• Structural Engineering and Mechanics
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• v.83 no.5
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• pp.617-625
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• 2022

A novel three variable refined plate theory (TVRPT) is developed in this article for laminated composite plates for the first time. The theory takes into account the nonlinear variation of transverse shear deformations, and satisfies the boundary conditions of zero traction on the plate surfaces without considering the "shear correction factor". The important characteristic of this new kinematic is that the unknowns numbers is only 3 as is employed in "classical plate theory" (CPT). The numerical results of the current theory are compared with 3D-elasticity solutions and the calculations of "first order theories" and other higher order models found in the literature.

• Structural Engineering and Mechanics
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• v.18 no.1
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• pp.41-58
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• 2004

The postbuckling behaviour of thin shells has fascinated researchers because the theoretical prediction and their experimental verification are often different. In reality, shell panels possess small imperfections and these can cause large reduction in static buckling strength. This is more relevant in thin laminated composite shells. To study the postbuckling behaviour of thin, imperfect laminated composite shells using finite elements, explicit incremental or secant matrices have been presented in this paper. These incremental matrices which are derived using Marguerre's shallow shell theory can be used in combination with any thin plate/shell finite element (Classical Laminated Plate Theory - CLPT) and can be easily extended to the First Order Shear deformation Theory (FOST). The advantage of the present formulation is that it involves no numerical approximation in forming total potential energy of the shell during large deformations as opposed to earlier approximate formulations published in the literature. The initial imperfection in shells could be modeled by simply adjusting the ordinate of the shell forms. The present formulation is very easy to implement in any existing finite element codes. The secant matrices presented in this paper are shown to be very accurate in tracing the postbuckling behaviour of thin isotropic and laminated composite shells with general initial imperfections.

• Structural Engineering and Mechanics
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• v.51 no.6
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• pp.893-907
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• 2014

Meshless local collocation method produces much better conditioned matrices than meshless global collocation methods. In this paper, the meshless local collocation method based on thin plate spline radial basis function and first-order shear deformation theory are used to calculate the natural frequencies and mode shapes of laminated composite shells. Through numerical experiments, the accuracy and efficiency of present method are demonstrated.

• Steel and Composite Structures
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• v.34 no.1
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• pp.141-154
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• 2020

In the present paper, free vibration analysis of angle-ply laminated composite annular and circular plates is performed by numerical methods. First-order shear deformation plate theory is used for kinematic relations. The related governing equations of motion are discretized via differential quadrature and discrete singular convolution methods. Frequency values are obtained for different lamina scheme, thickness-to-radius ratio, and mode numbers. The advantages and accuracy of these two methods are also tested in detail.

• Advances in Computational Design
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• v.3 no.3
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• pp.213-232
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• 2018

First time, an exact solution for free vibration of the Levy-type rectangular laminated plate is developed considering the most efficient Zig-Zag theory (ZIGT) and third order theory (TOT). The plate is subjected to hard simply supported boundary condition (Levy-type) along x axis. Using the equilibrium equations and the plate constitutive relations, a set of 12 m first order differential homogenous equations are obtained, containing displacements and stress resultant as primary variables. The natural frequencies of a single-layer isotropic, multi-layer composites and sandwich plates are tabulated for three values of length-to-thickness ratio (S) and five set of boundary conditions and further assessed by comparing with existing literature and recently developed 3D EKM (extended Kantorovich method) solution. It is found that for the symmetric composite plate, TOT produces better results than ZIGT. For antisymmetric and sandwich plates, ZIGT predicts the frequency for different boundary conditions within 3% error with respect to 3D elasticity solution while TOT gives 10% error. But, ZIGT gives better predictions than the TOT concerning the displacement and stress variables.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.4 s.247
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• pp.409-419
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• 2006

