• Advanced Composite Materials
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• v.16 no.1
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• pp.63-81
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• 2007

Based on the Kirchhoff hypothesis of normal-remain-normal, the present work analyses piezoelectric laminated plates, wherein poled piezoelectric laminae are transversely isotropic and function as actuators. A quadric electric field is induced inside a piezoelectric lamina under a given applied voltage and mechanical bending. The governing equations for the piezoelectric laminated plate derived from the principle of virtual work in terms of the electric enthalpy have the same forms as those for a conventional composite laminated plate. We use rectangular sandwich plates of Al/PZT/Al and PZT/Al/PZT with four simply supported edges to demonstrate the prediction of the maximum bending stress in the PZT layer. The analytic solutions are verified by three-dimensional finite element analysis.

• Steel and Composite Structures
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• v.11 no.5
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• pp.403-421
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• 2011

In the present manuscript, geometrically nonlinear free vibration analysis of thin laminated plates resting on non-linear elastic foundations is investigated. Winkler-Pasternak type foundation model is used. Governing equations of motions are obtained using the von Karman type nonlinear theory. The method of discrete singular convolution is used to obtain the discretised equations of motion of plates. The effects of plate geometry, boundary conditions, material properties and foundation parameters on nonlinear vibration behavior of plates are presented.

• Structural Engineering and Mechanics
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• v.77 no.1
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• pp.137-149
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• 2021

In engineering design, the axial equivalent elastic modulus of laminated FRP pipe was mostly calculated by the average elastic modulus method or the classical laminated plate theory method, which are based on relatively simplified assumptions, and may be not accurate enough sometimes. A new analytical calculation method for the axial equivalent elastic modulus of laminated FRP pipe was established based on three-dimensional stress state. By comparing the results calculated by this method with those by the above two traditional analytical methods and the finite element method, it is found that this method for the axial equivalent elastic modulus fits well not only for thin-walled pipes with orthotropic layers, but also for thick-walled pipes with arbitrary layers. Besides, the influence of the layer stacking on the axial equivalent elastic modulus was studied with this method. It is found that a proper content of circumferential layer is beneficial for improving the axial equivalent elastic modulus of the laminated FRP pipe with oblique layers, and then can reduce its material quantity under the premise that its axial stiffness remains unchanged. Finally, the meso-mechanical mechanism of this effect was analyzed. The improving effect of circumferential layer on the axial equivalent elastic modulus of the laminated FRP pipe with oblique layers is mainly because that, the circumferential fibers can restrain the rigid body rotations of the oblique fibers, which tend to cause the significant deformations of the pipe wall units and the relatively low axial equivalent elastic modulus of the pipe.

• Geomechanics and Engineering
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• v.12 no.2
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• pp.327-346
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• 2017

Laminated plates have many applications in different industrials. Buckling analysis of these structures with the nano-scale reinforcement has not investigated yet. However, buckling analysis of embedded laminated plates with nanocomposite layers is studied in this paper. Considering the single-walled carbon nanotubes (SWCNTs) as reinforcement of layers, SWCNTs agglomeration effects and nonlinear analysis using numerical method are the main contributions of this paper. Mori-Tanaka model is applied for obtaining the equivalent material properties of structure and considering agglomeration effects. The elastic medium is simulated by spring and shear constants. Based on first order shear deformation theory (FSDT), the governing equations are derived based on energy method and Hamilton's principle. Differential quadrature method (DQM) is used for calculating the buckling load of system. The effects of different parameters such as the volume percent of SWCNTs, SWCNTs agglomeration, number of layers, orientation angle of layers, elastic medium, boundary conditions and axial mode number of plate on the buckling of the structure are shown. Results indicate that increasing volume percent of SWCNTs increases the buckling load of the plate. Furthermore, considering agglomeration effects decreases the buckling load of system. In addition, it is found that the present results have good agreement with other works.

• Steel and Composite Structures
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• v.35 no.5
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• pp.659-670
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• 2020

This paper proposes the use of a porous core between layers of laminated composite plates to examine its effect on the natural frequencies of the resulted porous laminated composite sandwich plate (PLCSP) resting on a two-parameter elastic foundation. Moreover, it has been suggested that the dispersion of porosity has two different functionally graded (FG) patterns which are compared with a uniformly dispersed (UD) profile to find their best vibrational efficiency in the proposed PLCSPs. In FG patterns, two types of dispersions, including symmetric (FG-S) and asymmetric (FG-A) patterns have been considered. To derive the governing Eigen value equation of such structures, the first order shear deformation theory (FSDT) of plates has been employed. Accordingly, a finite element method (FEM) is developed to solve the derived Eigen value equation. Using the mentioned theory and method, the effects of porosity parameters, fiber orientation of laminated composite, geometrical dimensions, boundary conditions and elastic foundation on the natural frequencies of the proposed PLCSPs have been studied. It is observed that embedding porosity in core layer leads to a significant improvement in the natural frequencies of PLCSPs. Moreover, the natural frequencies of PLCSPs with FG porous core are higher than those with UD porous core.

