remarkable three-dimensional accuracy in the analysis of even short and nonhomogeneous structures with arbitrary geometry through a significant reduction in computational cost.