Influence of Functionally Graded Material on Buckling of Skew Plates under Mechanical Loads
01 Aug 2006-Journal of Engineering Mechanics-asce (American Society of Civil Engineers)-Vol. 132, Iss: 8, pp 902-905
TL;DR: In this article, the critical buckling of simply supported functionally graded skew plate subjected to mechanical compressive loads is evaluated using first-order shear deformation theory in conjunction with the finite element approach.
Abstract: In this technical note, the critical buckling of simply supported functionally graded skew plate subjected to mechanical compressive loads is evaluated using first-order shear deformation theory in conjunction with the finite element approach. The material properties are assumed to vary in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents. The effective material properties are estimated from the volume fractions and the properties of the constituents using the Mori–Tanaka homogenization method. The effects of aspect ratio, material gradient index, and skew angle on the critical buckling loads of functionally graded material plates are highlighted.
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TL;DR: A comprehensive review of various theories for the modeling and analysis of functionally graded plates and shells is presented in this paper, where a thorough review of the literature related to the development of three-dimensional elasticity solutions and a unified formulation is also presented.
Abstract: In this paper, a comprehensive review of various theories for the modeling and analysis of functionally graded plates and shells is presented. The review is devoted to theoretical models which were developed to predict the global responses of functionally graded plates and shells under mechanical and thermal loadings. This review mainly focuses on the equivalent single layer theories including the classical plate theory, first-order shear deformation theory, higher-order shear deformation theories, simplified theories and mixed theories since they were widely used in the modeling of functionally graded plates and shells. In addition, a thorough review of the literature related to the development of three-dimensional elasticity solutions and a unified formulation is also presented.
273 citations
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TL;DR: In this article, a non-uniform rational B-spline based iso-geometric finite element method is used to study the static and dynamic characteristics of functionally graded material (FGM) plates.
Abstract: In this paper, a non-uniform rational B-spline based iso-geometric finite element method is used to study the static and dynamic characteristics of functionally graded material (FGM) plates. The material properties are assumed to be graded only in the thickness direction and the effective properties are computed either using the rule of mixtures or by Mori–Tanaka homogenization scheme. The plate kinematics is based on the first order shear deformation plate theory (FSDT). The shear correction factors are evaluated employing the energy equivalence principle and a simple modification to the shear correction factor is presented to alleviate shear locking. Static bending, mechanical and thermal buckling, linear free flexural vibration and supersonic flutter analysis of FGM plates are numerically studied. The accuracy of the present formulation is validated against available three-dimensional solutions. A detailed numerical study is carried out to examine the influence of the gradient index, the plate aspect ratio and the plate thickness on the global response of functionally graded material plates.
237 citations
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TL;DR: In this article, a new sinusoidal shear deformation theory is developed for bending, buckling, and vibration of functionally graded plates, and the closed-form solutions of simply supported plates are obtained.
Abstract: 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.
174 citations
Cites background from "Influence of Functionally Graded Ma..."
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TL;DR: In this article, a stochastic perturbation-based finite element for buckling statistics of functionally graded plates (FGM) with uncertain material properties in thermal environments is investigated, where the effective material properties of the gradient plates are assumed to be temperature-dependent and vary in the thickness direction only according to the power law distribution of the volume fractions of the constituents.
Abstract: In the present study, stochastic perturbation-based finite element for buckling statistics of functionally graded plates (FGM) with uncertain material properties in thermal environments is investigated. The effective material properties of the gradient plates are assumed to be temperature-dependent and vary in the thickness direction only according to the power-law distribution of the volume fractions of the constituents. An improved structural kinematics proposed earlier by author’s is employed which accounts parabolic variations for the transverse shear strains with stress free boundary conditions at the top and bottom faces of the plate. An efficient C0 stochastic finite element based on the first-order perturbation technique (FOPT) is proposed, and the fundamental equations are obtained using variational approach. Convergence and comparison studies have been performed to describe the efficiency of the present formulation. The numerical results are highlighted with different system parameters and boundary conditions.
62 citations
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TL;DR: In this article, the effect of local defects, viz., cracks and cutouts on the buckling behavior of functionally graded material plates subjected to mechanical and thermal load is numerically studied.
