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.

Laminated Composite Plate Theory With Improved In-Plane Responses

1986 ◽  
Vol 53 (3) ◽  
pp. 661-666 ◽  
Author(s):  
H. Murakami
Keyword(s):  
Variational Principle ◽  
Composite Plate ◽  
Plate Theory ◽  
Laminated Composite ◽  
Laminated Plates ◽  
Thickness Variation ◽  
Laminated Plate ◽  
Laminated Composite Plate ◽  
Cylindrical Bending ◽  
Shear Deformable

In order to improve the accuracy of the in-plane response of the shear, deformable laminated composite plate theory, a new laminated plate theory has been developed based upon a new variational principle proposed by Reissner (1984). The improvement is achieved by including a zigzag-shaped C0 function to approximate the thickness variation of in-plane displacements. The accuracy of this theory is examined by applying it to a problem of cylindrical bending of laminated plates which has been solved exactly by Pagano (1969). The comparison of the in-plane response with the exact solutions for symmetric three-ply and five-ply layers has demonstrated that the new theory predicts the in-plane response very accurately even for small span-to-depth ratios.

The Bending of Symmetrical Laminated Composite Plate Based on Symplectic Method

2011 ◽  
Vol 328-330 ◽  
pp. 1646-1649
Author(s):  
Y.Z. Yang
Keyword(s):  
Composite Plate ◽  
Separation Of Variables ◽  
Laminated Composite ◽  
Transcendental Equation ◽  
Laminated Plates ◽  
Symplectic Space ◽  
Variation Principle ◽  
Symplectic Method ◽  
Stress Distributions ◽  
Dual Variables

This paper applies a symplectic method to study analytically the stress distributions of Composite laminated plates. Using variation principle and introducing separation of variables, dual equations were presented. Then in the symplectic space which consists of the original variables and their dual variables,the problem can be solved via effective mathematical physics methods such as the method of sepatation of variables and eigenfunction vector expansion. The transcendental equation and eigen-vector are deduced. The results of cross-ply and angle-ply laminated graphite–epoxy composite plate are shown, which is compared with established results. The parameters’ influences on mechanical property are also discussed.

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.

Non-linear bending of shear deformable laminated plates under lateral pressure and thermal loading and resting on elastic foundations

2000 ◽  
Vol 35 (2) ◽  
pp. 93-103 ◽  
Author(s):  
Hui-Shen Shen
Keyword(s):  
Thermal Loading ◽  
Lateral Pressure ◽  
Plate Theory ◽  
Perturbation Technique ◽  
Laminated Plates ◽  
Graphical Form ◽  
Elastic Foundations ◽  
Non Linear ◽  
Shear Deformable ◽  
Two Parameter

A non-linear bending analysis is presented for a simply supported shear deformable composite laminated plate subjected to a combined uniform lateral pressure and thermal loading and resting on a two-parameter (Pasternak-type) elastic foundation. The formulations are based on Reddy's higher-order shear deformation plate theory, including the plate-foundation interaction and thermal effects. The analysis uses a mixed Galerkin-perturbation technique to determine the load-deflection curves and load-bending moment curves. Numerical examples are presented that relate to the performances of antisymmetric angleply and symmetric cross-ply laminated plates subjected to thermomechanical loading and resting on two-parameter elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The influences due to a number of effects e.g. foundation stiffness, plate aspect ratio, total number of plies, fibre orientation and initial thermal bending stress, are studied. Typical results are presented in a dimensionless graphical form.

Investigation on Nonlinear Trends of Composite Laminated Plate

2012 ◽  
Author(s):  
Wei Zhang ◽  
Jianen Chen ◽  
Qian Wang ◽  
Min Sun
Keyword(s):  
Multiple Scales ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Laminated Plates ◽  
Laminated Plate ◽  
Response Curves ◽  
Composite Laminated Plate ◽  
Nonlinear Trend ◽  
Nonlinear Trends

The nonlinear trends of composite laminated plates are investigated. The governing equations of motion for the plate are derived with the von Karman strain-displacement relations for the geometric nonlinearity and the Reddy’s third-order shear deformation plate theory. The four dimensional nonlinear averaged equations with the case of 1/2-subharmonic resonance and principal parametric resonance for the first mode and primary resonance for the second mode are obtained by applying the method of multiple scales. The frequency-response curves are analyzed under consideration of strongly coupled of two modes. The influences of the coefficients in dynamic equations and the detuning parameters on the nonlinear trend are studied, and the results indicate that the composite laminated plate may have different trends of nonlinearity under aforementioned resonance conditions. The sweep experiment is conducted to find the softening and hardening nonlinearity. The different trends are obtained when the excitation amplitude is 1.2g. The spectrums of the different stages of the test show that the change of the nonlinear trend may be caused from the sub-harmonic resonance in this test.

