• Structural Engineering and Mechanics
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• v.18 no.6
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• pp.807-829
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• 2004

The Element-Based Lagrangian Formulation of a 9-node resultant-stress shell element is presented for the isotropic and anisotropic composite material. The effect of the coupling term between the bending strain and displacement has been investigated in the warping problem. The strains, stresses and constitutive equations based on the natural co-ordinate have been used throughout the Element-Based Lagrangian Formulation of the present shell element which offers an advantage of easy implementation compared with the traditional Lagrangian Formulation. The element is free of both membrane and shear locking behavior by using the assumed natural strain method such that the element performs very well in thin shell problems. In composite plates and shells, the transverse shear stiffness is defined by an equilibrium approach instead of using the shear correction factor. The arc-length control method is used to trace complex equilibrium paths in thin shell applications. Several numerical analyses are presented and discussed in order to investigate the capabilities of the present shell element. The results showed very good agreement compared with well-established formulations in the literature.

• Journal of Korean Society of Steel Construction
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• v.9 no.3 s.32
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• pp.333-340
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• 1997

This paper will expand the third-order shear deformation theory by the double-Fourier series and reduce to the solution of a system of ordinary differential equations in time, which are integrated numerically using Newmark's direct integration method and clarify the undamped dynamic responses for the cross-ply and antisymmetric angle-ply laminated composite plates and shells with simply supported boundary condition. Numerical results for deflections are presented showing the effect of side-to-thickness ratio, aspect ratio, material anisotropy, and lamination scheme.

• Journal of Korean Society of Steel Construction
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• v.10 no.1 s.34
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• pp.11-24
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• 1998

The composite sandwich plate is constructed by combining two laminated facings with high strength and a thick core of light weight material. The governing equations for the analysis of bending of simply supported sandwich plates with laminated facings are derived and analysed using the analytical method including the local shear deformations. The accuracy of the approach is ascertained by comparing solutions from the sandwich plate theory with composite facings to the laminate plate theory. Since the present analysis considers the bending stiffness of the core and also the transverse shear deformations of the laminated facings, it is expected that the analysis is capable to analyze the general anisotropic laminated plates with global shear deformations.

• 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.

• Journal of Korean Society of Steel Construction
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• v.13 no.1
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• pp.101-113
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• 2001

The main purpose of this paper is to present deflections of laminated composite plates on the two-parameter foundations. that is an elastic foundation with shear layer. This paper focuses on the deformation behaviour of anisotropic structures on elastic foundations. The third-order shear deformation theory is applied by using the double-fourier series. To validate the derived equations the obtained displacements for simply supported isotropic and orthotropic plates on elastic foundations are compared with those of Timoshenko and LUSAS program. The results show an excellent agreement for the isotropic and LUSAS program. The results show an excellent agreement for the isotropic and orthotropic plates on the elastic foundations. Numerical results for displacements are presented to show the effects of side-to-thickness ratio aspect ratio, material anisotropy and shear modulus of foundations.

• Journal of the Korea institute for structural maintenance and inspection
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• v.9 no.4
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• pp.159-168
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• 2005

This study carries out a finite difference nonlinear analysis of anisotropic advanced composite plate structures with various layer sequences. In the numerical analysis of various mechanical problems involving complex partial differential equations, the finite difference method (FDM) developed in this study has an advantage over the finite element method in its ability to avoid mesh generation and numerical integration. Many studies in FDM have been made on clamped or simple boundary conditions using merely an energy approach. These approaches cannot be satisfied, however, with pivotal points along the free boundary. Therefore, this study addresses the nonlinear problem of anisotropic plates by adopting a finite difference modeling elimination of pivotal difference points in the case of a free boundary condition. Complex nonlinear behaviors of composite plate structures for various parameters, especially for layer sequences, are analyzed using the proposed approach.

