• Composites Research
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• v.29 no.6
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• pp.347-352
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• 2016

This work presents the free vibration characteristics of laminated composite corrugated rectangular plates using the analytical method. Because it is very difficult to determine its mechanical behavior of 3-dimensional corrugated structures analytically, the equivalent homogenization model is adapted to investigate the overall mechanical behavior of corrugated structures. The corrugated element can be homogenized as an orthotropic material. Both the effective extensional and flexural stiffness of this homogenized equivalent orthotropic material are considered in the analysis. The present analytical results are validated by those obtained from 3D finite element analysis based on shell elements. The natural frequencies and global vibration mode shapes obtained from present analytical and finite element analysis are presented. Some numerical results are presented to check the effect of the geometric properties.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.327-334
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• 1998

A method of calculating the natural frequency corresponding to the first mode of vibration of beams and toll.or structures, with irregular cross sections and with arbitrary boundary conditions was developed and reported by Kim, D. H. in 1974. In this paper, the result of application of this method to the special orthotropic plates with free edges supported on elastic foundation and with a pair of opposite edges under axial forces is presented. Such plates represent the concrete highway slab and hybrid composite pavement of bridges. The reinforced concrete slab can be assumed as a special orthotropic plate, as a close approximation. The highway slab is supported on elastic foundation, with free boundaries. Sometimes, the pair of edges perpendicular to the traffic direction may be subject to the axial forces. The plate is subject to the concentrated load/loads, in the form of traffic loads, or the test equipments. Any method nay be used to obtain the deflection influence surfaces needed for this vibration analysis. Finite difference method is used for this purpose, in this paper. The influence of the modulus of the foundation, the aspect ratio of the plate, and the magnitudes of the axial forces and the concentrated attached mass on the plate, on the natural frequency is thoroughly studied.

• Journal of Korean Society of Steel Construction
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• v.18 no.1
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• pp.93-100
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• 2006

A simple but precise method of calculating the natural vibration frequencies of composite laminated plates with all-simple support and under axial loadings is presented herein. This method uses deflection influence surfaces, which can be obtained by any method for vibration analysis and member due to the inertia force under resonance condition. Beginning with an initially guessed mode shape, the exact mode shape is obtained by the process similar to iteration. In this paper, equations are given for the case of special orthotropic laminates. The same equations, however, can be used for any laminate as long as ${B_1_6}$, ${B_2_6}$, ${D_1_6}$, and ${D_2_6}$ are negligible as the number of plies increases. Some laminates that possess such properties are presented in the paper.

• Composites Research
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• v.16 no.5
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• pp.28-38
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• 2003

In this study, the analytical investigation of orthotropic rectangular plate is presented. The loaded edges are assumed to be simply supported and the unloaded edges could have elastically restrained boundary conditions including the extreme boundary condition such as simple, fixed, and free. Using the closed-form solutions, the buckling analyses of orthotropic plate with arbitrary boundary conditions are performed. Based on the data obtained by conducting numerical analysis, the simplified form of equation for finding the buckling coefficient of plate with elastically restrained boundary conditions at the unloaded edges is suggested as a function of aspect ratio, elastic restraint. and material properties of the plate. The results of buckling analyses by closed-form solution and simplified form of solution are compared for various orthotropic material properties. It is confirmed that the difference of results is less than 1.5%.

• Structural Engineering and Mechanics
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• v.18 no.3
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• pp.377-388
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• 2004

Based on the basic equations of elasticity, free-edge effects on stresses in cross-ply laminated plates are found by using the state space method. The laminates are subjected to uniaxial-uniform extension plate, which is a typical example of general plane strain problem. The study takes into account material constants of all individual material layers and the state equation of a laminate is solved analytically in the through thickness direction. By this approach, a composite plate may be composed of an arbitrary number of orthotropic layers, each of which may have different material properties and thickness. The solution provides a continuous displacement and inter-laminar stress fields across all material interfaces and an approxiamte prediction to the singularity of stresses occurring in the boundary layer region of a free-edge. Numerical solutions are obtained and compared with the results obtained from an alternative numerical method.

