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 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.

A Novel Finite-Element– Numerical-Integration Model for Composite Laminates Supported on Opposite Edges

2007 ◽  
Vol 74 (6) ◽  
pp. 1114-1124 ◽  
Author(s):  
Tarun Kant ◽  
Sandeep S. Pendhari ◽  
Yogesh M. Desai
Keyword(s):  
Finite Element ◽  
Differential Equations ◽  
Composite Laminates ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Composite Plates ◽  
Coupled System ◽  
Integration Model ◽  
Numerical Integrators ◽  
Support Conditions

An attempt is made here to devise a new methodology for an integrated stress analysis of laminated composite plates wherein both in-plane and transverse stresses are evaluated simultaneously. The method is based on the governing three-dimensional (3D) partial differential equations (PDEs) of elasticity. A systematic procedure is developed for a case when one of the two in-plane dimensions of the laminate is considered infinitely long (y direction) with no changes in loading and boundary conditions in that direction. The laminate could then be considered in a two-dimensional (2D) state of plane strain in x-z plane. It is here that the governing 2D PDEs are transformed into a coupled system of first-order ordinary differential equations (ODEs) in transverse z direction by introducing partial discretization in the finite inplane direction x. The mathematical model thus reduces to solution of a boundary value problem (BVP) in the transverse z direction in ODEs. This BVP is then transformed into a set of initial value problems (IVPs) so as to use the available efficient and effective numerical integrators for them. Through thickness displacement and stress fields at the finite element discrete nodes are observed to be in excellent agreement with the elasticity solution. A few new results for cross-ply laminates under clamped support conditions are also presented for future reference and also to show the generality of the formulation.

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.

3D Riveting Process Simulation of Laminated Composites

2007 ◽  
Vol 334-335 ◽  
pp. 405-408 ◽  
Author(s):  
Seung Jo Kim ◽  
Seung Hoon Paik ◽  
Kuk Hyun Ji ◽  
Tae Ho Yoon
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Composite Laminates ◽  
Three Dimensional ◽  
Compressive Load ◽  
Laminated Composite ◽  
Composite Plates ◽  
Element Model ◽  
Interference Fit ◽  
Riveting Process

Laminated composite plates have lower interlaminar strength making it difficult to apply interference-fit rivet joining. In this paper, a three-dimensional finite element model has been developed in order to simulate the riveting process on composite plates. The finite element model is based on continuum elements and accounts for some important mechanisms involved in a whole riveting process. The stresses around the rivet hole and the deformed shapes of the rivet are presented together with the effects of the interference fit and the geometry of the washer when the rivet joints are subjected to the compressive load. The numerical results show the applicability of an interference-fit riveting in composite laminates.

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.

Dynamic instability of laminated composite rectangular plates subjected to non-uniform harmonic in-plane edge loading

2000 ◽  
Vol 214 (5) ◽  
pp. 295-312 ◽  
Author(s):  
S K Sahu ◽  
P K Datta
Keyword(s):  
Shear Deformation ◽  
Composite Laminates ◽  
Dynamic Instability ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Geometrical Parameters ◽  
Rectangular Plates ◽  
Element Analysis ◽  
Instability Regions

The dynamic instability behaviour of isotropic, cross-ply and angle-ply laminated composite plates under combined uniaxial and harmonically varying in-plane point or patch loads is investigated using finite element analysis. The first-order shear deformation theory is used to model the composite laminates, considering the effects of transverse shear deformation and rotary inertia. The effects of various geometrical parameters, boundary conditions, lamination and load parameters on the principal dynamic instability regions of composite plates are studied in detail. The preferential orientations depending on the instability regions for simply supported patch and point loaded plates have been suggested for angle-ply plates. The dynamic instability region has been influenced by the restraint provided at the edges.

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.

Three-dimensional multi-patch isogeometric analysis of composite laminates with a discontinuous Galerkin approach

2020 ◽  
pp. 147509022092573
Author(s):  
M Amin Obohat ◽  
Ehsan Tahvilian ◽  
M Erden Yildizdag ◽  
Ahmet Ergin
Keyword(s):  
Discontinuous Galerkin ◽  
Composite Laminates ◽  
Isogeometric Analysis ◽  
Numerical Models ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Point Of View ◽  
B Spline ◽  
Elasticity Solutions ◽  
Three Dimensional Elasticity

In this study, a three-dimensional discontinuous Galerkin isogeometric analysis framework is presented for the analysis of composite laminates. Non-uniform rational B-splines are employed as basis functions for both geometric and computational implementations. From a practical point of view, modeling with multiple non-uniform rational B-spline patches is required in many different applications due to the complexity of computational domains. Then, a special numerical technique is necessary to couple different non-uniform rational B-spline patches to carry out the isogeometric analysis. In this study, therefore, one of the discontinuous Galerkin methods, namely, symmetric interior penalty Galerkin formulation is utilized to deal with multi-patch isogeometric analysis applications. In order to show the applicability of the proposed framework, composite laminates under sinusoidally distributed load with different stacking sequences are studied in the numerical examples. The predicted results are compared with those obtained by the three-dimensional elasticity solutions and various numerical models available in the literature.

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