On the Generalization of Reissner Plate Theory to Laminated Plates, Part II: Comparison with the Bending-Gradient Theory

Adhesive joint technology has been developed gradually, and the application fields of this type of joints have been expanded increasingly since they reduce the weight of the applications, provide uniform stress distribution across the joints, allow to bond similar, and dissimilar materials, and contribute to dampen the shock, and vibration. However, the performance of the adhesive joints under high loading rate such as blast or ballistic loading has been studied by few researchers. In this study, fully laminated plates consisting of 6061 aluminum plates (15” in diameter and 1/16” thick) and FM300K epoxy film adhesive were tested under shock wave loading. Full displacement field over the testing plates were obtained by TRC-SDIC technique, and the strain on the plates were computed by classical plate theory for large deflections. FEM model was analyzed and the results were compared with experimental results.

Download Full-text

A Composite Plate Theory for Arbitrary Laminate Configurations

Journal of Applied Mechanics ◽

10.1115/1.3172955 ◽

1987 ◽

Vol 54 (1) ◽

pp. 181-189 ◽

Cited By ~ 181

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.

Download Full-text

Vibration of thermally postbuckled FG-GRC laminated plates resting on elastic foundations

Journal of Vibration and Control ◽

10.1177/1077546319825671 ◽

2019 ◽

Vol 25 (9) ◽

pp. 1507-1520 ◽

Cited By ~ 5

Author(s):

Hui-Shen Shen ◽

Y Xiang ◽

Yin Fan

Keyword(s):

Large Amplitude ◽

Plate Theory ◽

Micromechanical Model ◽

Functionally Graded ◽

Laminated Plates ◽

Perturbation Approach ◽

Elastic Foundations ◽

Vibration Responses ◽

Uniform Temperature Field ◽

Thermal Postbuckling

This paper investigates the small- and large-amplitude vibrations of thermally postbuckled graphene-reinforced composite (GRC) laminated plates resting on elastic foundations. The piecewise GRC layers are arranged in a functionally graded (FG) pattern along the thickness direction of the plate. The anisotropic and temperature-dependent material properties of the FG-GRC layers are estimated through the extended Halpin–Tsai micromechanical model. Based on the Reddy's higher order shear deformation plate theory and the von Kármán strain–displacement relationships, the motion equations of the plates are derived. The foundation support, the thermal effect, and the initial deflection caused by thermal postbuckling are also included in the derivation. A two-step perturbation approach is applied to determine the thermal postbuckling equilibrium paths as well as the nonlinear vibration solutions for the FG-GRC laminated plates. The numerical illustrations concern small- and large-amplitude vibration characteristics of thermally postbuckled FG-GRC laminated plates under a uniform temperature field. The effects of graphene reinforcement distributions and foundation stiffnesses on the vibration responses of FG-GRC laminated plates are examined in detail.

Download Full-text

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

Journal of Applied Mechanics ◽

10.1115/1.2041657 ◽

2005 ◽

Vol 72 (6) ◽

pp. 809-817 ◽

Cited By ~ 28

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.

Download Full-text

Free Vibration of Buckled Laminated Plates by Finite Element Method

Journal of Vibration and Acoustics ◽

10.1115/1.2889774 ◽

1997 ◽

Vol 119 (4) ◽

pp. 635-640 ◽

Cited By ~ 11

Author(s):

Le-Chung Shiau ◽

Teng-Yuan Wu

Keyword(s):

Free Vibration ◽

Plate Theory ◽

Equations Of Motion ◽

Composite Plates ◽

Laminated Plates ◽

Squeezing Effect ◽

Governing Equations ◽

Amplitude Vibration ◽

Equilibrium Profile ◽

Sudden Jump

Free vibration behavior of buckled composite plates are studied by using a high precision triangular plate element. This element is developed based on a simplified high order plate theory and von Ka´rma´n large deformation assumptions. The nonlinear governing equations of motion for the plates is linearized into two sets of equations by assuming small amplitude vibration of the laminates about its buckled static equilibrium profile. Results show that, in the postbuckling regime, the fundamental mode may be shifted from the first mode to the second due to squeezing effect of the in-plane force on the plate. For plate with certain boundary conditions, the natural frequency may have a sudden jump due to buckle pattern change of the plate in the postbuckling regime.

Download Full-text

Effect of Sinusoidal Corrugated Geometries on the Vibrational Response of Viscoelastic Nanoplates

Applied Sciences ◽

10.3390/app8091432 ◽

2018 ◽

Vol 8 (9) ◽

pp. 1432 ◽

Cited By ~ 12

Author(s):

Mohammad Malikan ◽

Rossana Dimitri ◽

Francesco Tornabene

Keyword(s):

Plate Theory ◽

Practical Interest ◽

Viscoelastic Behavior ◽

Local Strain ◽

Strain Gradient Theory ◽

Gradient Theory ◽

Vibrational Response ◽

Non Local ◽

Voigt Model ◽

Local Parameters

The vibrational behavior of viscoelastic nanoplates with a corrugated geometry is a key topic of practical interest. This problem is addressed here for wrinkled nanoplates with small corrugations related to incorrect manufacturing. To this end, a new One-Variable First-order Shear Deformation plate Theory (OVFSDT) is proposed in a combined form with a non-local strain gradient theory. The Kelvin–Voigt model is employed to describe the viscoelastic behavior of the nanoplate, whereby the frequency equations are solved numerically according to Navier’s approach, for simply-supported nanostructures. A comparative evaluation between the proposed theory and other approaches in the literature is successfully performed. It follows a large parametric study of the vibration response for varying geometry corrugations and non-local parameters.

Download Full-text