• Structural Engineering and Mechanics
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• v.40 no.2
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• pp.257-277
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• 2011

In this paper the geometrically nonlinear continuum plate finite element model, hitherto not reported in the literature, is developed using the total Lagrange formulation. With the layerwise displacement field of Reddy, nonlinear Green-Lagrange small strain large displacements relations (in the von Karman sense) and linear elastic orthotropic material properties for each lamina, the 3D elasticity equations are reduced to 2D problem and the nonlinear equilibrium integral form is obtained. By performing the linearization on nonlinear integral form and then the discretization on linearized integral form, tangent stiffness matrix is obtained with less manipulation and in more consistent form, compared to the one obtained using laminated element approach. Symmetric tangent stiffness matrixes, together with internal force vector are then utilized in Newton Raphson's method for the numerical solution of nonlinear incremental finite element equilibrium equations. Despite of its complex layer dependent numerical nature, the present model has no shear locking problems, compared to ESL (Equivalent Single Layer) models, or aspect ratio problems, as the 3D finite element may have when analyzing thin plate behavior. The originally coded MATLAB computer program for the finite element solution is used to verify the accuracy of the numerical model, by calculating nonlinear response of plates with different mechanical properties, which are isotropic, orthotropic and anisotropic (cross ply and angle ply), different plate thickness, different boundary conditions and different load direction (unloading/loading). The obtained results are compared with available results from the literature and the linear solutions from the author's previous papers.

• Structural Engineering and Mechanics
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• v.67 no.4
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• pp.403-415
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• 2018

In the present study, nonlinear dynamic response of polymer-CNT-fiber multiscale nanocomposite plate resting on elastic foundations in thermal environments using the finite element method is performed. In this regard, the governing equations are derived based on Inverse Hyperbolic Shear Deformation Theory and von $K{\acute{a}}rm{\acute{a}}n$ geometrical nonlinearity. Three type of distribution of temperature through the thickness of the plate namely, uniform linear and nonlinear are considered. The considered element is C1-continuous with 15 DOF at each node. The effective material properties of the multiscale composite are calculated using Halpin-Tsai equations and fiber micromechanics in hierarchy. The carbon nanotubes are assumed to be uniformly distributed and randomly oriented through the epoxy resin matrix. Five types of impulsive loads are considered, namely the step, sudden, triangular, half-sine and exponential pulses. After examining the validity of the present work, the effects of the weight percentage of SWCNTs and MWCNTs, nanotube aspect ratio, volume fraction of fibers, plate aspect, temperature, elastic foundation parameters, distribution of temperature and shape of impulsive load on nonlinear dynamic response of CNT reinforced multi-phase laminated composite plate are studied in details.

• Composites Research
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• v.18 no.5
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• pp.15-20
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• 2005

In this paper, damage induced acoustic emission in the composite plate in numerically simulated by using the three dimensional finite element method and explicit time integration. Acoustic source is modeled by equivalent volume source. To verify the proposed method, dynamic displacements due to the elastic wave are compared with the experiment when the fiber is broken in the single fiber embedded isotropic plate. For the laminated composite plates, the results are compared between homogenized model and DNS approach which models fibers and matrix separately. To capture high frequencies in the elastic wave, small time step size and a large number of meshes are required. The parallel computing technology is introduced to solve a large scale problem efficiently.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2011.04a
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• pp.681-688
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• 2011

Structural model of laminated composite plates based on the first order shear deformable plate theory and subjected to a combination of magnetic and thermal fields is developed. Coupled equations of motion are derived via Hamilton's principle on the basis of electromagnetic equations (Faraday, Ampere, Ohm, and Lorenz equations) and thermal equations which are involved in constitutive equations. In order to obtain the implications of a number of geometrical and physical features of the model, one special case is investigated, that is, free vibration of a composite plate immersed in a transversal magnetic field. Special coupling effects between the magnetic and elastic fields are revealed in this paper.

• Structural Engineering and Mechanics
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• v.74 no.5
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• pp.577-588
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• 2020

A unified solution is presented for the buckling analysis of rectangular laminated composite plates with elastically restrained edges. The plate is subjected to biaxial in-plane compression, and the boundary conditions are simulated by employing uniform distribution of linear and rotational springs at all edges. The critical values of buckling loads and corresponding modes are calculated based on classical lamination theory and using the Ritz method. The deflection function is defined based on simple polynomials without any auxiliary function. The verifications of the current study are carried out with available combinations of classic boundary conditions in the literature. Through parametric study with a wide range of spring factors with some classical as well as some not classical boundary conditions, competency of the present model of boundary conditions is proved.

