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H Matsunaga - One of the best experts on this subject based on the ideXlab platform.
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thermal buckling of functionally graded plates according to a 2d higher order deformation Theory
Composite Structures, 2009Co-Authors: H MatsunagaAbstract:A two-dimensional (2D) global Higher-Order deformation Theory is presented for thermal buckling of plates made of functionally graded materials (FGMs). The modulus of elasticity of functionally graded (FG) plates is assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. By using the method of power series expansion of displacement components, a set of fundamental equations of a 2D Higher-Order Theory for rectangular functionally graded (FG) plates is derived through the principle of virtual work. Several sets of truncated approximate theories are applied to solve the eigenvalue problems of FG plates with simply supported edges. In order to assure the accuracy of the present Theory, convergence properties of the critical temperature are examined in detail. A comparison of the present critical temperatures of isotropic and FG plates is also made with previously published results. Critical temperatures of simply supported FG plates are obtained for uniformly and linearly distributed temperatures through the thickness of plates. Modal transverse shear and normal stresses are calculated by integrating the three-dimensional (3D) equations of equilibrium in the thickness direction satisfying the stress boundary conditions at the top and bottom surfaces. The internal and external works are calculated and compared to prove the numerical accuracy of solutions. It is noticed that the present Higher-Order approximate theories can predict accurately the critical temperatures of simply supported FG plates.
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free vibration and stability of functionally graded plates according to a 2 d higher order deformation Theory
Composite Structures, 2008Co-Authors: H MatsunagaAbstract:Abstract Natural frequencies and buckling stresses of shallow shells made of functionally graded materials (FGMs) are analyzed by taking into account the effects of transverse shear and normal deformations, and rotatory inertia. The modulus of elasticity of shells is assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a two-dimensional (2D) Higher-Order Theory for rectangular functionally graded (FG) shallow shells is derived through Hamilton’s principle. Several sets of truncated approximate theories are applied to solve the eigenvalue problems of FG shallow shells with simply supported edges. Three types of simply supported shallow shells with positive, zero and negative Gaussian curvature are considered. In order to assure the accuracy of the present Theory, convergence properties of the fundamental natural frequency and also buckling stress are examined in detail. Critical buckling stresses of FG shells subjected to in-plane stresses are also obtained and a relation between the buckling stress and natural frequency of simply supported FG shells without in-plane stresses is presented. The modal transverse stresses have been obtained by integrating the three-dimensional (3D) equations of motion in the thickness direction with satisfying the surface boundary conditions of a shell. The present numerical results are also verified by satisfying the energy balance of external and internal works are considered to be sufficient with respect to the accuracy of solutions. It is noticed that the present 2D Higher-Order approximate theories can predict accurately the natural frequencies and buckling stresses of simply supported FG shallow shells.
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thermal buckling of angle ply laminated composite and sandwich plates according to a global higher order deformation Theory
Composite Structures, 2006Co-Authors: H MatsunagaAbstract:Abstract A two-dimensional global Higher-Order deformation Theory is presented for thermal buckling of angle-ply laminated composite and sandwich plates. By using the method of power series expansion of continuous displacement components, a set of fundamental governing equations which can take into account the effects of both transverse shear and normal stresses is derived through the principle of virtual work. Several sets of truncated M th order approximate theories are applied to solve the eigenvalue problems of simply supported laminated composite and sandwich plates. In order to assure the accuracy of the present Theory, convergence properties of the critical temperatures are examined in detail. Numerical results are compared with those of the published three-dimensional layerwise Theory in which both in-plane and normal displacements are assumed to be C 0 continuous in the continuity conditions at the interface between layers. Modal transverse shear and normal stresses can be calculated by integrating the three-dimensional equations of equilibrium in the thickness direction, and satisfying the continuity conditions at the interface between layers and stress boundary conditions at the external surfaces. Effects of the difference of displacement continuity conditions between the three-dimensional layerwise Theory and the global Higher-Order Theory are clarified in thermal buckling problems of angle-ply laminated and sandwich plates.