Abstract: In this paper, the effect of local defects, viz., cracks and cutouts on the buckling behaviour of functionally graded material plates subjected to mechanical and thermal load is numerically studied. The internal discontinuities, viz., cracks and cutouts are represented independent of the mesh within the framework of the extended finite element method and an enriched shear flexible 4-noded quadrilateral element is used for the spatial discretization. The properties are assumed to vary only in the thickness direction and the effective properties are estimated using the Mori-Tanaka homogenization scheme. The plate kinematics is based on the first order shear deformation theory. The influence of various parameters, viz., the crack length and its location, the cutout radius and its position, the plate aspect ratio and the plate thickness on the critical buckling load is studied. The effect of various boundary conditions is also studied. The numerical results obtained reveal that the critical buckling load decreases with increase in the crack length, the cutout radius and the material gradient index. This is attributed to the degradation in the stiffness either due to the presence of local defects or due to the change in the material composition.
50 citations
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References
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01 Jan 1989
TL;DR: In this article, the methodes are numeriques and the fonction de forme reference record created on 2005-11-18, modified on 2016-08-08.
Abstract: Keywords: methodes : numeriques ; fonction de forme Reference Record created on 2005-11-18, modified on 2016-08-08
17,323 citations
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TL;DR: In this paper, a method of calculating the average internal stress in the matrix of a material containing inclusions with transformation strain is presented. But the authors do not consider the effects of the interaction among the inclusions and of the presence of the free boundary.
Abstract: Having noted an important role of image stress in work hardening of dispersion hardened materials, (1,3) the present paper discusses a method of calculating the average internal stress in the matrix of a material containing inclusions with transformation strain. It is shown that the average stress in the matrix is uniform throughout the material and independent of the position of the domain where the average treatment is carried out. It is also shown that the actual stress in the matrix is the average stress plus the locally fluctuating stress, the average of which vanishes in the matrix. Average elastic energy is also considered by taking into account the effects of the interaction among the inclusions and of the presence of the free boundary.
6,312 citations
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TL;DR: In this paper, a reconsideration and reformulation of the Mori-Tanaka's theory in its application to the computation of the effective properties of composites is presented, which is a straightforward exposition and interpretation of the method which are different than those existing in previous formulations.
Abstract: This paper is a reconsideration and reformulation of the Mori-Tanaka's theory in its application to the computation of the effective properties of composites. Previous applications of the theory in this context continued to be linked with eigenstrain, equivalent inclusion, and back stress concepts, and many times involved energy considerations. In this paper we adopt the ‘direct approach’ of defining and computing effective moduli. By elucidating the nature of the approximation in applying Mori—Tanaka's theory to composites insofar as the ‘concentration-factor’ tensors are concerned, we achieve a straightforward exposition and interpretation of the method which are different than those existing in previous formulations. The analysis is given for two-phase composites with anisotropic elastic constituents and an inclusion phase consisting of aligned or randomly oriented ellipsoidal particles. The derived simple expressions for the predicted stiffness and compliance tensors permit a proof of the self-consistency of the method, a discussion of the predictions' relation to the Hashin-Shtrikman bounds in the case of isotropic constituents and randomly oriented ellipsoidal particles, and finally a derivation of some new results in randomly cracked bodies with penny-shaped cracks.
2,214 citations
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TL;DR: In this paper, the axisymmetric large deflection bending of a functionally graded circular plate under mechanical, thermal and combined thermal-mechanical loadings, respectively, was investigated.
Abstract: Based on the classical nonlinear von Karman plate theory, axisymmetric large deflection bending of a functionally graded circular plate is investigated under mechanical, thermal and combined thermal–mechanical loadings, respectively, and axisymmetric thermal post-buckling behavior of a functionally graded circular plate is also investigated. The mechanical and thermal properties of functionally graded material (FGM) are assumed to vary continuously through the thickness of the plate, and obey a simple power law of the volume fraction of the constituents. Governing equations for the problem are derived, and then a shooting method is employed to numerically solve the equations. Effects of material constant n and boundary conditions on the temperature distribution, nonlinear bending, critical buckling temperature and thermal post-buckling behavior of the FGM plate are discussed in details.
278 citations