Sound Radiation From Shear Deformable Stiffened Laminated Plates With Multiple Compliant Layers

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Xiongtao Cao ◽  
Hongxing Hua
Keyword(s):  
High Frequency ◽  
Sound Pressure ◽  
Plate Theory ◽  
Sound Radiation ◽  
Laminated Plates ◽  
Far Field ◽  
Frequency Range ◽  
First Order ◽  
Shear Deformable ◽  
Field Sound

Sound radiation from shear deformable stiffened laminated plates with multiple compliant layers is theoretically studied. Equations of motion for the composite laminated plates are on the basis of the first-order shear deformation plate theory, and the transfer matrix method is used to describe sound transmission through compliant layers. The first and second sets of stiffeners interact with the plate through normal line forces. By using the Fourier transform and stationary phase method, the far-field sound pressure is obtained in terms of analytical expressions. Comparisons are made between the first-order shear deformation plate theory and the classical thin plate theory. Three principal conclusions are drawn in the study. (1) The transverse point force acting on the stiffeners yields lower far-field sound pressure in the middle and high frequency range. Specifically, the transverse point force exerting on the large stiffeners produces the lowest far-field sound pressure among three different reactive points at the plate, small stiffener and large stiffener. (2) The far-field sound pressure spectra are confined by an acoustic circle and remain unchanged. Lots of flexural waves in the structure cannot radiate sound into the far field. (3) The sound attenuation of stiffened plates with compliant layers is mainly caused by the sound isolation of compliant layers rather than vibrational reduction. Compliant layers can effectively reduce the radiated sound pressure in the medium and high frequency range.

A Laminated Plate Model of an Adhesive-Bonded Taper-Taper Joint Under Tension

1997 ◽  
Vol 119 (4) ◽  
pp. 408-414 ◽  
Author(s):  
Jack E. Helms ◽  
Chihdar Yang ◽  
Su-Seng Pang
Keyword(s):  
Analytical Model ◽  
Plate Theory ◽  
Variable Coefficients ◽  
Stress Distributions ◽  
Laminated Plate ◽  
Flat Plates ◽  
First Order ◽  
Bonded Joint ◽  
Commercial Software Package ◽  
Taper Joint

An analytical model of the strain and stress distributions in a taper-taper adhesive-bonded joint between two composite flat plates has been developed using first-order laminated plate theory. A correction for transverse shear deformation effects was included. The model was derived under the assumption of plane strain in the adherends and consists of eighteen first-order, linear, coupled ordinary differential equations with variable coefficients. The model was solved numerically using the Linear Shooting Method. Finite element models were also developed to verify the results of the analytical model using the COSMOS/M commercial software package.

Incremental Deformations in Orthotropic Laminated Plates Under Initial Stress

1973 ◽  
Vol 40 (1) ◽  
pp. 193-200 ◽  
Author(s):  
C. T. Sun
Keyword(s):  
Wave Propagation ◽  
Initial Stress ◽  
Composite Plate ◽  
Plate Theory ◽  
Harmonic Wave ◽  
Composite Plates ◽  
Laminated Plates ◽  
Flexural Wave ◽  
Plate Equations ◽  
Flexural Wave Propagation

Plate equations for the incremental deformation in composite plates with orthotropic constituent layers are derived according to Trefftz’s formulation for elastic bodies under initial stress. The plate theory thus derived includes the microdeformation which can account for the heterogeneity of the plate. Flexural wave propagation under initial stress and buckling of a simply supported rectangular composite plate are investigated. In a special case of harmonic wave propagation in a free composite plate dispersion curves predicted by the plate equations are compared with the exact curve. Good agreement is observed for the complete plate theory and Approximation I, while the adequacy of the other two sets of simplified equations, Approximations II and III, depends vitally on the ratio of the transverse shear rigidities of the constituent materials.

Transient Response of Strain Rate Dependent Composite Plates Using Finite Difference Method

2010 ◽  
Author(s):  
M. M. Shokrieh ◽  
A. Karamnejad
Keyword(s):  
Finite Difference ◽  
Strain Rate ◽  
Composite Plate ◽  
Plate Theory ◽  
Static Model ◽  
Laminated Plate ◽  
Difference Model ◽  
Strain Rate Effects ◽  
Rate Dependent ◽  
Rate Effects

In the present work, the response of laminated composite plate under dynamic loading is investigated using a macro-mechanical approach by use of a finite difference model which accounts for geometric nonlinearity and strain rate effects. Coupled nonlinear equations of motion of a laminated plate based on classical laminated plate theory (CLPT) and first-order shear deformation laminated plate theory (FSDT) are derived and reduced to nonlinear ordinary differential equations in time domain by finite difference approximations for displacements. Newmark time integration scheme in association with Newton-Raphson iteration method is applied to solve the system of nonlinear equations. Sudden material property degradation rules are modified to account for strain rate effects. A progressive damage model is developed based on the modified material property degradation rules and Hashin-type failure criteria and added to a finite difference model. The model is implemented into a computer code in Mathematica 6. The model is validated by comparison of the present results with those are available in the literature. The effects of transverse shear strain are studied by comparison of the results obtained using CLPT and FSDT. In order to investigate the strain rate effects, a clamped Glass/Epoxy composite plate subjected to a triangular load is considered. Results for static model, in which the mechanical properties are constant and dynamic model which has strain rate dependent mechanical properties are compared for various stacking sequences and load magnitudes. The results show that the deflections are overestimated by static model and the difference between static and dynamic models results increases with the magnitude of load. Furthermore, the variation trend of maximum displacement with stacking sequence is the same for both material models.

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