The actuating performance of plate-type unimorph piezoelectric composite actuators having various stacking sequences was evaluated by three dimensional finite element analysis on the basis of thermal analogy model. Thermal residual stress distribution at each layer in an asymmetrically laminated plate with PZT ceramic layer and thermally induced dome height were predicted using classical laminated plate theory. Thermal analogy model was applied to a bimorph cantilever beam and LIPCA-C2 actuator in order to confirm its validity. Finite element analysis considering thermal residual deformation showed that the bending behavior of piezoelectric composite actuator subjected to electric loads was significantly different according to the stacking sequence, thickness of constituent PZT ceramic and boundary conditions. In particular, the increase of thickness of PZT ceramic led to the increase of the bending stiffness of piezoelectric composite actuator but it did not always lead to the decrease of actuation distance according to the stacking sequences of piezoelectric composite actuator. Therefore, it is noted that the actuating performance of unimorph piezoelectric composite actuator is rather affected by bending stiffness than actuation distance.

• Steel and Composite Structures
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• v.21 no.2
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• pp.395-409
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• 2016

Nonlinear vibration characteristics of composite laminated trapezoidal plates are studied. The geometric nonlinearity of the plate based on the von Karman's large deformation theory is considered, and the finite element method (FEM) is proposed for the present nonlinear modeling. Hamilton's principle is used to establish the equation of motion of every element, and through assembling entire elements of the trapezoidal plate, the equation of motion of the composite laminated trapezoidal plate is established. The nonlinear static property and nonlinear vibration frequency ratios of the composite laminated rectangular plate are analyzed to verify the validity and correctness of the present methodology by comparing with the results published in the open literatures. Moreover, the effects of the ply angle and the length-high ratio on the nonlinear vibration frequency ratios of the composite laminated trapezoidal plates are discussed, and the frequency-response curves are analyzed for the different ply angles and harmonic excitation forces.

• Steel and Composite Structures
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• v.43 no.5
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• pp.639-660
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• 2022

The bending and buckling behaviours of FG-GRNC laminated sandwich plates are investigated by using novel five-variables quasi 3D higher order shear deformation plate theory by considering the modified continuum nonlocal strain gradient theory. To calculate the effective Young's modulus of the GRNC sandwich plate along the thickness direction, and Poisson's ratio and mass density, the modified Halpin-Tsai model and the rule of the mixture are employed. Based on a new field of displacement, governing equilibrium equations of the GRNC sandwich plate are solved using a developed approach of Galerkin method. A detailed parametric analysis is carried out to highlight the influences of length scale and material scale parameters, GPLs distribution pattern, the weight fraction of GPLs, geometry and size of GPLs, the geometry of the sandwich plate and the total number of layers on the stresses, deformation and critical buckling loads. Some details are studied exclusively for the first time, such as stresses and the nonlocality effect.

• Structural Engineering and Mechanics
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• v.65 no.4
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• pp.369-380
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• 2018

In this paper, a multi-layered finite element model for laminated glass plates is introduced. A layer-wise theory is applied to the analysis of laminated glass due to the combination of stiff and soft layers; the independent layers are connected via Lagrange multipliers. The von $K{\acute{a}}rm{\acute{a}}n$ large deflection plate theory and the constant Poisson ratio for constitutive equations are assumed to capture the possible effects of geometric nonlinearity and the time/temperature-dependent response of the plastic foil. The linear viscoelastic behavior of a polymer foil is included by the generalized Maxwell model. The proposed layer-wise model was implemented into the MATLAB code and verified against detailed three-dimensional models in ADINA solver using different hexahedral finite elements. The effects of temperature, load duration, and creep/relaxation are demonstrated by examples.

• Journal of Korean Society of Steel Construction
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• v.9 no.4 s.33
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• pp.601-609
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• 1997

Bending and vibration results for a laminated plate base on a simplified higher-order plate theory with four variables are presented. Assuming a constant in-plane rotation tensor through the thickness in Reddy's higher-order shear deformation theory it is shown that a simpler higher-order theory can be obtained with the reduction of one variable without significant loss in the accuracy. This simple higher-order shear deformation theory is then used for predicting the natural frequencies and deflection of simply-supported laminated composite plates. The results obtained for antisymmetrical laminated composite plates compare favorably with third-order and first-order shear deformation theory. The information presented should be useful to composite-structure designers, to researchers seeking to obtain better correlation between theory and experiment and to numerical analysts in checking out their programs.