• Structural Engineering and Mechanics
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• v.53 no.6
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• pp.1215-1240
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• 2015

In this work, a novel simple first-order shear deformation plate theory based on neutral surface position is developed for bending and free vibration analysis of functionally graded plates and supported by either Winkler or Pasternak elastic foundations. 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 governing equations are derived by employing the Hamilton's principle and the physical neutral surface concept. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. Numerical results of present theory are compared with results of the traditional first-order and the other higher-order theories reported in the literature. It can be concluded that the proposed theory is accurate and simple in solving the static bending and free vibration behaviors of functionally graded plates.

• Steel and Composite Structures
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• v.29 no.1
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• pp.53-66
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• 2018

A high-order nonlocal strain gradient model is developed for wave propagation analysis of porous FG nanoplates resting on a gradient hybrid foundation in thermal environment, for the first time. Material properties are assumed to be temperature-dependent and graded in the nanoplate thickness direction. To consider the thermal effects, uniform, linear, nonlinear, exponential, and sinusoidal temperature distributions are considered for temperature-dependent FG material properties. On the basis of the refined-higher order shear deformation plate theory (R-HSDT) in conjunction with the bi-Helmholtz nonlocal strain gradient theory (B-H NSGT), Hamilton's principle is used to derive the equations of wave motion. Then the dispersion relation between frequency and wave number is solved analytically. The influences of various parameters (such as temperature rise, volume fraction index, porosity volume fraction, lower and higher order nonlocal parameters, material characteristic parameter, foundations components, and wave number) on the wave propagation behaviors of porous FG nanoplates are investigated in detail.

• International Journal of Aeronautical and Space Sciences
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• v.7 no.2
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• pp.104-109
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• 2006

In this study, the equivalent plate model is developed using a finite element method(FEM) based on the first order shear deformation theory(FSDT). The substructure synthesis method is used to consider the control surface. For the verification of the equivalent model, the results of free vibration analysis are compared with the ones of 3D wing structure modeled by using the MSC/NASTRAN.

• Structural Engineering and Mechanics
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• v.6 no.7
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• pp.727-746
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• 1998

Finite element models and numerical results are presented for bending and natural vibration using the unified third-order plate theory developed in Part 1 of this paper. The unified third-order theory contains the classical, first-order, and other third-order plate theories as special cases. Analytical solutions are developed using the Navier and L$\acute{e}$vy solution procedures (see Part 1 of the paper). Displacement finite element models of the unified third-order theory are developed herein. The finite element models are based on $C^0$ interpolation of the inplane displacements and rotation functions and $C^1$ interpolation of the transverse deflection. Numerical results of bending and natural vibration are presented to evaluate the accuracy of various plate theories.

• Structural Engineering and Mechanics
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• v.70 no.1
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• pp.125-131
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• 2019

A nine node isoparametric plate bending element is used for bending analysis of laminated composite skew cylindrical shell panels. Both thick and thin shell panels are solved. Rotary inertia and shear deformation are incorporated by considering first order shear deformation theory. The analysis is performed considering shallow shell theory. Both shallow and moderately deep skew cylindrical shells are investigated. Skew cylindrical shell panels having different thickness ratios (h/a), radius to length ratios (R/a), ply angle orientations, number of layers, aspect ratio (b/a), boundary conditions and various loading (concentrated, uniformly distributed, linear varying and doubly sinusoidal varying) conditions are analysed. Various new results are presented.

• Steel and Composite Structures
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• v.26 no.2
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• pp.125-137
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• 2018

In this work, the bending and free vibration analysis of multilayered plates and shells is presented by utilizing a new higher order shear deformation theory (HSDT). The proposed involves only four unknowns, which is even less than the first shear deformation theory (FSDT) and without requiring the shear correction coefficient. Unlike the conventional HSDTs, the present one presents a novel displacement field which incorporates undetermined integral variables. The equations of motion are derived by using the Hamilton's principle. These equations are then solved via Navier-type, closed form solutions. Bending and vibration results are found for cylindrical and spherical shells and plates for simply supported boundary conditions. Bending and vibration problems are treated as individual cases. Panels are subjected to sinusoidal, distributed and point loads. Results are presented for thick to thin as well as shallow and deep shells. The computed results are compared with the exact 3D elasticity theory and with several other conventional HSDTs. The proposed HSDT is found to be precise compared to other several existing ones for investigating the static and dynamic response of isotropic and multilayered composite shell and plate structures.

