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Huu-tai Thai - One of the best experts on this subject based on the ideXlab platform.
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analytical solutions of refined plate theory for bending buckling and vibration analyses of thick plates
Applied Mathematical Modelling, 2013Co-Authors: Huu-tai Thai, Dongho ChoiAbstract:Abstract Analytical solutions for bending, buckling, and vibration analyses of thick rectangular plates with various boundary conditions are presented using two variable refined plate theory. The theory accounts for parabolic variation of transverse Shear stress through the thickness of the plate without using Shear Correction Factor. In addition, it contains only two unknowns and has strong similarities with the classical plate theory in many aspects such as equations of motion, boundary conditions, and stress resultant expressions. Equations of motion are derived from Hamilton’s principle. Closed-form solutions of deflection, buckling load, and natural frequency are obtained for rectangular plates with two opposite edges simply supported and the other two edges having arbitrary boundary conditions. Comparison studies are presented to verify the validity of present solutions. It is found that the deflection, stress, buckling load, and natural frequency obtained by the present theory match well with those obtained by the first-order and third-order Shear deformation theories.
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a simple refined theory for bending buckling and vibration of thick plates resting on elastic foundation
International Journal of Mechanical Sciences, 2013Co-Authors: Huu-tai Thai, Minwo Park, Dongho ChoiAbstract:Abstract A simple refined Shear deformation theory is proposed for bending, buckling, and vibration of thick plates resting on elastic foundation. The theory accounts for parabolic distribution of transverse Shear stress, and satisfies the free transverse Shear stress conditions on the top and bottom surfaces of the plate without using Shear Correction Factor. The number of unknowns of present theory is two as against three in the case of other Shear deformation theories. The elastic foundation is modeled as two-parameter Pasternak foundation. Equations of motion are derived from Hamilton's principle. Analytical solutions are obtained for rectangular plates with two opposite edges simply supported and the other two edges having arbitrary boundary conditions. Comparison studies are presented to verify the validity of present solutions. It can be concluded that the proposed theory is accurate and efficient in predicting the bending, buckling, and vibration responses of thick plates resting on elastic foundation.
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a new sinusoidal Shear deformation theory for bending buckling and vibration of functionally graded plates
Applied Mathematical Modelling, 2013Co-Authors: Huu-tai ThaiAbstract:A new sinusoidal Shear deformation theory is developed for bending, buckling, and vibration of functionally graded plates. The theory accounts for sinusoidal distribution of transverse Shear stress, and satisfies the free transverse Shear stress conditions on the top and bottom surfaces of the plate without using Shear Correction Factor. Unlike the conventional sinusoidal Shear deformation theory, the proposed sinusoidal Shear deformation theory contains only four unknowns and has strong similarities with classical plate theory in many aspects such as equations of motion, boundary conditions, and stress resultant expressions. The material properties of plate are assumed to vary according to power law distribution of the volume fraction of the constituents. Equations of motion are derived from the Hamilton’s principle. The closed-form solutions of simply supported plates are obtained and the results are compared with those of first-order Shear deformation theory and higher-order Shear deformation theory. It can be concluded that the proposed theory is accurate and efficient in predicting the bending, buckling, and vibration responses of functionally graded plates.
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a simple higher order Shear deformation theory for bending and free vibration analysis of functionally graded plates
Composite Structures, 2013Co-Authors: Huu-tai Thai, Seungeock KimAbstract:Abstract In this paper, a new higher-order Shear deformation theory for bending and free vibration analysis of functionally graded plates is developed. The present theory has only four unknowns, but it accounts for a parabolic variation of transverse Shear strains through the thickness of the plate. A Shear Correction Factor is, therefore, not required. Equations of motion are derived from Hamilton’s principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The obtained results are compared with 3D and quasi-3D solutions and those predicted by other plate theories. Results show that the present theory can achieve the same accuracy of the existing higher-order Shear deformation theories which have more number of unknowns, but its accuracy is not comparable with those of 3D and quasi-3D models which include the thickness stretching effect.
