Theory and Analysis of Plates, Classical and Numberical Methods

Szilard, Rudolph; Nash, W. A.

doi:10.1115/1.3423469

Cited by 103 publications

(106 citation statements)

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“…ð22Þ Following Navier's solution procedure [2,3,30], the solution to the displacement variables satisfying the above boundary conditions can be expressed in the following forms:…”

Section: Analytical Solutionsmentioning

confidence: 99%

“…To use them efficiently a good understanding of their structural and dynamical behaviour and also an accurate knowledge of the deformation characteristics, stress distribution, natural frequencies and buckling loads under various load conditions are needed. The classical laminate plate theory (CLPT) [1], which is an extension of classical plate theory (CPT) [2,3], neglects the effects of outof-plane strains. The greater differences in elastic properties between fibre filaments and matrix materials lead to a high ratio of in-plane young's modulus to transverse shear modulus for most of the composite laminates developed to date.…”

Section: Introductionmentioning

confidence: 99%

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Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory

Kant

Swaminathan

2002

Composite Structures

315

116

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Analytical formulations and solutions to the static analysis of simply supported composite and sandwich plates hitherto not reported in the literature based on a higher order refined theory developed by the first author and already reported in the literature are presented. The theoretical model presented herein incorporates laminate deformations which account for the effects of transverse shear deformation, transverse normal strain/stress and a nonlinear variation of in-plane displacements with respect to the thickness coordinate -thus modelling the warping of transverse cross-sections more accurately and eliminating the need for shear correction coefficients. In addition, a few higher order theories and the first order theory developed by other investigators and already available in the literature are also considered for the evaluation. The equations of equilibrium are obtained using principle of minimum potential energy (PMPE). Solutions are obtained in closed form using Navier's technique by solving the boundary value problem. The comparison of the present results with the available elasticity solutions and the results computed independently using the first order and the other higher order theories available in the literature shows that this refined theory predicts the transverse displacement and the stresses more accurately than all other theories considered in this paper. After establishing the accuracy of present results for composite and sandwich plates, new results for the stretching-bending coupling behaviour of antisymmetric sandwich laminates using all the theories considered in this paper are presented which will serve as a benchmark for future investigations.

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“…ð22Þ Following Navier's solution procedure [2,3,30], the solution to the displacement variables satisfying the above boundary conditions can be expressed in the following forms:…”

Section: Analytical Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory

Kant

Swaminathan

2002

Composite Structures

315

116

View full text Add to dashboard Cite

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“…Equation (15) can be readily extended to enable the analysis of vibrating plates under the influence of in-plane loads. In this case, the use of D'Alembert's Principle yields where to represents the frequency of free vibration and [M] is the overall consistent mass matrix derived in reference [4].…”

Section: Theorymentioning

confidence: 99%

“…These will be taken as the two nodal lines for the element. Since the displacement function w is a function of u, the continuity requirement across the element boundaries is The total potential energy 7r r of the plate element due to the in-plane forces and transverse loading may be expressed in the form [15] -f Jq(x,y)wcm dx / \ dx dy (2) where N x , N y and N xy represent the in-plane forces, q(x, y) is the transverse load per unit area, h denotes the thickness of the plate and {a}, {e} are respectively the generalized stress and strain vectors defined by…”

Section: Theorymentioning

confidence: 99%

Buckling analysis of plates of arbitrary shape

Bucco

Mazumdar

1984

J. Aust. Math. Soc. Series B, Appl. Math

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A simple and efficient numerical technique for the buckling analysis of thin elastic plates of arbitrary shape is proposed. The approach is based upon the combination of the standard Finite Element Method with the constant deflection contour method. Several representative plate problems of irregular boundaries are treated and where possible, the obtained results are validated against corresponding results in the literature.

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“…3 has been solved by Szilard [12] and Melnikov [13]. The concentrated load is set at the center of the plate in the Szilard's solution.…”

Section: Illustrative Examples Casementioning

confidence: 99%

An Analytical Approach for the Green's Functions of Biharmonic Problems with Circular and Annular Domains

2009

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In this paper, an analytical approach for deriving the Green's function of circular and annular plate was presented. Null-field integral equations were employed to solve the plate problems while kernel functions were expanded to degenerate kernels. The unknown boundary data of the displacement, slope, normal moment and effective shear force were expressed in terms of Fourier series. It was noticed that all the improper integrals were avoided when the degenerate kernels were used. After determining the unknown Fourier coefficients, the displacement, slope, normal moment and effective shear force of the plate could be obtained by using the boundary integral equations. The present approach was seen as an "analytical" approach for a series solution. Finally, several analytical solutions were obtained. To see the validity of the present method, FEM solutions using ABAQUS were compared well with our analytical solutions. The displacement, radial moment and shear variations of radial and angular positions were presented.

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Theory and Analysis of Plates, Classical and Numberical Methods

Cited by 103 publications

References 0 publications

Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory

Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory

Buckling analysis of plates of arbitrary shape

An Analytical Approach for the Green's Functions of Biharmonic Problems with Circular and Annular Domains

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