Assessment of Shear Deformation Theories for Multilayered Composite Plates

1989 ◽  
Vol 42 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Ahmed K. Noor ◽  
W. Scott Burton
Keyword(s):  
Shear Deformation ◽  
Three Dimensional ◽  
Composite Plates ◽  
Linear Displacement ◽  
Two Dimensional ◽  
Multilayered Composite ◽  
Standard Of Comparison ◽  
Elasticity Solutions ◽  
Shear Deformation Theories ◽  
Three Dimensional Elasticity

A review is made of the different approaches used for modeling multilayered composite plates. Discussion focuses on different approaches for developing two-dimensional shear deformation theories; classification of two-dimensional theories based on introducing plausible displacement, strain and/or stress assumptions in the thickness direction; and first-order shear deformation theories based on linear displacement assumptions in the thickness coordinate. Extensive numerical results are presented showing the effects of variation in the lamination and geometric parameters of simply supported composite plates on the accuracy of the static and vibrational responses predicted by six different modeling approaches (based on two-dimensional shear deformation theories). The standard of comparison is taken to be the exact three-dimensional elasticity solutions. Some of the future directions for research on the modeling of multilayered composite plates are outlined.

Assessment of Computational Models for Multilayered Composite Shells

1990 ◽  
Vol 43 (4) ◽  
pp. 67-97 ◽  
Author(s):  
Ahmed K. Noor ◽  
W. Scott Burton
Keyword(s):  
Shear Deformation ◽  
Strain Energy ◽  
Computational Models ◽  
Three Dimensional ◽  
Linear Displacement ◽  
Two Dimensional ◽  
Composite Shells ◽  
Response Characteristics ◽  
Multilayered Composite ◽  
Shear Deformation Theories

A review is made of the different approaches used for modeling multilayered composite shells. Discussion focuses on different approaches for developing two-dimensional shear deformation theories; classification of two-dimensional theories based on introducing plausible displacement, strain and/or stress assumptions in the thickness direction; first-order shear deformation theories based on linear displacement assumptions in the thickness coordinate; and efficient computational strategies for anisotropic composite shells. Extensive numerical results are presented showing the effects of variation in the lamination and geometric parameters of simply supported composite cylinders on the accuracy of the static and vibrational responses predicted by eight different modeling approaches (based on two-dimensional shear deformation theories). The standard of comparison is taken to be the exact three-dimensional elasticity solutions. The quantities compared include both the gross response characteristics (eg, vibration frequencies and strain energy components); and detailed, through-the-thickness distributions of displacements, stresses, and strain energy densities. Some of the future directions for research on the modeling of multilayered composite shells are outlined.

Three-Dimensional Solutions for Antisymmetrically Laminated Anisotropic Plates

1990 ◽  
Vol 57 (1) ◽  
pp. 182-188 ◽  
Author(s):  
Ahmed K. Noor ◽  
W. Scott Burton
Keyword(s):  
Three Dimensional ◽  
Composite Plates ◽  
Double Fourier Series ◽  
Stress And Strain ◽  
Anisotropic Plates ◽  
Stress Components ◽  
Strain Components ◽  
Elasticity Solutions ◽  
Vibration Problems ◽  
Three Dimensional Elasticity

Analytic three-dimensional elasticity solutions are presented for the stress and free vibration problems of multilayered anisotropic plates. The plates are assumed to have rectangular geometry and antisymmetric lamination with respect to the middle plane. A mixed formulation is used with the fundamental unknowns consisting of the six stress components and the three displacement components of the plate. Each of the plate variables is decomposed into symmetric and antisymmetric components in the thickness direction, and is expressed in terms of a double Fourier series in the Cartesian surface coordinates. Extensive numerical results are presented showing the effects of variation in the lamination and geometric parameters of composite plates on the importance of the transverse stress and strain components.