• Computers and Concrete
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• v.25 no.6
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• pp.537-549
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• 2020

Geometrically nonlinear axisymmetric bending analysis of shear deformable circular plates on a nonlinear three-parameter elastic foundation was made. Plates ranging from "thin" to "moderately thick" were investigated for three types of material: isotropic, transversely isotropic, and orthotropic. The differential equations were discretized by means of the finite difference method (FDM) and the differential quadrature method (DQM). The Newton-Raphson method was applied to find the solution. A parametric investigation using seven unknowns per node was presented. The novelty of the paper is that detailed numerical simulations were made to highlight the combined effects of the material properties and the boundary conditions on (i) the deflection, (ii) the stress resultants, and (iii) the external load. The formulation was verified through comparison studies. It was observed that the results are highly influenced from the boundary conditions, and from the material properties.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.6
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• pp.1520-1534
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• 1994

A new analytical method for the prediction of the buckling behavior of laminated plates consisting of layers having different properties in tension and compression, so called bimodulus, is proposed in this paper. Buckling analysis of bimodular composite laminated paltes are performed with the results reduced from plate bending analysis. The governing equations of bimodular plates are based on the first shear deformation theory. As a case study, bending and buckling of simply supported, multilayered, symmetric, antisymmtric, and specially orthotropic laminates under uniformly distributed lateral load for bending analysis and in-plane load for buckling are considered. The results of the bending analysis are compared with the previous papers. Then, the fundamental critical buckling loads and buckling modes are calculated for the various bimodular composite rectangular thin plates.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.77-83
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• 1998

The most of the design engineers for construction has academic background of bachelors degree. Theories for advanced composite structures are too difficult for such engineers and some simple but accurate enough methods are necessary. The senior author has reported that some laminate orientations have decreasing values of B$_{16}$, B$_{26}$, D$_{26}$, and D$_{26}$ stiffnesses as the ply number increases. Such plates above behave as special orthotropic plates and simple formulas developed by the senior author［1, 3］ can be used. Most of the bridge and building slabs on girders have large aspect ratios. For such cases further simplification is possible by neglecting the effect of the longitudinal moment terms(M$_{x}$) on the relevant partial differential equations of equilibrium. In this paper, the result of the study on the subject problem is presented.ted.d.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.223-230
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• 1998

The most of the design engineers for construction has academic background of bachelors degree. Theories for advanced composite structures are too difficult for such engineers and some simple but accurate enough methods are necessary. The senior author has reported that some laminate orientations have decreasing values of D$_{16}$, B$_{16}$, D$_{26}$ and B$_{26}$ stiffnesses as the ply number increases. Such plates behave as special orthotropic plates and simple formulas developed by the author can be used. Most of the bridge and building slabs on girders have large aspect ratios. For such cases further simplification is possible by neglecting the effect of the longitudinal moment terms(M$_{x}$) on the relevant partial differential equations of equilibrium. In this paper, the result of the study on the subject problem is presented.ented.d.

• Steel and Composite Structures
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• v.12 no.2
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• pp.129-147
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• 2012

In this paper, the thermal buckling analysis of rectangular composite laminated plates is investigated using the Differential Quadrature (DQ) method. The composite plate is subjected to a uniform temperature distribution and arbitrary boundary conditions. The analysis takes place in two stages. First, pre-buckling forces due to a temperature rise are determined by using a membrane solution. In the second stage, the critical temperature is predicted based on the first-order shear deformation theory. To verify the accuracy of the method, several case studies were used and the numerical results were compared with those of other published literatures. Moreover, the effects of several parameters such as aspect ratio, fiber orientation, modulus ratio, and various boundary conditions on the critical temperature were examined. The results confirm the efficiency and accuracy of the DQ method in dealing with this class of engineering problems.