Analytical solutions for vibrations of laminated and sandwich plates using mixed theory

Rao, M. Kameswara; Desai, Yogesh M.

doi:10.1016/s0263-8223(03)00185-5

Cited by 128 publications

(65 citation statements)

References 20 publications

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“…Nevertheless, the computational cost increases with the number of numerical layers. For recent studies, the reader can also refer to [Icardi 2001;Rao and Desai 2004;Gherlone and di Sciuva 2007].…”

Section: (Mixed)mentioning

confidence: 99%

“…In this family, some studies take into account transverse normal deformation. A nonconstant polynomial expression for the out-of-plane displacement is considered in [Kant et al 1997;Cook and Tessler 1998;Barut et al 2001;Kant and Swaminathan 2002;Matsunaga 2002;Rao and Desai 2004;Subramanian 2006;Swaminathan and Patil 2007] with a higher-order theory. Specific functions such as the exponential are also used [Soldatos and Watson 1997;Liu and Soldatos 2002].…”

Section: Introductionmentioning

confidence: 99%

“…A mixed formulation also exists [Mau 1973;Murakami 1986]. Again, some models taking into account the transverse normal effect have been developed: [Icardi 2001;Pai and Palazotto 2001] within a displacement based approach and [Carrera 1999;2000b;2004;Rao and Desai 2004] within a mixed formulation. For the thermomechanical analysis, readers can refer to [Robaldo 2006] (displacement) and [Carrera 2000a;Gherlone and di Sciuva 2007] …”

Section: Introductionmentioning

confidence: 99%

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A refined sine-based finite element with transverse normal deformation for the analysis of laminated beams under thermomechanical loads

Vidal¹,

Polit²

2009

JOMMS

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In the framework of a sine model family, two new three-node beam finite elements including the transverse normal effect are designed for the analysis of laminated beams. They are based on a sine distribution with layer refinement and a second-order expansion for the deflection. The transverse shear strain is obtained using a cosine function, avoiding the use of shear correction factors. This kinematics accounts for the interlaminar continuity conditions on the interfaces between layers, and the boundary conditions on the upper and lower surfaces of the beam. A conforming FE approach is carried out using Lagrange and Hermite interpolations. It is important to notice that the number of unknowns is independent of the number of layers.Both mechanical and thermomechanical tests for thin and thick beams are presented in order to evaluate the capability of these new finite elements to give accurate results with respect to elasticity or finite element reference solutions. Both convergence velocity and accuracy are discussed and this new finite element yields very satisfactory results at a low computational cost. In particular, the transverse stress computed from the constitutive relation is well estimated with regards to classical equivalent single layer models. This work focuses on the necessity to take into account the transverse normal stress, especially for thick beam and coupled analysis.

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Section: (Mixed)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A refined sine-based finite element with transverse normal deformation for the analysis of laminated beams under thermomechanical loads

Vidal¹,

Polit²

2009

JOMMS

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“…Lin et al [4] performed the vibration analysis of angleply laminated composite plates with an embedded piezoceramic layer. A semi-analytical method has been used by the Rao and Desai [14] to evaluate the natural frequencies as well as displacement and stress eigenvectors for simply supported, cross-ply laminated and sandwich plates by using higher order mixed theory. Patel et al [15] was used the finite element method for analyzing the free vibration of laminated anisotropic composite conical cylindrical shell structures.…”

Section: Introductionmentioning

confidence: 99%

Prediction of Natural Frequency of Laminated Composite Plates Using Artificial Neural Networks

Mutra¹,

Reddy²,

Reddy³

et al. 2012

ENG

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The paper is focused on the application of artificial neural networks (ANN) in predicting the natural frequency of laminated composite plates under clamped boundary condition. For training and testing of the ANN model, a number of finite element analyses have been carried out using D-optimal design in the design of experiments (DOE) by varying the fibre orientations, -45˚, 0˚, 45˚ and 90˚. The composite plate is modeled using linear layered structural shell element. The natural frequencies were found by analyses which were done by finite element (FE) analysis software. The ANN model has been developed using multilayer perceptron (MLP) back propagation algorithm. The adequacy of the developed model is verified by coefficient of determination (R). It was found that the R 2 (R: coefficient of determination) values are 1 and 0.998 for train and test data respectively. The results showed that, the training algorithm of back propagation was sufficient enough in predicting the natural frequency of laminated composite plates. To judge the ability and efficiency of the developed ANN model, absolute relative error has been used. The results predicted by ANN are in very good agreement with the finite element (FE) results. Consequently, the D-optimal design and ANN are shown to be effective in predicting the natural frequency of laminated composite plates.

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“…Nevertheless, the computational cost increases with the number of numerical layers. For recent studies, the reader can also refer to [12,23,24].…”

Section: Introductionmentioning

confidence: 99%

A Refined Sine Finite Element with Transverse Normal Stress for Thermoelastic Analysis of Laminated Composite in Cylindrical Bending

Vidal¹,

Polit²

2011

Journal of Thermal Stresses

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Analytical solutions for vibrations of laminated and sandwich plates using mixed theory

Cited by 128 publications

References 20 publications

A refined sine-based finite element with transverse normal deformation for the analysis of laminated beams under thermomechanical loads

A refined sine-based finite element with transverse normal deformation for the analysis of laminated beams under thermomechanical loads

Prediction of Natural Frequency of Laminated Composite Plates Using Artificial Neural Networks

A Refined Sine Finite Element with Transverse Normal Stress for Thermoelastic Analysis of Laminated Composite in Cylindrical Bending

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