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thermal buckling of cross ply laminated composite and sandwich plates according to a global higher order deformation Theory
Composite Structures, 2005Co-Authors: H MatsunagaAbstract:A two-dimensional global Higher-Order deformation Theory is presented for thermal buckling of cross-ply laminated composite and sandwich plates. By using the method of power series expansion of continuous displacement components, a set of fundamental governing equations which can take into account the effects of both transverse shear and normal stresses is derived through the principle of virtual work. Several sets of truncated Mth-order approximate theories are applied to solve the eigenvalue problems of a simply supported multilayered plate. Modal transverse shear and normal stresses can be calculated by integrating the three-dimensional equations of equilibrium in the thickness direction, and satisfying the continuity conditions at the interface between layers and stress boundary conditions at the external surfaces. Numerical results are compared with those of the published three-dimensional layerwise Theory in which both in-plane and normal displacements are assumed to be C0 continuous in the continuity conditions at the interface between layers. Effects of the difference of displacement continuity conditions between the three-dimensional layerwise Theory and the global Higher-Order Theory are clarified in thermal buckling problems of multilayered composite plates.
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a comparison between 2 d single layer and 3 d layerwise theories for computing interlaminar stresses of laminated composite and sandwich plates subjected to thermal loadings
Composite Structures, 2004Co-Authors: H MatsunagaAbstract:Abstract A two-dimensional global Higher-Order deformation Theory is presented for the evaluation of interlaminar stresses and displacements in cross-ply multilayered composite and sandwich plates subjected to thermal loadings. By using the method of power series expansion of continuous displacement components, a set of fundamental governing equations which can take into account the effects of both transverse shear and normal stresses is derived through the principle of virtual work. Several sets of truncated M th order approximate theories are applied to solve the static boundary value problems of a simply supported multilayered composite plate. Transverse shear and normal stresses can be calculated by integrating the three-dimensional equations of equilibrium in the thickness direction, and satisfying the continuity conditions at the interface between layers and stress boundary conditions at the external surfaces. Numerical results are compared with those of the published three-dimensional layerwise Theory in which both in-plane and normal displacements are assumed to be C 0 continuous in the continuity conditions at the interface between layers. Effects of the difference of displacement continuity conditions between the three-dimensional layerwise Theory and the global Higher-Order Theory are clarified in multilayered composite and sandwich plates subjected to thermal loadings.
Wu Zhen - One of the best experts on this subject based on the ideXlab platform.
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c0 type global local higher order Theory including transverse normal thermal strain for laminated composite plates under thermal loading
Composite Structures, 2013Co-Authors: Wu ZhenAbstract:Abstract In order to consider the transverse normal strain for thermal expansion problems of laminated composites, the expansion order of the transverse displacement is generally increased, so additional displacement variables will be involved in the displacement fields. Differing from the previous methods, this paper proposes a global–local Higher-Order Theory for thermal stress analysis of simply supported laminated composite plates by introducing transverse normal thermal deformation in transverse displacement field. Although transverse normal deformation is considered, the additional displacement variables have not increased in the proposed model since thermal loads could be included in the generalized force vector. The proposed model a priori satisfies the continuity conditions of transverse shear stresses at interfaces, and the number of displacement variables involved in the present model does not depend on the number of layers in laminates. The equilibrium equations are obtained by using the principle of virtual displacements, and results are computed by using Navier’s technique. Comparing to the three-dimensional Theory, the proposed Higher-Order Theory is acceptable even in the case of thick multilayerd composite plates subjected to thermal loads.