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bending and free vibration of functionally graded beams using various higher order Shear deformation beam theories
International Journal of Mechanical Sciences, 2012Co-Authors: Huu-tai ThaiAbstract:In this paper, various higher-order Shear deformation beam theories for bending and free vibration of functionally graded beams are developed. The developed theories account for higher-order variation of transverse Shear strain through the depth of the beam, and satisfy the stress-free boundary conditions on the top and bottom surfaces of the beam. A Shear Correction Factor, therefore, is not required. In addition, these theories have strong similarities with Euler–Bernoulli beam theory in some aspects such as equations of motion, boundary conditions, and stress resultant expressions. The material properties of the functionally graded beam are assumed to vary according to power law distribution of the volume fraction of the constituents. Equations of motion and boundary conditions are derived from Hamilton's principle. Analytical solutions are presented, and the obtained results are compared with the existing solutions to verify the validity of the developed theories. Finally, the influences of power law index and Shear deformation on the bending and free vibration responses of functionally graded beams are investigated.
Teik-cheng Lim - One of the best experts on this subject based on the ideXlab platform.
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Improved Shear Correction Factors for deflection of simply supported very thick rectangular auxetic plates
International Journal of Mechanical and Materials Engineering, 2016Co-Authors: Teik-cheng LimAbstract:The first-order Shear deformation theory (FSDT) for plates requires a Shear Correction Factor due to the assumption of constant Shear strain and Shear stress across the thickness; hence, the Shear Correction Factor strongly influences the accuracy of the deflection solution; the third-order Shear deformation theory (TSDT) does not require a Correction Factor because it facilitates the change in Shear strain across the plate thickness. This paper obtains an improved Shear Correction Factor for simply supported very thick rectangular plates by matching the deflection of the Mindlin plate (FSDT) with that of the Reddy plate (TSDT). As a consequence, the use of the exact Shear Correction Factor for the Mindlin plate gives solutions that are exactly the same as for the Reddy plate. The customary adoption of 5/6 Shear Correction Factor is a lower bound, and the exact Shear Correction Factor is higher for the following: (a) very thick plates, (b) narrow or long plates, (c) high Poisson’s ratio plate material, and (d) highly patterned loads, while the commonly used Shear Correction Factor of 5/6 is still valid for the following: (i) marginally thick plates, (ii) square plates, (iii) negative Poisson’s ratio materials, and (d) uniformly distributed loadings.
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Refined Shear Correction Factor for very thick simply supported and uniformly loaded isosceles right triangular auxetic plates
Smart Materials and Structures, 2016Co-Authors: Teik-cheng LimAbstract:For moderately thick plates, the use of First order Shear Deformation Theory (FSDT) with a constant Shear Correction Factor of 5/6 is sufficient to take into account the plate deflection arising from transverse Shear deformation. For very thick plates, the use of Third order Shear Deformation Theory (TSDT) is preferred as it allows the Shear strain distribution to be varied through the plate thickness. Therefore no Correction Factor is required in TSDT, unlike FSDT. Due to the complexity involved in TSDT, this paper obtains a more accurate Shear Correction Factor for use in FSDT of very thick simply supported and uniformly loaded isosceles right triangular plates based on the TSDT. By matching the maximum deflections for this plate according to FSDT and TSDT, a variable Shear Correction Factor is obtained. Results show that the Shear Correction Factor for the simplified TSDT, i.e. 14/17, is least accurate. The commonly adopted Shear Correction Factor of 5/6 in FSDT is valid only for very thin or highly auxetic plates. This paper provides a variable Shear Correction for FSDT deflection that matches the plate deflection by TSDT. This variable Shear Correction Factor allows designers to justify the use of a commonly adopted Shear Correction Factor of 5/6 even for very thick plates as long as the Poisson's ratio of the plate material is sufficiently negative.