Three-Dimensional Solutions for the Free Vibrations and Buckling of Thermally Stressed Multilayered Angle-Ply Composite Plates

1992 ◽  
Vol 59 (4) ◽  
pp. 868-877 ◽  
Author(s):  
Ahmed K. Noor ◽  
W. Scott Burton
Keyword(s):  
Three Dimensional ◽  
Composite Plates ◽  
Double Fourier Series ◽  
Free Vibrations ◽  
Thermal Deformations ◽  
Sensitivity Derivatives ◽  
Neumann Type ◽  
Elasticity Solutions ◽  
Three Dimensional Elasticity ◽  
Thermally Stressed

Analytic three-dimensional elasticity solutions are presented for the free vibration and buckling of thermally stressed, multilayered, angle-ply composite plates. Sensitivity derivatives are also evaluated and used to study the sensitivity of the vibration and buckling responses to variations in the different lamination and material parameters of the plate. The plates are assumed to have rectangular geometry and an antisymmetric lamination with respect to the middle plane. The temperature is assumed to be independent of the surface coordinates, but has an arbitrary symmetric variation through the thickness of the plate. A linear, Duhamel-Neumann type constitutive model is used, and the material properties are assumed to be independent of temperature. The thermal plate response is subjected to time-varying perturbation displacements, strains, and stresses. A mixed formulation is used with the fundamental unknowns consisting of the six perturbation stress components and the three perturbation displacement components of the plate. The initial thermal deformations are accounted for. Each of the plate variables is decomposed into symmetric and antisymmetric components in the thickness direction, and is expressed in terms of a double Fourier series in the Cartesian surface coordinates. Numerical results are presented showing the effects of variations in material characteristics and fiber orientation of different layers, as well as the effects of initial thermal deformations on the vibrational and buckling responses of the plate, as well as their sensitivity derivatives.

scholarly journals Three-Dimensional Elasticity Solutions for Isotropic and Generally Anisotropic Bodies

2006 ◽  
Vol 5-6 ◽  
pp. 541-550 ◽  
Author(s):  
J.R. Barber
Keyword(s):  
Exact Solution ◽  
General Solution ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Axial Coordinate ◽  
Similar Strategy ◽  
Anisotropic Bodies ◽  
Elasticity Solutions ◽  
Three Dimensional Elasticity

Classical methods of two-dimensional elasticity can be extended to give an exact solution of the three-dimensional problem for the beam — i.e. a general solution for the pris- matic bar loaded on its lateral surfaces, subject only to the restriction that the tractions can be expanded as power series in the axial coordinate z. A series of sub-problems Pj is defined by successive partial differentiations with respect to z. For isotropic materials, a recursive al- gorithm can be used for generating the solution to Pj+1 from that for Pj in the context of the Papkovich-Neuber solution. For the generally anisotropic material, a similar strategy is proposed, based on partial integrations of Stroh’s formulation of the two-dimensional problem.

Bending Response of Exponentially Graded Plates by a Meshless Method

2013 ◽  
Vol 787 ◽  
pp. 1085-1088
Author(s):  
Ying Tao Chen ◽  
Song Xiang
Keyword(s):  
Basis Function ◽  
Material Properties ◽  
Meshless Method ◽  
Three Dimensional ◽  
Thickness Direction ◽  
Elasticity Solutions ◽  
Shear Deformation Theories ◽  
Three Dimensional Elasticity ◽  
Bending Response ◽  
Exponentially Graded

In the present paper, the higher order shear deformation theories of Touratier and Karama and meshless global collocation method based on the inverse multiquadric radial basis function are used to analyze the bending response of the exponentially graded plates. The material properties of the plates vary exponentially in the thickness direction. The present results are compared with three-dimensional elasticity solutions.

A Variational Approach to Three-Dimensional Elasticity Solutions of Laminated Composite Plates

1992 ◽  
Vol 59 (2S) ◽  
pp. S166-S175 ◽  
Author(s):  
M. Savoia ◽  
J. N. Reddy
Keyword(s):  
Composite Laminates ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Composite Plates ◽  
Approximate Solutions ◽  
Transverse Load ◽  
Rectangular Plates ◽  
Elasticity Solutions ◽  
Three Dimensional Elasticity

The displacements in a laminated composite are represented as products of two sets of unknown functions, one of which is only a function of the thickness coordinate and the other is a function of the in-plane coordinates (i.e., separation of variables approach), and the minimization of the total potential energy is reduced to a sequence of iterative linear problems. Analytical solutions are developed for cross-ply and angle-ply laminated composite rectangular plates. The solution for simply-supported cross-ply plates under sinusoidal transverse load reduces to that of Pagano. Numerical results for stresses and displacements for antisymmetric angle-ply laminates are presented. The three-dimensional elasticity solutions developed are important because they can be used to study the behavior of composite laminates, in addition to serving as reference for approximate solutions by numerical methods and twodimensional theories.

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