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an accurate higher order Theory and c0 finite element for free vibration analysis of laminated composite and sandwich plates
Composite Structures, 2010Co-Authors: Wu Zhen, Chen Wanji, Ren XiaohuiAbstract:Abstract At present, it is difficult to accurately predict natural frequencies of sandwich plates with soft core by using the C 0 plate bending elements. Thus, the C 1 plate bending elements have to be employed to predict accurately dynamic response of such structures. This paper proposes an accurate Higher-Order C 0 Theory which is very different from other published Higher-Order Theory satisfying the interlaminar stress continuity, as the first derivative of transverse displacement has been taken out from the in-plane displacement fields of the present Theory. Therefore, the C 0 interpolation functions is only required during its finite element implementation. Based on the Hamilton’s principle and Navier’s technique, analytical solutions to the natural frequency analysis of simply-supported laminated plates have been presented. To further extend the ranges of application of the proposed Theory, an eight-node C 0 continuous isoparametric element is used to model the proposed Theory. Numerical results show the present C 0 finite element can accurately predict the natural frequencies of sandwich plate with soft core, whereas other global Higher-Order theories are unsuitable for free vibration analysis of such soft-core structures.
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a global local higher order Theory including interlaminar stress continuity and c0 plate bending element for cross ply laminated composite plates
Computational Mechanics, 2010Co-Authors: Wu Zhen, Chen WanjiAbstract:A C0-type global-local higher order Theory including interlaminar stress continuity is proposed for the cross-ply laminated composite and sandwich plates in this paper, which is able to a priori satisfy the continuity conditions of transverse shear stresses at interfaces. Moreover, total number of unknowns involved in the model is independent of number of layers. Compared to other Higher-Order theories satisfying the continuity conditions of transverse shear stresses at interfaces, merit of the proposed model is that the first derivatives of transverse displacement w have been taken out from the in-plane displacement fields, so that the C0 interpolation functions is only required during its finite element implementation. To verify the present model, a C0 three-node triangular element is used for bending analysis of laminated composite and sandwich plates. It ought to be shown that all variables involved in present model are discretized by only using linear interpolation functions within an element. Numerical results show that the C0 plate element based on the present Theory may accurately calculate transverse shear stresses without any postprocessing, and the present results agree well with those obtained from the C1-type higher order Theory. Compared with the C1 plate bending element, the present finite element is simple, convenient to use and accurate enough.
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a quadrilateral element based on refined global local higher order Theory for coupling bending and extension thermo elastic multilayered plates
International Journal of Solids and Structures, 2007Co-Authors: Wu Zhen, Chen WanjiAbstract:In this paper a refined Higher-Order global-local Theory is presented to analyze the laminated plates coupled bending and extension under thermo-mechanical loading. The in-plane displacement fields are composed of a third-order polynomial of global coordinate z in the thickness direction and 1,2–3 order power series of local coordinate fk in the thickness direction of each layer, which is identical to the 1,2–3 global-local Higher-Order Theory by Li and Liu [Li, X.Y., Liu, D., 1997. Generalized laminate theories based on double superposition hypothesis. Int. J. Numer. Methods Eng. 40, 1197–1212] Moreover, a second-order polynomial of global coordinate z in the thickness direction is chosen as transverse displacement field. The transverse shear stresses can satisfy continuity at interfaces, and the number of unknowns does not depend on the layer numbers of the laminate. Based on this Theory, a quadrilateral laminated plate element satisfying the requirement of C 1 continuity is presented. By solving both bending and thermal expansion problems of laminates, it can be found that the present refined Theory is very accurate and obviously superior to the existing 1,2–3 global-local Higher-Order Theory. The most attractive feature of this Theory is that the transverse shear stresses can be accurately predicted from direct use of constitutive equations without any post-processing method. It is also shown that the present quadrilateral element possesses higher accuracy. � 2006 Elsevier Ltd. All rights reserved.
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an efficient higher order Theory and finite element for laminated plates subjected to thermal loading
Composite Structures, 2006Co-Authors: Wu Zhen, Chen WanjiAbstract:In the present paper, the global–local Higher-Order Theory is simply derived, which satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. Moreover, the number of unknowns of this Theory is independent of the layer numbers of the laminate. Based on the global–local Higher-Order Theory, the discrete Kirchhoff element PDKT and refined triangular plate element PRT9 are presented for predicting interlaminar stresses and displacements in laminated plates subjected to thermal loading. The two triangular elements satisfy the interelement C1 continuity conditions. The numerical examples show that the in-plane stresses and transverse shear stresses can be accurately calculated by the direct constitutive equation approach. The equilibrium equation approach is employed to predict transverse normal stresses.