• Steel and Composite Structures
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• v.32 no.2
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• pp.173-187
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• 2019

This study is concerned with the stability of laminated composite plates modelled using Eringen's nonlocal differential model (ENDM) and a novel refined-hyperbolic-shear-deformable plate theory. The plate is assumed to be lying on the Pasternak elastic foundation and is under the influence of an in-plane magnetic field. The governing equations and boundary conditions are obtained through Hamilton's principle. An analytical approach considering Navier series is used to fine the critical bucking load. After verifying with existing results for the reduced cases, the present model is then used to study buckling of the laminated composite plate. Numerical results demonstrate clearly for the first time the roles of size effects, magnetic field, foundation parameters, moduli ratio, geometry, lay-up numbers and sequences, fiber orientations, and boundary conditions. These results could be useful for designing better composites and can further serve as benchmarks for future studies on the laminated composite plates.

• Structural Engineering and Mechanics
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• v.50 no.6
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• pp.773-796
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• 2014

This paper deals with free vibration analysis of continuous grading fiber reinforced (CGFR) and bi-directional FG annular sector plates on two-parameter elastic foundations under various boundary conditions, based on the three-dimensional theory of elasticity. The plates with simply supported radial edges and arbitrary boundary conditions on their circular edges are considered. A semi-analytical approach composed of differential quadrature method (DQM) and series solution is adopted to solve the equations of motion. Some new results for the natural frequencies of the plate are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. Results indicate that the non-dimensional natural frequency parameter of a functionally graded fiber volume fraction is larger than that of a discrete laminated and close to that of a 2-layer. It results that the CGFR plate attains natural frequency higher than those of traditional discretely laminated composite ones and this can be a benefit when higher stiffness of the plate is the goal and that is due to the reduction in spatial mismatch of material properties. Moreover, it is shown that a graded ceramic volume fraction in two directions has a higher capability to reduce the natural frequency than conventional one-dimensional functionally graded material. The multidirectional graded material can likely be designed according to the actual requirement and it is a potential alternative to the unidirectional functionally graded material. The new results can be used as benchmark solutions for future researches.

• Steel and Composite Structures
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• v.53 no.1
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• pp.1-27
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• 2024

This work presents the effectiveness of differential quadrature shape functions (i.e., Lagrange interpolation polynomial, Cardinal sine function, Delta Lagrange kernel and Regularized Shannon kernel) in the solution of nonlinear vibration of multilayers piezoelectric plates with nonlinear elastic support. A piezoelectric composite laminated plate is rested on nonlinear Winkler and Visco-Pasternak elastic foundations problems. Based on 3D elasticity theory and piezoelectricity, the governing equations of motion are derived. Differential quadrature methods based on four shape functions are presented as numerical techniques for solving this problem. The perturbation method is implemented to solve the obtained nonlinear eigenvalue problem. A MATLAB code is written for each technique for solving this problem and extract the numerical results. To validate these methods, the computed results are we compare with the previous exact results. In addition, parametric analyses are offered to investigate the influence of length to thickness ratio, elastic foundation parameters, various boundary conditions, and piezoelectric layers thickness on the natural frequencies and mode shapes. Consequently, it is discovered that the obtained results via the proposed schemes can be applied in structural health monitoring.

• Journal of the Korean Society for Advanced Composite Structures
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• v.1 no.2
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• pp.1-13
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• 2010

Delamination reduces an elastic buckling load of the laminated composite structures and lead to global structural failure at loads below the design level. Therefore, the problem of the delamination buckling of laminated composite structures has generated significant research interest and has been the subject of many theoretical and experimental investigations. However, questions still remain regarding a complete understanding and details of the phenomena involved. In this paper an efficient finite element model is presented for analyzing the elastic buckling behavior of laminated composite plates with square embedded delamination using a solid element based on a three-dimensional theory. The solid finite element, named by EAS-SOLID8, based on an enhanced assumed strain method is developed. The study for elastic buckling behavior of laminated composite plates with embedded square delaminations are focused on various parameters, such as support condition and width-to-thickness ratio. Both graphs and buckling modes in this paper are good guide for design of the laminated composite plates with embedded square delamination.

• Steel and Composite Structures
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• v.24 no.6
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• pp.697-709
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• 2017

The current study addresses the local buckling analysis of an infinite thin rectangular symmetrically laminated composite plate restrained by a tensionless Winkler foundation and subjected to uniform in-plane shear loading. An analytic method (i.e., one-dimensional mathematical method) is used to achieve the analytical solution estimate of the contact buckling coefficient. In addition, to study the effect of ply angle and foundation stiffness on the critical buckling coefficients for the laminated composite plates, the parametric studies are implemented. Moreover, the convergence for finite element (FE) mesh is analysed, and then the examples in the parametric study are validated by the FE analysis. The results show that the FE analysis has a good agreement with the analytical solutions. Finally, an example with the analytical solution and FE analysis is presented to demonstrate the availability and feasibility of the presented analytical method.