• International Journal of Aerospace System Engineering
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• v.3 no.1
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• pp.10-16
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• 2016

A trigonometric Layerwise higher order shear deformation theory (TLHSDT) is developed and implemented for free vibration and buckling analysis of laminated composite and sandwich plates by analytical and finite element formulation. The present model assumes parabolic variation of out-plane stresses through the depth of the plate and also accomplish the zero transverse shear stresses over the surface of the plate. Thus a need of shear correction factor is obviated. The present zigzag model able to meet the transverse shear stress continuity and zigzag form of in-plane displacement continuity at the plate interfaces. Hence, botheration of shear correction coefficient is neglected. In the case of analytical method, the governing differential equation and boundary conditions are obtained from the principle of virtual work. For the finite element formulation, an efficient eight noded $C^0$ continuous isoparametric serendipity element is established and employed to examine the dynamic analysis. Like FSDT, the considered mathematical model possesses similar number of variables and which decides the present models computationally more effective. Several numerical predictions are carried out and results are compared with those of other existing numerical approaches.

• Coupled systems mechanics
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• v.13 no.2
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• pp.95-113
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• 2024

In this paper, we will analyse the thermo-elastic behavior of the plate element of a structure arranged in a climatically aggressive environment (extreme temperature), we use a refined four-variable thick plate theory to take the shear effect into consideration, the proposed theory less computationally expensive and more accurate so that it incorporates the shear effect into the formulation. The plate is assumed to be simply supported on its four edges, so exact (closed-form) solutions are found according to the Navier expansion, and the governing stability equations and associated boundary conditions of the problem are obtained via the virtual works principle. The plate studied ismade of laminated composite materials, so a parametric study is needed to see the effect of different types of parameters and coupling on the critical temperature value causing thermo-elastic instability of the plate and also on the natural frequency of free vibration, as well as for other parameters such as anisotropy, slenderness and aspect ratio of the plate and finally the lamination angle. Numerical results are obtained for specially orthotropic and antisymmetrical plates and are compared with those obtained by othertheoriesin the literature to validate the analysis approach used.

• Structural Engineering and Mechanics
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• v.3 no.1
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• pp.49-60
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• 1995

In the present study, a finite strip method for the vibration and stability analyses of anisotropic laminated composite plates is developed according to the higher-order shear deformation theory. This theory accounts for the parabolic distribution of the transverse shear strains through the thickness of the plate and for zero transverse shear stresses on the plate surfaces. In comparison with the finite strip method based on the first-order shear deformation theory, the present method gives improved results for very thick plates while using approximately the same number of degrees of freedom. It also eliminates the need for shear correction factors in calculating the transverse shear stiffness. A number of numerical examples are presented to show the effect of aspect ratio, length-to-thickness ratio, number of plies, fibre orientation and stacking sequence on the natural frequencies and critical buckling loads of simply supported rectangular cross-ply and arbitrary angle-ply composite laminates.

• Structural Engineering and Mechanics
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• v.56 no.6
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• pp.1041-1061
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• 2015

The influence of hygrothermal effects on the vibration frequency and buckling load of a shear deformable composite plate with arbitrary initial stresses was investigated. The governing equations of the effects of humid, thermal and initial stresses are established using the variational method. The material properties of the composite plate are affected by both temperature and moisture. The initial stress is taken to be a combination of uniaxial load and pure bending in a hygrothermal environment. The influence of various parameters, such as the fiber volume fraction, temperature, moisture concentration, length/thickness ratios, initial stresses and bending stress ratio on the vibration and stability of the response of a laminated plate are studied in detail. The behavior of vibration and stability are sensitive to temperature, moisture concentration, fiber volume fraction and initial stresses.

• Journal of the Korea institute for structural maintenance and inspection
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• v.18 no.1
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• pp.150-159
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• 2014

A simplified method for the calculation of buckling and vibrational characteristics of initially stressed rectangular plate and antisymmetric angle-ply laminated plates is presented in this paper using the natural frequencies under unloading state. The equation of motion of rectangular plate with two opposite edges simply supported is investigated on the basis of Rayleigh-Ritz method and Mindlin plate theory with effect of the curvature term. The relationships of the non-dimensional natural frequencies with initial stresses the coeffcients of critical buckling and the boundaries of the dynamic principal instability region can be characterized by the non-dimensional natureal frequencies under unloading state. Numerical examples are presented to verify the simplified equations and to illustrate potential applications of the analysis.