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Elastic stability analysis of auxetic columns using third-order Shear deformation theory
physica status solidi (b), 2015Co-Authors: Teik-cheng LimAbstract:The analysis of auxetic structural elements undergoing transverse Shear deformation has so far been largely confined to the first-order Shear deformation theory (FSDT), which requires a Shear Correction Factor; analysis using the third-order Shear deformation theory (TSDT), which does not require a Shear Correction Factor, is currently lacking in regard to auxetic structural elements. This paper adopts the TSDT to evaluate the elastic stability of isotropic columns with special emphasis on auxetic ones for pinned–pinned columns with springs of equal rotational stiffness at both ends. Results on columns with pinned–pinned (zero stiffness) and fixed–fixed (infinite stiffness) end conditions with square and circular cross sections reveal that auxeticity (i) reduces the transverse Shear deformation, (ii) allows the use of classical theories, and (iii) provides higher elastic stability.
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Shear Deformation in Auxetic Solids
Auxetic Materials and Structures, 2014Co-Authors: Teik-cheng LimAbstract:This chapter establishes the effect of auxeticity on Shear deformation in laterally-loaded thick beams, laterally-loaded thick circular, polygonal and rectangular plates, buckling of thick columns and plates , and vibration of thick plates. Results show that Shear deformation reduces as the Poisson’s ratio becomes more negative, thereby implying that geometrically thick beams and plates are mechanically thin beams and plates, respectively, if the Poisson’s ratio is sufficiently negative. In other words, results of deflections in Timoshenko beam and Mindlin plate approximate those by Euler-Bernoulli beam and Kirchhoff plate, respectively, as the Poisson’s ratio approaches −1. In the study of buckling of isotropic columns, it was found that auxeticity increases the buckling load such that the buckling loads of Timoshenko columns approximate those of Euler-Bernoulli columns as \(v \to - 1\). In the case of vibration of thick isotropic plates, it was shown that as a plate’s Poisson’s ratio becomes more negative, the Mindlin-to-Kirchhoff natural frequency ratio increases with diminishing rate. Furthermore, simplifying assumptions such as constant Shear Correction Factor and exclusion of rotary inertia is valid for plates with positive Poisson’s ratio, and that the assumptions of constant Shear Correction Factor and no rotary inertia for auxetic plates give overestimated natural frequency.
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Vibration of thick auxetic plates
Mechanics Research Communications, 2014Co-Authors: Teik-cheng LimAbstract:Abstract This short communication investigates the effect of negative Poisson's ratio on the natural frequency of thick plates of arbitrary shape. Using the Mindlin plate theory, it was generally found that as the plate's Poisson's ratio becomes more negative, the Mindlin-to-Kirchhoff natural frequency ratio increases with decreasing rate. Upon comparing (a) the use of the simplified constant Shear Correction Factor and the more accurate variable Shear Correction Factor, (b) with and without rotary inertia, it was found that all the four combinations stated in (a) and (b) do not give appreciable difference when the Poisson's ratio of the plate is positive. However in the case of plates with negative Poisson's ratio, results reveal that when at least one of the simplifying assumptions is used, the Mindlin-to-Kirchhoff natural frequency ratio is overestimated, and that the overestimation further increases when both the simplifying assumptions are used. When benchmarked against Reddy plate theory, the use of variable Shear Correction Factor has almost the same effect as the inclusion of rotary inertia. Hence the use of either variable Shear Correction Factor or rotary inertia is proposed for modeling the vibrational frequencies of conventional and auxetic isotropic plates.
Ömer Civalek - One of the best experts on this subject based on the ideXlab platform.
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A size-dependent beam model for stability of axially loaded carbon nanotubes surrounded by Pasternak elastic foundation
Composite Structures, 2017Co-Authors: Bekir Akgöz, Ömer CivalekAbstract:Abstract Microstructure-dependent buckling behavior of single-walled carbon nanotubes (SWCNTs) surrounded by a two-parameter elastic foundation is investigated. The governing equations and corresponding boundary conditions in buckling are achieved by implementing minimum total potential energy principle via modified strain gradient theory and several beam theories. The resulting equations are analytically solved by employing Navier’s solution procedure for simply supported boundary conditions. A detailed parametric study is performed to indicate effects of diameter-to-length scale parameter ratio, diameter-to-length ratio, Shear deformation, Shear Correction Factor and foundation parameters on buckling loads of SWCNTs. Numerical results reveal that the classical buckling loads evaluated by all Shear deformation beam theories agree well with each other while a discrepancy occurs between the size-dependent buckling loads of parabolic beam theory (PBT), sinusoidal beam theory (SBT) and Timoshenko beam theory with proposed Shear Correction Factor (TBT ∗ ), and those of Timoshenko beam theory (TBT).
