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.

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.

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.

Three-Dimensional Elasticity Solution of a Composite Beam

1967 ◽  
Vol 1 (2) ◽  
pp. 122-135 ◽  
Author(s):  
Staley F. Adams ◽  
M. Maiti ◽  
Richard E. Mark
Keyword(s):  
Three Dimensional ◽  
Solid Wood ◽  
Theory Of Elasticity ◽  
Orthotropic Materials ◽  
Stress And Strain ◽  
Cantilever Beams ◽  
Dimensional Theory ◽  
Reinforced Plastics ◽  
Three Dimensional Elasticity ◽  
Moduli Of Elasticity

This investigation was undertaken to develop a rigorous mathe matical solution of stress and strain for a composite pole con sisting of a reinforced plastics jacket laminated on a solid wood core. The wood and plastics are treated as orthotropic materials. The problem of bending of such poles as cantilever beams has been determined by the application of the principles of three- dimensional theory of elasticity. Values of all components of the stress tensor in cylindrical coordinates are given for the core and jacket. Exact values for the stresses have been obtained from computer results, using the basic elastic constants—Poisson's ratios, moduli of elasticity and moduli of rigidity—for each ma terial. A comparison of the numerical results of the exact solu tion with strength of materials solutions has been completed.

Three-Dimensional Plate Theory for Flexible Multibody Dynamics

2015 ◽  
Author(s):  
Shilei Han ◽  
Olivier A. Bauchau
Keyword(s):  
Plate Theory ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Flexible Multibody Dynamics ◽  
Composite Plates ◽  
Complex Stress ◽  
Mindlin Plate ◽  
Stress States ◽  
Three Dimensional Elasticity ◽  
Material Line

In structural analysis, many components are approximated as plates. More often that not, classical plate theories, such as Kirchhoff or Reissner-Mindlin plate theories, form the basis of the analytical developments. The advantage of these approaches is that they leads to simple kinematic descriptions of the problem: the plate’s normal material line is assumed to remain straight and its displacement field is fully defined by three displacement and two rotation components. While such approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. For instance, it is well known from three-dimensional elasticity theory that the normal material line will warp under load for laminated composite plates, leading to three-dimensional deformations that generate complex stress states. To overcome this problem, several high-order, refined plate theories have been proposed. While these approaches work well for some cases, they often lead to inefficient formulations because they introduce numerous additional variables. This paper presents a different approach to the problem: based on a finite element semi-discretization of the normal material line, plate equations are derived from three-dimensional elasticity using a rigorous dimensional reduction procedure.

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