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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.
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.
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.
S. Kapuria - One of the best experts on this subject based on the ideXlab platform.
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third Order Theory based quadrilateral element for delaminated composite plates with a hybrid method for satisfying continuity at delamination fronts
Composite Structures, 2017Co-Authors: Adnan Ahmed, S. KapuriaAbstract:Abstract We present a four-node quadrilateral element based on the third Order Theory for analysis of composite plates with multiple delaminations, by employing a novel hybrid method for satisfying the continuity conditions at the delaminated fronts. In this method, the continuity of inplane displacement variables is satisfied by directly satisfying them at the midplanes of the sublaminates separated by delaminations, and employing the least squares method with respect to the shear rotation variables. The element is shown to yield very good accuracy in general, in comparison with experimental and three dimensional finite element (FE) solutions, and yield superior results to the other available analytical and FE solutions for static and free vibration responses of delaminated composite beams, and rectangular and skew composite plates under different boundary conditions. It is seen that the results from the existing continuity methods can have large error for thick beams/plates and for higher vibration modes, while the proposed hybrid method is generally very accurate and much superior to the existing methods.
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a quadrilateral shallow shell element based on the third Order Theory for functionally graded plates and shells and the inaccuracy of rule of mixtures
European Journal of Mechanics A-solids, 2015Co-Authors: S. Kapuria, Mayank Patni, Yaqoob M YasinAbstract:Abstract A four-node quadrilateral element is developed for the dynamic analysis of doubly curved functionally graded material (FGM) shallow shells, using the refined third Order Theory. Two micromechanics models, the Voigt's rule of mixtures (ROM) and the Mori–Tanaka model, are considered for computing the effective material properties at a point. The accuracy of the element is examined by comparing with various three dimensional elasticity and two dimensional (2D) analytical and finite element solutions available in the literature for static and free vibration responses of FGM plates and shells. It is shown that the present element, with the least number of degrees of freedom, achieves similar or better accuracy compared to other available 2D finite elements some of which are even based on higher Order theories. Using this element, we also make a systematic assessment of the accuracy of the widely used ROM in predicting the behavior of FGM structures, for different values of the inhomogeneity parameter, and different geometrical parameters, boundary conditions, and material combinations. It is revealed that there can be very significant error in the deflection, stresses and natural frequencies predicted by the ROM, depending primarily on the inhomogeneity parameter and the difference in the material properties of the constituents.
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A new discrete Kirchhoff quadrilateral element based on the third-Order Theory for composite plates
Computational Mechanics, 2007Co-Authors: S. D. Kulkarni, S. KapuriaAbstract:A new discrete Kirchhoff quadrilateral element based on the refined third-Order Theory is developed for the analysis of composite plates. The element has seven degrees of freedom per node, namely, the three displacements, two rotations and two transverse shear strain components at the mid-surface. The inplane displacements and the shear strains are interpolated using bilinear interpolation functions and the mid-surface rotations are interpolated using bi-quadratic functions based on the discrete Kirchhoff technique. The element stiffness matrix and the consistent load vector are developed using the principle of virtual work. The finite element formulation is validated by comparing the results for simply-supported plate with the analytical Navier solution. Comparison of the present results with those using other available elements based on the TOT establishes the superiority of the present element in respect of simplicity, accuracy and computational efficiency. The element is free from shear locking
M Ganapathi - One of the best experts on this subject based on the ideXlab platform.
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panel flutter characteristics of sandwich plates with cnt reinforced facesheets using an accurate higher Order Theory
Journal of Fluids and Structures, 2014Co-Authors: A Sankar, Sundararajan Natarajan, Mohamed Haboussi, K Ramajeyathilagam, M GanapathiAbstract:Abstract In this paper, the flutter characteristics of sandwich panels with carbon nanotube (CNT) reinforced face sheets are investigated using QUAD-8 shear flexible element developed based on higher-Order structural Theory. The formulation accounts for the realistic variation of the displacements through the thickness, the possible discontinuity in the slope at the interface, and the thickness stretch affecting the transverse deflection. The in-plane and rotary inertia terms are also included in the formulation. The first-Order high Mach number approximation to linear potential flow Theory is employed for evaluating the aerodynamic pressure. The solutions of the complex eigenvalue problem, developed based on Lagrange׳s equation of motion are obtained using the standard method for finding the eigenvalues. The accuracy of the present formulation is demonstrated considering the problems for which solutions are available. A detailed numerical study is carried out to bring out the efficacy of the higher-Order model over the first-Order Theory and also to examine the influence of the volume fraction of the CNT, core-to-face sheet thickness, the plate thickness and the aspect ratio, damping and the temperature on the flutter boundaries and the associated vibration modes.
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dynamic analysis of laminated cross ply composite non circular thick cylindrical shells using higher Order Theory
International Journal of Solids and Structures, 2002Co-Authors: M Ganapathi, B P Patel, D S PawargiAbstract:Abstract Here, the dynamic analysis of laminated cross-ply composite non-circular thick cylindrical shells subjected to thermal/mechanical load is carried out based on higher-Order Theory. The formulation accounts for the variation of the in-plane and transverse displacements through the thickness, abrupt discontinuity in slope of the in-plane displacements at the interfaces, and includes in-plane, rotary inertia terms, and also the inertia contributions due to the coupling between the different Order displacement terms. The strain–displacement relations are accurately accounted for in the formulation. The shell responses are obtained employing finite element approach in conjunction with direct time integration technique. A detailed parametric study is carried out to bring out the effects of length and thickness ratios, eccentricity parameters and number of layers on the thermal/mechanical response characteristics of non-circular shells.
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hygrothermal effects on the structural behaviour of thick composite laminates using higher Order Theory
Composite Structures, 2002Co-Authors: B P Patel, M Ganapathi, D P MakhechaAbstract:Here, static and dynamic characteristics of thick composite laminates exposed to hygrothermal environment are studied using a realistic higher-Order Theory developed recently. The formulation accounts for the nonlinear variation of the in-plane and transverse displacements through the thickness, and abrupt discontinuity in slope of the in-plane displacements at any interface. The analysis is carried out employing a C 0 QUAD-8 isoparametric higher-Order finite element. It is shown that the shear deformation Theory without accounting for the thickness-stretching effect and slope discontinuity in the in-plane displacements may not be adequate for the analysis of fairly thick composite laminates exposed to hygrothermal loading. The significance of retaining various higher-Order terms in the present model, in evaluating the deflection, buckling and natural frequency for composite laminates at different moisture concentration and temperature, is brought out through parametric study. 2002 Elsevier Science Ltd. All rights reserved.