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Effects of thermal and Shear deformation on vibration response of functionally graded thick composite microbeams
Composites Part B: Engineering, 2017Co-Authors: Bekir Akgöz, Ömer CivalekAbstract:Abstract In this paper, thermal and Shear deformation effects on the vibrational response of non-homogeneous microbeams made of functionally graded (FG) materials are carried out. It is assumed that the temperature-dependent material properties of FG microbeams change smoothly and gradually throughout the height according to the classical rule of mixture. The governing differential equations and related boundary conditions are derived by implementing Hamilton's principle on the basis of hyperbolic Shear deformation beam and modified couple stress theories and they are analytically solved. The results are given together with other beam theories. A detailed parametric study is performed to indicate the influences of slenderness ratio, material length scale parameter, gradient index, Shear Correction Factors and temperature rise on natural frequencies of FG microbeams. It is revealed that the use of modified Shear Correction Factor can provide more accurate and valid results for first-order Shear deformable microbeam model.
Abdelouahed Tounsi - One of the best experts on this subject based on the ideXlab platform.
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influence of boundary conditions on the bending and free vibration behavior of fgm sandwich plates using a four unknown refined integral plate theory
Computers and Concrete, 2020Co-Authors: Mohammed Cherif Rahmani, Abdelmoumen Anis Bousahla, Abdelhakim Kaci, S R Mahmoud, El Abbes Adda Bedia, Fouad Bourada, Abdeldjebbar Tounsi, Kouider Halim Benrahou, Abdelouahed TounsiAbstract:The influence of boundary conditions on the bending and free vibration behavior of functionally graded sandwich plates resting on a two-parameter elastic foundation is examined using an original novel high order Shear theory. The Hamilton\'s principle is used herein to derive the equations of motion. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. This theory includes indeterminate integral variables and contains only four unknowns in which any Shear Correction Factor not used, with even less than the conventional theory of first Shear strain (FSDT). Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five, six or more in the case of other Shear deformation theories. Galerkin\'s approach is utilized for FGM sandwich plates with six different boundary conditions. The accuracy of the proposed solution is checked by comparing it with other closed form solutions available in the literature.
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a novel four unknown integral model for buckling response of fg sandwich plates resting on elastic foundations under various boundary conditions using galerkin s approach
Geomechanics and Engineering, 2020Co-Authors: Sara Chelahi Chikr, Abdelmoumen Anis Bousahla, Abdelhakim Kaci, S R Mahmoud, Fouad Bourada, Abdeldjebbar Tounsi, Kouider Halim Benrahou, E Adda A Bedia, Abdelouahed TounsiAbstract:In this work, the buckling analysis of material sandwich plates based on a two-parameter elastic foundation under various boundary conditions is investigated on the basis of a new theory of refined trigonometric Shear deformation. This theory includes indeterminate integral variables and contains only four unknowns in which any Shear Correction Factor not used, with even less than the conventional theory of first Shear strain (FSDT). Applying the principle of virtual displacements, the governing equations and boundary conditions are obtained. To solve the buckling problem for different boundary conditions, Galerkin\'s approach is utilized for symmetric EGM sandwich plates with six different boundary conditions. A detailed numerical study is carried out to examine the influence of plate aspect ratio, elastic foundation coefficients, ratio, side-to-thickness ratio and boundary conditions on the buckling response of FGM sandwich plates. A good agreement between the results obtained and the available solutions of existing Shear deformation theories that have a greater number of unknowns proves to demonstrate the precision of the proposed theory.