• Steel and Composite Structures
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• v.7 no.4
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• pp.339-354
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• 2007

Arched Corrugated Steel Roof (ACSR) is a kind of thin-walled steel shell, composing of arched panels with transverse small corrugations. Four full-scale W666 ACSR samples with 18m and 30m span were tested under full and half span static vertical uniform loads. Displacement, bearing capacities and failure modes of the four samples were measured. The web and bottom flange in ACSR with transverse small corrugations are simplified to anisotropic curved plates, and the equivalent tensile modulus, shear modulus and Poisson's ratio of 18m span ACSR were measured. Two 18 m-span W666 ACSR samples were analyzed with the Finite Element Analysis program ABAQUS. Base on the tests, the limit bearing capacity of ACSR is low, and for half span loading, it is 74-75% compared with the full span loading. When the testing load approached to the limit value, the bottom flange at the sample's bulge place locally buckled first, and then the whole arched roof collapsed suddenly. If the vertical loads apply along the full span, the deformation shape is symmetric, but the overall failure mode is asymmetric. For half span vertical loading, the deformation shape and the overall failure mode of the structure are asymmetric. The ACSR displacement under the vertical loads is large and the structural stiffness is low. There is a little difference between the FEM analysis results and testing data, showing the simplify method of small corrugations in ACSR and the building techniques of FEM models are rational and useful.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.7
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• pp.3207-3215
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• 2012

In this paper, we study the bending and free vibration analysis of nano plate, using a nonlocal elasticity theory of Eringen with a third-order shear deformation theory. This theory has ability to capture the both small scale effects and quadratic variation of shear strain and consequently shear stress through the plate thickness. Analytical solutions of bending and vibration of a laminated composite nano plate are presented using this theory to illustrate the effect of nonlocal theory on deflection of the nano plates. The relations between nonlocal third-order and local theories are discussed by numerical results. Further, effects of (i) nonlocal parameters, (ii) laminate schemes, (iii) directions of the fiber angle and (iv) number of layers on nondimensional deflections are investigated. In order to validate the present solutions, the reference solutions are used and discussed. The results of anisotropic nano plates using the nonlocal theory may be the benchmark test for the bending analysis.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.4
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• pp.375-387
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• 2004

A new finite element model will be presented to analyze the nonlinear behavior of RC beams and slabs strengthened by a patch repair. The numerical approach is based on the p-version degenerate shell element including theory of anisotropic laminated composites, theory of materially and geometrically nonlinear plates. In the nonlinear formulation of this model, the total Lagrangian formulation is adopted with large deflections and moderate rotations being accounted for in the sense of von Karman hypothesis. The material model is based on hardening rule, crushing condition, plate-end debonding strength model and so on. The Gauss-Lobatto numerical quadrature is applied to calculate the stresses at the nodal points instead of Gauss points. The validity of the proposed p-version nonlinear finite element model is demonstrated through the load-deflection curves, the ultimate loads, and the failure modes of RC beams or slabs bonded with steel plates or FRP plates compared with available result of experiment and other numerical methods.

• Journal of Korean Society of Steel Construction
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• v.10 no.2 s.35
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• pp.201-209
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• 1998

The presence of elevated temperature can alter significantly the structural response of fibre-reinforced laminated composites. A thermal environment causes degradation in both strength and constitutive properties, particularly in the case of fibre-reinforced polymeric composites. Furthermore, associated thermal expansion, either alone or in combination with mechanically induced deformation, can result in buckling, large deflections, and excessively high stress levels. Consequently, it is often imperative to consider environmental effects in the analysis and design of laminated systems. Exact analytical solutions of higher-order shear deformation theory is developed to study the thermal buckling of cross-ply and antisymmetric angle-ply rectangular plates. The buckling behavior of moderately thick cross-ply and antisymmetric angle-ply laminates that are simply supported and subject to a uniform temperature rise is analyzed. Numerical results are presented for fiber-reinforced laminates and show the effects of ply orientation, number of layers, plate thickness, and aspects ratio on the critical buckling temperature and compared with those obtained using the classical and first-order shear deformation theory.