• Steel and Composite Structures
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• v.32 no.6
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• pp.821-832
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• 2019

An analysis on thermal buckling and postbuckling of composite laminated plates reinforced with a low amount of graphene platelets is performed in the current investigation. It is assumed that graphaene platelets are randomly oriented and uniformly dispersed in each layer of the composite media. Elastic properties of the nanocomposite media are obtained by means of the modified Halpin-Tsai approach which takes into account the size effects of the graphene reinforcements. By means of the von $K{\acute{a}}rm{\acute{a}}n$ type of geometrical nonlinearity, third order shear deformation theory and nonuniform rational B-spline (NURBS) based isogeometric finite element method, the governing equations for the thermal postbuckling of nanocomposite plates in rectangular shape are established. These equations are solved by means of a direct displacement control strategy. Numerical examples are given to study the effects of boundary conditions, weight fraction of graphene platelets and distribution pattern of graphene platelets. It is shown that, with introduction of a small amount of graphene platelets into the matrix of the composite media, the critical buckling temperature of the plate may be enhanced and thermal postbuckling deflection may be alleviated.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.4
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• pp.335-345
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• 2008

In this study, we suggest a stochastic finite element scheme for the probabilistic analysis of the composite laminated plates, which have been applied to variety of mechanical structures due to their high strength to weight ratios. The applied concept in the formulation is the weighted integral method, which has been shown to give the most accurate results among others. We take into account the elastic modulus and in-plane shear modulus as random. For individual random parameters, independent stochastic field functions are assumed, and the effect of these random parameters on the response are estimated based on the exponentially varying auto- and cross-correlation functions. Based on example analyses, we suggest that composite plates show a less coefficient of variation than plates of isotropic and orthotropic materials. For the validation of the proposed scheme, Monte Carlo analysis is also performed, and the results are compared with each other.

• Advances in nano research
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• v.12 no.2
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• pp.117-137
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• 2022

Effect of thickness stretching on free vibration, bending and buckling behavior of carbon nanotubes reinforced composite (CNTRC) laminated nanoplates rested on new variable elastic foundation is investigated in this paper using a developed four-unknown quasi-3D higher-order shear deformation theory (HSDT). The key feature of this theoretical formulation is that, in addition to considering the thickness stretching effect, the number of unknowns of the displacement field is reduced to four, and which is more than five in the other models. Two new forms of CNTs reinforcement distribution are proposed and analyzed based on cosine functions. By considering the higher-order nonlocal strain gradient theory, microstructure and length scale influences are included. Variational method is developed to derive the governing equation and Galerkin method is employed to derive an analytical solution of governing equilibrium equations. Two-dimensional variable Winkler elastic foundation is suggested in this study for the first time. A parametric study is executed to determine the impact of the reinforcement patterns, nonlocal parameter, length scale parameter, side-t-thickness ratio and aspect ratio, elastic foundation and various boundary conditions on bending, buckling and free vibration responses of the CNTRC plate.

• Composites Research
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• v.32 no.4
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• pp.185-190
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• 2019

This work investigates the elastic buckling characteristics of laminated composite trapezoidal corrugated plates with simply supported edges using the analytical method. In the analysis, three types of in-plane loading conditions: uniaxial, biaxial and shear loads are considered. Because it is very difficult to determine the mechanical behavior of 3-dimensional corrugated structures analytically, the equivalent homogenization model is adapted to investigate the overall mechanical behavior of corrugated plates. The corrugated element is homogenized as an orthotropic material. The previous formulae for bending rigidities of corrugated plate are adapted in this paper. The comparisons of the proposed analytical results with those of FEA based on the shell element are made to verify the proposed analytical method. In the comparison study both the critical buckling loads and the buckling mode shapes are presented. Some numerical results are presented to check the effect of the geometric properties.

• Journal of Ship and Ocean Technology
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• v.4 no.2
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• pp.38-57
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• 2000

This paper deals with reliability analysis of specially orthotropic plates subjected to transverse lateral pressure loads by using Monte Carlo simulation method. The plates are simply supported around their all edges and have a low short span to plate depth ratio with rectangular plate shapes. Various levels of reliability analyses of the plates are performed within the context of First-Ply-Failure(FPF) analysis such as ply-/laminate-level reliability analyse, failure tree analysis and sensitivity analysis of basic design variables to estimated plate reliabilities. In performing all these levels of reliability analyses, the followings are considered within the Monte Carlo simulation method: (1) input parameters to the strengths of the plates such as applied transverse lateral pressure loads, elastic moduli, geometric including plate thickness and ultimate strength values of the plates are treated as basic design variables following a normal probability distribution; (2) the mechanical responses of the plates are calculated by using simplified higher-order shear deformation theory which can predict the mechanical responses of thick laminated plates accurately; and (3) the limit state equations are derived from polynomial failure criteria for composite materials such as maximum stress, maximum strain, Tsai-Hill, Tsai-Wu and Hoffman.