Chen Wanji - One of the best experts on this subject based on the ideXlab platform.
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an accurate higher order Theory and c0 finite element for free vibration analysis of laminated composite and sandwich plates
Composite Structures, 2010Co-Authors: Wu Zhen, Chen Wanji, Ren XiaohuiAbstract:Abstract At present, it is difficult to accurately predict natural frequencies of sandwich plates with soft core by using the C 0 plate bending elements. Thus, the C 1 plate bending elements have to be employed to predict accurately dynamic response of such structures. This paper proposes an accurate Higher-Order C 0 Theory which is very different from other published Higher-Order Theory satisfying the interlaminar stress continuity, as the first derivative of transverse displacement has been taken out from the in-plane displacement fields of the present Theory. Therefore, the C 0 interpolation functions is only required during its finite element implementation. Based on the Hamilton’s principle and Navier’s technique, analytical solutions to the natural frequency analysis of simply-supported laminated plates have been presented. To further extend the ranges of application of the proposed Theory, an eight-node C 0 continuous isoparametric element is used to model the proposed Theory. Numerical results show the present C 0 finite element can accurately predict the natural frequencies of sandwich plate with soft core, whereas other global Higher-Order theories are unsuitable for free vibration analysis of such soft-core structures.
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a global local higher order Theory including interlaminar stress continuity and c0 plate bending element for cross ply laminated composite plates
Computational Mechanics, 2010Co-Authors: Wu Zhen, Chen WanjiAbstract:A C0-type global-local higher order Theory including interlaminar stress continuity is proposed for the cross-ply laminated composite and sandwich plates in this paper, which is able to a priori satisfy the continuity conditions of transverse shear stresses at interfaces. Moreover, total number of unknowns involved in the model is independent of number of layers. Compared to other Higher-Order theories satisfying the continuity conditions of transverse shear stresses at interfaces, merit of the proposed model is that the first derivatives of transverse displacement w have been taken out from the in-plane displacement fields, so that the C0 interpolation functions is only required during its finite element implementation. To verify the present model, a C0 three-node triangular element is used for bending analysis of laminated composite and sandwich plates. It ought to be shown that all variables involved in present model are discretized by only using linear interpolation functions within an element. Numerical results show that the C0 plate element based on the present Theory may accurately calculate transverse shear stresses without any postprocessing, and the present results agree well with those obtained from the C1-type higher order Theory. Compared with the C1 plate bending element, the present finite element is simple, convenient to use and accurate enough.
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a quadrilateral element based on refined global local higher order Theory for coupling bending and extension thermo elastic multilayered plates
International Journal of Solids and Structures, 2007Co-Authors: Wu Zhen, Chen WanjiAbstract:In this paper a refined Higher-Order global-local Theory is presented to analyze the laminated plates coupled bending and extension under thermo-mechanical loading. The in-plane displacement fields are composed of a third-order polynomial of global coordinate z in the thickness direction and 1,2–3 order power series of local coordinate fk in the thickness direction of each layer, which is identical to the 1,2–3 global-local Higher-Order Theory by Li and Liu [Li, X.Y., Liu, D., 1997. Generalized laminate theories based on double superposition hypothesis. Int. J. Numer. Methods Eng. 40, 1197–1212] Moreover, a second-order polynomial of global coordinate z in the thickness direction is chosen as transverse displacement field. The transverse shear stresses can satisfy continuity at interfaces, and the number of unknowns does not depend on the layer numbers of the laminate. Based on this Theory, a quadrilateral laminated plate element satisfying the requirement of C 1 continuity is presented. By solving both bending and thermal expansion problems of laminates, it can be found that the present refined Theory is very accurate and obviously superior to the existing 1,2–3 global-local Higher-Order Theory. The most attractive feature of this Theory is that the transverse shear stresses can be accurately predicted from direct use of constitutive equations without any post-processing method. It is also shown that the present quadrilateral element possesses higher accuracy. � 2006 Elsevier Ltd. All rights reserved.