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galerkin s approach for buckling analysis of functionally graded anisotropic nanoplates different boundary conditions
Engineering With Computers, 2019Co-Authors: Behrouz Karami, Maziar Janghorban, Abdelouahed Tounsi, Abdelouahed TounsiAbstract:For the first time, buckling behavior of functionally graded (FG) nanoplates made of anisotropic material (beryllium crystal as a hexagonal material) is investigated. Also, it is the first time that the size-dependent behavior of nanostructured systems is studied for buckling response of the graded anisotropic material. The properties of graded material are assumed vary exponentially through the z-direction. Nonlocal strain gradient theory is utilized to predicate the size-dependent buckling behavior of the nanoplate. The nanoplate is modeled by a higher order Shear deformation refined plate theory in which any Shear Correction Factor not used. Governing equations and boundary conditions are obtained using a virtual work of variational approach. To solve the buckling problem for different boundary conditions, Galerkin’s approach is utilized. Finally, the influences of different boundary conditions, small-scale parameters, geometry parameters and exponential Factor are studied and discussed in detail. It is hoped that the present numerical results can help the engineers and designers to understand and predict the buckling response of FG anisotropic materials.
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Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT
Engineering with Computers, 2019Co-Authors: Mokhtar Khiloun, Abdelouahed Tounsi, Abdelmoumen Anis Bousahla, Abdelhakim Kaci, Aicha Bessaim, S R MahmoudAbstract:This work presents an efficient and original high-order Shear and normal deformation theory for the static and free vibration analysis of functionally graded plates. The Hamilton’s principle is used herein to derive the equations of motion. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. The present plate theory approach accounts for both transverse Shear and normal deformations and satisfies the zero traction boundary conditions on the surfaces of the plate without using Shear Correction Factor. Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five or more in the case of other Shear and normal deformation theories. The accuracy of the proposed solution is checked by comparing it with other closed form solutions available in the literature.
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effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations
International Journal of Mechanics and Materials in Design, 2017Co-Authors: Hassen Ait Atmane, Abdelouahed Tounsi, Fabrice BernardAbstract:The novelty of this paper is the use of an efficient beam theory for bending, free vibration and buckling analysis of functionally graded material (FGM) beams on two-parameter elastic foundation. The present theory accounts for both Shear deformation and thickness stretching effects by a parabolic variation of all displacements across the thickness, and satisfies the stress-free boundary conditions on the upper and lower surfaces of the beam without requiring any Shear Correction Factor. Due to porosities, possibly occurring inside FGMs during fabrication, it is therefore necessary to consider the vibration, bending and buckling behaviors of beams having porosities in this work. The equation of motion for FGM beams is obtained through Hamilton’s principle. The closed form solutions are obtained by using Navier technique, and then fundamental frequencies are found by solving the results of eigenvalue problems. The validity of the present theory is investigated by comparing some of the present in literature. It can be concluded that the proposed theory is accurate and simple in solving the bending, free vibration and buckling behaviors of FGM sandwich beams.
Yuwaraj M. Ghugal - One of the best experts on this subject based on the ideXlab platform.
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BENDING, VIBRATION AND BUCKLING OF LAMINATED COMPOSITE PLATES USING A SIMPLE FOUR VARIABLE PLATE THEORY
Latin American Journal of Solids and Structures, 2016Co-Authors: Atteshamuddin S. Sayyad, Bharti M. Shinde, Yuwaraj M. GhugalAbstract:In the present study, a simple trigonometric Shear deformation theory is applied for the bending, buckling and free vibration of cross-ply laminated composite plates. The theory involves four unknown variables which are five in first order Shear deformation theory or any other higher order theories. The in-plane displacement field uses sinusoidal function in terms of thickness co-ordinate to include the Shear deformation effect. The transverse displacement includes bending and Shear components. The present theory satisfies the zero Shear stress conditions at top and bottom surfaces of plates without using Shear Correction Factor. Equations of motion associated with the present theory are obtained using the dynamic version of virtual work principle. A closed form solution is obtained using double trigonometric series suggested by Navier. The displacements, stresses, critical buckling loads and natural frequencies obtained using present theory are compared with previously published results and found to agree well with those.
