An accurate, simple theory of the statics and dynamics of elastic plates

Levinson, M.

doi:10.1016/0093-6413(80)90049-x

Cited by 571 publications

(172 citation statements)

References 4 publications

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“…They include Kirchhoff theory, Mindlin [6] theory, Reissner [7] theory, Shimpi [8] refined theory, Reddy [9] theory, Levinson [10] theory, Osadebe [11] plate model, etc. Kirchhoff plate theory, also called the classical small deflection theory of thin plates is the simplest and most commonly used theory of plates.…”

Section: Plate Theories and Modelsmentioning

confidence: 99%

Theory of Elasticity Formulation of the Mindlin Plate Equations

Nwoji¹,

C.U.²,

H.N³

et al. 2017

IJET

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Abstract-In this work, the mathematical theory of elasticity has been used to formulate and derive from fundamental principles, the first order shear deformation theory originally presented by Mindlin using variational calculus. A relaxation of the Kirchhoff's normality hypothesis was used to account for the effect of the transverse shear strains in the behaviour of the plate. This made the resulting theory appropriate for use for moderately thick plates. A simultaneous use of the strain-displacement relations for small-deformation elasticity, stress-strain laws and the stress differential equations of equilibrium was used to obtain the differential equations of static flexure for Mindlin plates in terms of three unknown generalised displacements. The equations were found to be coupled in the unknown displacements; but reducible to the Kirchhoff plate equations when the removed Kirchhoff normality hypothesis was introduced. This showed the Kirchhoff plate theory to be a specialization of the Mindlin plate theory. The theory of elasticity foundations of the Mindlin and Kirchhoff plate theories are thus highlighted.

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Section: Plate Theories and Modelsmentioning

confidence: 99%

Theory of Elasticity Formulation of the Mindlin Plate Equations

Nwoji¹,

C.U.²,

H.N³

et al. 2017

IJET

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“…Yildirim and Kiral [16] have presented that the effects of inter laminar shear stress need to be taken into account in the study of laminated beams due to their low inter laminar shear modulus. Levinsion [17] has developed High order shear theories and compared with the First Order Shear Deformation Laminate Theory. Murthy [18] has given a improved model of transverse shear deformation theory for laminated anisotropic plates.…”

Section: Literature Reviewmentioning

confidence: 99%

Effect of Fiber Orientation and Position of Circular Hole on Torsional Natural Frequency of Laminated Composite Beam

Padhi¹

2018

IJRASET

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The composite materials are well known by their excellent combination of high structural stiffness and low weight. The main feature of these anisotropic materials is their ability to be tailored for specific applications by optimizing design parameters such as stacking sequence, ply orientation and performance targets. Finding free torsional vibrations characteristics of laminated composite beams is one of the bases for designing and modeling of industrial products. With these requirements, this work considers the free torsional vibrations for laminated composite beams of doubly symmetrical cross sections. The torsional vibrations of the laminated beams are analyzed analytically based on the classical lamination theory, and accounts for the coupling of flexural and torsional modes due to fiber orientation of the laminated beams are neglected. Also, the torsional vibrations of the laminated beams analyzed by shear deformation theory in which the shear deformation effects are considered. Numerical analysis has been carried out using finite element method (FEM). The finite element software package ANSYS 13.0 is used to perform the numerical analyses using an eight-node layered shell element to describe the torsional vibration of the laminated beams. The rotary inertia and shear deformation effects of the element are taken. The influence of fiber directions and stacking sequences of laminates on torsional natural frequencies were investigated. Also, the effects of boundary conditions are demonstrated. Numerical results, obtained by the ANSYS 13.0, classical lamination theory, and shear deformation theory are presented to highlight the effects of fibers orientation and layers stacking sequence on torsional frequencies of the beams. The results obtained by ANSYS are compared against the classical lamination theory, as well as shear deformation theory.

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“…Several other theories have been proposed to describe the behaviour of plates under loads. They include -Reissner's sixth order plate theory [8], [9] for moderately thin plates; Von Karman plate theory for plates under large deformation; Mindlin plate theory for moderately thick plates, shear deformation plate theories [10,11,12]. The focus of this paper is the Kirchhoff plate theory.…”

Section: Introductionmentioning

confidence: 99%