• Structural Engineering and Mechanics
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• v.71 no.3
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• pp.283-290
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• 2019

In global competition manufacturing companies have to produce modern, new constructions from advanced materials in order to increase competitiveness. The aim of my research was to develop a new composite cellular plate structure, which can be primarily used for structural elements of road, rail, water and air transport vehicles (e.g. vehicle bodies, ship floors). The new structure is novel and innovative, because all materials of the components of the newly developed structure are composites (laminated Carbon Fiber Reinforced Plastic (CFRP) deck plates with pultruded Glass Fiber Reinforced Plastic (GFRP) stiffeners), furthermore combines the characteristics of sandwich and cellular plate structures. The material of the structure is much more advantageous than traditional steel materials, due mainly to its low density, resulting in weight savings, causing lower fuel consumption and less environmental damage. In the study the optimal construction of a given geometry of a structural element of a road truck trailer body was defined by single- and multi-objective optimization (minimal cost and weight). During the single-objective optimization the Flexible Tolerance Optimization method, while during the multi-objective optimization the Particle Swarm Optimization method were used. Seven design constraints were considered: maximum deflection of the structure, buckling of the composite plates, buckling of the stiffeners, stress in the composite plates, stress in the stiffeners, eigenfrequency of the structure, size constraint for design variables. It was confirmed that the developed structure can be used principally as structural elements of transport vehicles and unit load devices (containers) and can be applied also in building construction.

• Structural Engineering and Mechanics
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• v.29 no.4
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• pp.455-467
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• 2008

This paper deals with the buckling and postbuckling responses and the progressive failure of square symmetric laminates with rectangular cutouts under uniaxial compression. A detailed investigation is made to show the effects of cutout size and cutout aspect ratio on prebuckling and postbuckling responses, failure loads and failure characteristics of $(+45/-45/0/90)_{2s}$, $(+45/-45)_{4s}$ and $(0/90)_{4s}$ laminates. The 3-D Tsai-Hill criterion is used to predict the failure of a lamina while the onset of delamination is predicted by the interlaminar failure criterion. In addition, the effects of boundary conditions on buckling load, failure loads, failure modes and maximum transverse deflection for a $(+45/-45/0/90)_{2s}$ laminate with and without cutout have also been presented. It is concluded that square laminates with small square cutouts have more postbuckling strength than without cutout, irrespective of boundary conditions.

• Journal of Korean Society of Steel Construction
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• v.16 no.5 s.72
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• pp.621-628
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• 2004

This paper introduces a new theory, that in a stiffened plate, a steel stiffener could be substituted a composite material in order to prevent from buckling. Changing a steel stiffener into a composite material would not only preclude welding, but could also prevent damage to the material due to fatigue and corrosion.A composite material is assumed to adhere to a steel plate, and is never separated from the plate until the steel plate reaches buckling.Such plate has variable shapes, with different lengths and widths, and also shows an anisotropic material property. LUSAS, a commercial finite element analysis package, was used in the buckling analysis.This paper investigated buckling behavior in anisotropic composite plates with variable parameters.

• Structural Engineering and Mechanics
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• v.68 no.5
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• pp.603-619
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• 2018

In this research, an effective computational technique is carried out for nonlinear and post-buckling analyses of cracked imperfect composite plates. The laminated plates are assumed to be moderately thick so that the analysis can be carried out based on the first-order shear deformation theory. Geometric non-linearity is introduced in the way of von-Karman assumptions for the strain-displacement equations. The Ritz technique is applied using Legendre polynomials for the primary variable approximations. The crack is modeled by partitioning the entire domain of the plates into several sub-plates and therefore the plate decomposition technique is implemented in this research. The penalty technique is used for imposing the interface continuity between the sub-plates. Different out-of-plane essential boundary conditions such as clamp, simply support or free conditions will be assumed in this research by defining the relevant displacement functions. For in-plane boundary conditions, lateral expansions of the unloaded edges are completely free while the loaded edges are assumed to move straight but restricted to move laterally. With the formulation presented here, the plates can be subjected to biaxial compressive loads, therefore a sensitivity analysis is performed with respect to the applied load direction, along the parallel or perpendicular to the crack axis. The integrals of potential energy are numerically computed using Gauss-Lobatto quadrature formulas to get adequate accuracy. Then, the obtained non-linear system of equations is solved by the Newton-Raphson method. Finally, the results are presented to show the influence of crack length, various locations of crack, load direction, boundary conditions and different values of initial imperfection on nonlinear and post-buckling behavior of laminates.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.1
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• pp.65-74
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• 1993

The buckling load of a blade stiffened laminated composite plate having midplane symmetry is maximized for a given total weight. The thicknesses of the layers and the width and height of the stiffener are taken as the design variables. Buckling analysis is carried out using a finite element method. The optimization problem is solved using an IMSL subroutine. Due to the highly nonlinear nature of the optimality equations, several local optimum solutions are found. Various combinations of fiber orientation for the laminate layers and the blade stiffener are investigated to examine their relative efficiency. Out of several cases examined, the best design was produced from the combination of ($0^{\circ}Beam/0^{\circ}/90^{\circ}$)s.