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an efficient higher order Theory and finite element for laminated plates subjected to thermal loading
Composite Structures, 2006Co-Authors: Wu Zhen, Chen WanjiAbstract:In the present paper, the global–local Higher-Order Theory is simply derived, which satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. Moreover, the number of unknowns of this Theory is independent of the layer numbers of the laminate. Based on the global–local Higher-Order Theory, the discrete Kirchhoff element PDKT and refined triangular plate element PRT9 are presented for predicting interlaminar stresses and displacements in laminated plates subjected to thermal loading. The two triangular elements satisfy the interelement C1 continuity conditions. The numerical examples show that the in-plane stresses and transverse shear stresses can be accurately calculated by the direct constitutive equation approach. The equilibrium equation approach is employed to predict transverse normal stresses.
Wanji Chen - One of the best experts on this subject based on the ideXlab platform.
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a model of composite laminated beam based on the global local Theory and new modified couple stress Theory
Composite Structures, 2013Co-Authors: Wanji ChenAbstract:Abstract In this paper, a model of composite laminated beam based on the global–local Theory for new modified couple-stress Theory is developed. For the modified couple-stress Theory, an anisotropic constitutive relation is suggested. There is only one microlength-scale parameter in each ply of the composite laminated beam. The Reddy beam model of global–local Higher-Order Theory proposed by Chen and Wu (2005) [1] , which satisfies free surface conditions and the geometric and stresses continuity conditions at interfaces, and is adopted to formulate this model. On the model of laminated beam of modified couple stress Theory, the transverse shear stress with scale effect is presented for the first time. Numerical results show that the proposed beam model can capture the scale effect at interfaces of the microstructure of the composite laminated beam.
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refined laminated composite plate element based on global local higher order shear deformation Theory
Composite Structures, 2005Co-Authors: Zhen Wu, Ronggeng Chen, Wanji ChenAbstract:Abstract Based on the 1,2-3 double-superposition Theory proposed by Li and Liu [Int. J. Numer. Meth. Eng. 1997;40:1197], a new global–local Higher-Order Theory for angle-ply laminated plates is derived. This Theory fully satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. The number of unknowns of the Higher-Order theories is independent of the layer numbers of the composite laminate. Based on the Higher-Order Theory, a refined four-noded quadrilateral plate element and a refined three-noded triangular element are presented. The interelement C 1 weak-continuity conditions can be satisfied. Numerical results show that in-plane stresses and transverse shear stresses can be accurately computed by the direct constitutive equation approach. In order to obtain transverse normal stresses, the equilibrium equation approach is employed here.
Ren Xiaohui - One of the best experts on this subject based on the ideXlab platform.
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an accurate higher order Theory and c0 finite element for free vibration analysis of laminated composite and sandwich plates
Composite Structures, 2010Co-Authors: Wu Zhen, Chen Wanji, Ren XiaohuiAbstract:Abstract At present, it is difficult to accurately predict natural frequencies of sandwich plates with soft core by using the C 0 plate bending elements. Thus, the C 1 plate bending elements have to be employed to predict accurately dynamic response of such structures. This paper proposes an accurate Higher-Order C 0 Theory which is very different from other published Higher-Order Theory satisfying the interlaminar stress continuity, as the first derivative of transverse displacement has been taken out from the in-plane displacement fields of the present Theory. Therefore, the C 0 interpolation functions is only required during its finite element implementation. Based on the Hamilton’s principle and Navier’s technique, analytical solutions to the natural frequency analysis of simply-supported laminated plates have been presented. To further extend the ranges of application of the proposed Theory, an eight-node C 0 continuous isoparametric element is used to model the proposed Theory. Numerical results show the present C 0 finite element can accurately predict the natural frequencies of sandwich plate with soft core, whereas other global Higher-Order theories are unsuitable for free vibration analysis of such soft-core structures.