Shear Deformation in Heterogeneous Anisotropic Plates

1970 ◽  
Vol 37 (4) ◽  
pp. 1031-1036 ◽  
Author(s):  
J. M. Whitney ◽  
N. J. Pagano
Keyword(s):  
Shear Deformation ◽  
Plate Theory ◽  
Flexural Vibration ◽  
Laminated Plates ◽  
Transverse Load ◽  
Laminated Plate ◽  
Anisotropic Plates ◽  
Reinforced Composite ◽  
Classical Elasticity Theory ◽  
Good Agreement

A bending theory for anisotropic laminated plates developed by Yang, Norris, and Stavsky is investigated. The theory includes shear deformation and rotary inertia in the same manner as Mindlin’s theory for isotropic homogeneous plates. The governing equations reveal that unsymmetrically laminated plates display the same bending-extensional coupling phenomenon found in classical laminated plate theory based on the Kirchhoff assumptions. Solutions are presented for bending under transverse load and for flexural vibration frequencies of symmetric and nonsymmetric lamninates. Good agreement is observed in numerical results for plate bending as compared to exact solutions obtained from classical elasticity theory. For certain fiber-reinforced composite materials, radical departure from classical laminated plate theory is indicated.

A Composite Plate Theory for Arbitrary Laminate Configurations

1987 ◽  
Vol 54 (1) ◽  
pp. 181-189 ◽  
Author(s):  
A. Toledano ◽  
H. Murakami
Keyword(s):  
Composite Plate ◽  
Plate Theory ◽  
Piecewise Linear ◽  
Present Theory ◽  
Laminated Plates ◽  
Stress Distributions ◽  
Laminated Plate ◽  
Individual Layer ◽  
Mixed Variational Principle ◽  
Shear Deformable

In order to improve the accuracy of in-plane responses of shear deformable composite plate theories, a new laminated plate theory was developed for arbitrary laminate configurations based upon Reissner’s (1984) new mixed variational principle. To this end, across each individual layer, piecewise linear continuous displacements and quadratic transverse shear stress distributions were assumed. The accuracy of the present theory was examined by applying it to the cylindrical bending problem of laminated plates which had been solved exactly by Pagano (1969). A comparison with the exact solutions obtained for symmetric, antisymmetric, and arbitrary laminates indicates that the present theory accurately estimates in-plane responses, even for small span-to-thickness ratios.

Enhanced First-Order Shear Deformation Theory for Laminated and Sandwich Plates

2005 ◽  
Vol 72 (6) ◽  
pp. 809-817 ◽  
Author(s):  
Jun-Sik Kim ◽  
Maenghyo Cho
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Plate Theory ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Laminated Plates ◽  
Sandwich Plates ◽  
First Order ◽  
Transverse Shear Strains

A new first-order shear deformation theory (FSDT) has been developed and verified for laminated plates and sandwich plates. Based on the definition of Reissener–Mindlin’s plate theory, the average transverse shear strains, which are constant through the thickness, are improved to vary through the thickness. It is assumed that the displacement and in-plane strain fields of FSDT can approximate, in an average sense, those of three-dimensional theory. Relationship between FSDT and three-dimensional theory has been systematically established in the averaged least-square sense. This relationship provides the closed-form recovering relations for three-dimensional variables expressed in terms of FSDT variables as well as the improved transverse shear strains. This paper makes two main contributions. First an enhanced first-order shear deformation theory (EFSDT) has been developed using an available higher-order plate theory. Second, it is shown that the displacement fields of any higher-order plate theories can be recovered by EFSDT variables. The present approach is applied to an efficient higher-order plate theory. Comparisons of deflection and stresses of the laminated plates and sandwich plates using present theory are made with the original FSDT and three-dimensional exact solutions.

Studies Regarding the Shear Correction Factor in the Mindlin Plate Theory for Sandwich Plates

2017 ◽  
Vol 21 ◽  
pp. 301-308 ◽  
Author(s):  
Mihai Vrabie ◽  
Radu Chiriac ◽  
Sergiu Andrei Băetu
Keyword(s):  
Shear Deformation ◽  
Correction Factor ◽  
Plate Theory ◽  
Plate Thickness ◽  
Shear Stiffness ◽  
Laminated Plates ◽  
Mindlin Plate ◽  
Sandwich Plates ◽  
Shear Correction Factor ◽  
Mindlin Plate Theory

The displacement field from the first-order shear deformation plate theory (FSDT) extents the cinematic aspect of the classical theory of laminated plates (CLPT), including a transverse shear deformation, considered constant on the plate thickness. In order to correct this aspect, in FSDT (named also the Mindlin plate theory) a coefficient Ks was inserted, named shear correction factor, used as a multiplier in the shear stiffness equation of the plate. In this paper are presented the most popular methods for determination of the shear correction factor, identifying the differences between them. To emphasize the influence of the shear correction factor on the stress response, a numerical parametric study was done on some sandwich plates filled with polyurethane foam. The processing of the obtained results allow drawing some conclusions useful in the designing of this type of sandwich plates.

The Effects of Shear Deformation and Rotary Inertia on the Lateral Frequencies of Cantilever Beams in Bending

1972 ◽  
Vol 94 (1) ◽  
pp. 267-278 ◽  
Author(s):  
W. Carnegie ◽  
J. Thomas
Keyword(s):  
Finite Difference ◽  
Shear Deformation ◽  
Matrix Equation ◽  
Equations Of Motion ◽  
Flexural Vibration ◽  
Experimental Results ◽  
Rotary Inertia ◽  
Cantilever Beams ◽  
Algebraic Equations ◽  
Good Agreement

This paper deals with the effect of shear deformation and rotary inertia on the frequencies of flexural vibration of pre-twisted and non-pre-twisted uniform and tapered cantilever beams. The equations of motion are derived and transformed into a set of linear simultaneous algebraic equations by using finite-difference solutions for the derivatives. The resulting eigenvalue matrix equation is solved for the frequency parameters by a QR transformation. The effects of various tapers, depth-to-length ratios and pre-twist angles on the frequencies of vibration are investigated for the first five modes. Results obtained are compared with those presented by other investigators where available and show good agreement. The experimental results presented also show good agreement with the corresponding theoretical values.

A Parametric Study on Natural Frequency of Sandwich Panel Using Refined Shear Model

2002 ◽  
Author(s):  
Qunli Liu ◽  
Yi Zhao
Keyword(s):  
Shear Deformation ◽  
Natural Frequency ◽  
Deformation Theory ◽  
Sandwich Panel ◽  
Plate Theory ◽  
Shear Deformation Theory ◽  
Nonlinear Behavior ◽  
Flexural Vibration ◽  
Element Analysis ◽  
Theoretical Predictions

The natural frequency of a thick rectangular sandwich panel was studied using refined shear deformation theory. Both faceshheets and core materials are orthotropic. Nonlinear behavior of shear deformation of sandwich panel was described by a proposed polynomial function. The effect of transverse shear modulus of sandwich core on flexural vibration of the panel was investigated. Comparison was made among the classical thin plate theory, low order shear deformation theory and high order refined shear theory. Results from finite element analysis were also provided to verify the theoretical predictions.

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