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on the free vibration analysis of laminated composite and sandwich plates a review of recent literature with some numerical results
Composite Structures, 2015Co-Authors: Atteshamuddin S. Sayyad, Yuwaraj M. GhugalAbstract:The present article reviews the recent research done on the free vibration analysis of multilayered laminated composite and sandwich plates using various methods available for the analysis of plates. Displacement fields of various displacement based Shear deformation theories have been presented and compared. Also, some numerical results related to fundamental flexural mode frequencies of laminated composite and sandwich plates are presented using a trigonometric Shear and normal deformation theory. The theory involves six unknown variables and does not require problem dependent Shear Correction Factor. Governing differential equations and associated boundary conditions of the theory are derived by employing the dynamic version of the principle of virtual work. Navier-type closed-form solutions are obtained for simply supported laminated composite and sandwich plates. The present results are compared with exact elasticity solution and other higher order Shear deformation theories wherever applicable. This article cites 391 references.
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Free vibration of thick orthotropic plates using trigonometric Shear deformation theory
Latin American Journal of Solids and Structures, 2011Co-Authors: Yuwaraj M. Ghugal, Atteshamuddin S. SayyadAbstract:In this paper a trigonometric Shear deformation theory is presented for the free vibration of thick orthotropic square and rectangular plates. In this displacement based theory the in-plane displacement field uses sinusoidal function in terms of thickness coordinate to include the Shear deformation effect. The cosine function in terms of thickness coordinate is used in transverse displacement to include the effect of transverse normal strain. The most important feature of the theory is that the transverse Shear stress can be obtained directly from the constitutive relations satisfying the Shear stress free surface conditions on the top and bottom surfaces of the plate. Hence the theory obviates the need of Shear Correction Factor. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Results obtained for frequency of bending mode, Shear mode and thickness stretch mode of free vibration of simply supported orthotropic square and rectangular plates are compared with those of other refined theories and exact solution from theory of elasticity wherever applicable.
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Free Vibration of Thick Isotropic Plates Using Trigonometric Shear Deformation Theory
Journal of Solid Mechanics, 2011Co-Authors: Yuwaraj M. Ghugal, Atteshamuddin S. SayyadAbstract:In this paper a variationally consistent trigonometric Shear deformation theory is presented for the free vibration of thick isotropic square and rectangular plate. In this displacement based theory, the in-plane displacement field uses sinusoidal function in terms of thickness coordinate to include the Shear deformation effect. The cosine function in terms of thickness coordinate is used in transverse displacement to include the effect of transverse normal strain. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Results of frequency of bending mode, thickness-Shear mode and thickness-stretch mode are obtained from free vibration of simply supported isotropic square and rectangular plates and compared with those of other refined theories and frequencies from exact theory. Present theory yields exact dynamic Shear Correction Factor π2/12 from thickness Shear motion of the plate.
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A HYPERBOLIC Shear DEFORMATION THEORY FOR FLEXURE AND VIBRATION OF THICK ISOTROPIC BEAMS
International Journal of Computational Methods, 2009Co-Authors: Yuwaraj M. Ghugal, Rajneesh SharmaAbstract:A Hyperbolic Shear Deformation Theory taking into account transverse Shear deformation effects, is presented for the static flexure and free flexural vibration analysis of thick isotropic beams. The displacement field of the theory contains two variables and does not require Shear Correction Factor. The hyperbolic sine function is used in the displacement field in terms of thickness coordinate to represent Shear deformation. The most important feature of the theory is that the transverse Shear stress can be obtained directly from the use of constitutive relation, satisfying the stress free boundary conditions at top and bottom of the beam. Hence, the theory obviates the need of Shear Correction Factor. Governing differential equations and boundary conditions of the theory are obtained using the principle of virtual work. Results obtained for flexure and free vibration of simply supported uniform, isotropic beams are compared with those of elementary, refined, and exact beam theories to validate the accuracy of the theory.