• Advances in nano research
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• v.12 no.4
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• pp.427-440
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• 2022

In the present study, the nonlocal strain gradient theory is used to predict the size-dependent buckling and post-buckling behavior of geometrically imperfect nano-scale piezo-flexomagnetic plate strips in two modes of direct and converse flexomagnetic effects. The first-order shear deformation plate theory is used to analyze analytically nano-strips with simply supported boundary conditions. The nonlinear governing equations of equilibrium and associated boundary conditions are derived using the principle of minimum total potential energy with consideration of the von Kármán-type of geometric nonlinearity. A closed-form solution of governing differential equation is obtained, which is easily usable for engineers and designers. To validate the presented formulations, whenever possible, a comparison with the results found in the open literature is reported for buckling loads. A parametric study is presented to examine the effect of scaling parameters, plate slenderness ratio, temperature, the mid-plane initial rise, flexomagnetic coefficient, different temperature distributions, and magnetic potential, in case of the converse flexomagnetic effect, on buckling and post-buckling loads in detail.

• Advances in nano research
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• v.17 no.1
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• pp.19-32
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• 2024

Functionally graded-carbon nanotube (FG-CNT) is expected to be a new generation of materials with a wide range of potential applications in technological fields such as aerospace, defense, energy, and structural industries. In this paper, an exact finite strip method for functionally graded-carbon nanotube sandwich plates is developed using first-order shear deformation theory to get the exact natural frequencies of the plates. The face sheets of the plates are made of FG-CNT with continuous and smooth grading based on the power law index. The equations of motion have been generated based on the Hamilton principle. By extracting the exact stiffness matrix for any strip of the sandwich plate as a non-algebraic function of natural frequencies, it is possible to calculate the exact free vibration frequencies. The accuracy and efficiency of the current method is established by comparing its findings to the results of the literature works. Examples are presented to prove the efficiency of the generated method to deal with various problems, such as the influence of the length-to-height ratio, the power law index, and a core-to-face sheet thickness of the single and multi-span sandwich plates with various boundary conditions on the natural frequencies. The exact results obtained from this analysis can check the validity and accuracy of other numerical methods.

• Steel and Composite Structures
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• v.25 no.3
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• pp.257-270
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• 2017

In this article, an efficient and simple refined theory is proposed for buckling analysis of functionally graded plates by using a new displacement field which includes undetermined integral variables. This theory contains only four unknowns, with is even less than the first shear deformation theory (FSDT). Governing equations are obtained from the principle of virtual works. The closed-form solutions of rectangular plates are determined. Comparison studies are carried out to check the validity of obtained results. The influences of loading conditions and variations of power of functionally graded material, modulus ratio, aspect ratio, and thickness ratio on the critical buckling load of functionally graded plates are examined and discussed.

• Journal of the Korea institute for structural maintenance and inspection
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• v.8 no.4
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• pp.107-114
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• 2004

In this paper, a simple improved 8-node finite element for the finite element analysis of fibrous composite plates is presented by using the direct modification. We drive explicit expressions of shape functions for the 8-node element with bilinear element geometry, which is modified so that it can represent any quadratic fields in Cartesian coordinates. The refined first-order shear deformation theory is proposed, which results in parabolic through-thickness distribution of the transverse shear strains and stresses from the formulation based on the third-order shear deformation theory. It eliminates the need for shear correction factors in the first-order theory. This finite element is further improved by combined use of assumed strain, modified shape function, and refined first-order theory. To show the effectiveness of our simple modification on the 8-node finite elements, numerical studies are carried out the static, buckling and free vibration analysis of fibrous composite plates.