• Structural Engineering and Mechanics
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• v.43 no.6
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• pp.739-759
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• 2012

The tailoring optimization technique recently developed by the author for improving structural response and energy absorption of composites is extended to sandwich shells using a previously developed zig-zag shell model with hierarchic representation of displacements. The in-plane variation of the stiffness properties of plies and the through-the thickness variation of the core properties are determined solving the Euler-Lagrange equations of an extremal problem in which the strain energy due to out-of-plane strains and stresses is minimised, while that due to their in-plane counterparts is maximised. In this way, the energy stored by unwanted out-of-plane modes involving weak properties is transferred to acceptable in-plane modes. As shown by the numerical applications, the critical interlaminar stress concentrations at the interfaces with the core are consistently reduced without any bending stiffness loss and the strength to debonding of faces from the core is improved. The structural model was recently developed by the author to accurately describe strain energy and interlaminar stresses from the constitutive equations. It a priori fulfills the displacement and stress contact conditions at the interfaces, considers a second order expansion of Lame's coefficients and a hierarchic representation that adapts to the variation of solutions. Its functional d.o.f. are the traditional mid-plane displacements and the shear rotations, so refinement implies no increase of the number of functional d.o.f. Sandwich shells are represented as multilayered shells made of layers with different thickness and material properties, the core being treated as a thick intermediate layer.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.11
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• pp.2696-2704
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• 2000

This paper presents a new laminated plate theory for the cylindrical bending of laminated plated. The theory assumes that in plane displacements vary exponentially through plate thickness. Analytical solutions are derived for simply supported plates subjected to transverse loading. The accuracy of the present theory is examined for unsymmetric laminates, and the numerical results are compared with three-dimensional elasticity solutions of Pagano. The present theory predicts displacements and stresses for very thick plates very accurately. In particular, transverse shear stresses obtained form constitutive equations are predicted very accurately.

• Structural Engineering and Mechanics
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• v.13 no.4
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• pp.411-428
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• 2002

The B-spline finite strip method is developed for the prediction of the buckling of rectangular composite laminated plates under the combined action of applied uniaxial mechanical stress and increasing temperature. The analysis is conducted in two stages, namely an in-plane stress analysis in the pre-buckling stage to determine the pre-buckling stresses, followed by a buckling analysis using these determined stresses. The buckling analysis is based on the use of first-order shear deformation plate theory. The permitted lay-up of the laminates is quite general, within the constraint that the plate remains flat prior to buckling, and a wide range of boundary conditions can be accommodated. A number of applications is described and comparison of the results generated using the finite strip method is made with the results of previous studies.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.19 no.4 s.74
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• pp.407-418
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• 2006

In this paper, an efficient yet accurate stress analysis based on the first-order shear deformation theory (FSDT) is presented. The transverse shear strain energy is modified via the mixed variational theorem, so that the shear correction factors are automatically involved in the formulation. In the mixed variational formulation, the transverse stresses are taken to be functions subject to variations. The transverse shear stresses based on an efficient higher order plate theory (EHOPT, Cho and Parmerter, 1993) are utilized and modified, while the transverse normal stress is assumed to be the third-order polynomial of thickness coordinates, which satisfies both zero transverse shear stresses and prescribed surface fractions in top and bottom surfaces. On the other hand, the displacements are assumed to be those of the FSDT Resulting strain energy expressions are referred to as an EFSDTM3D that stands for an enhanced first-order shear deformation theory based on the mixed formulation for three dimensional elasticity, The developed EFSDTM3D preserves the computational advantage of the classical FSDT while allowing for important local through-the-thickness variations of displacements and stresses through the recovery procedure that is based on the least square minimization of in-plane stresses. Comparisons of displacements and stresses of both laminated and sandwich plates using the present theory are made with the classical FSDT, three-dimensional exact solutions, and available data in the literature.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.217-224
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• 2005

A higher order zig-zag shell theory is developed to refine the predictions of the mechanical and thermal behaviors partially coupled. The in-plane displacement fields are constructed by superimposing linear zig-zag field to the smooth globally cubic varying field through the thickness. Smooth parabolic distribution through the thickness is assumed in the out-of-plane displacement in order to consider transverse normal deformation and stress. The layer-dependent degrees of freedom of displacement fields are expressed in terms of reference primary degrees of freedom by applying interface continuity conditions as well as bounding surface conditions of transverse shear stresses. Thus the proposed theory has only seven primary unknowns and they do not depend upon the number of layers. In the description of geometry and deformation of shell surface, all rigorous exact expressions are used. Through the numerical examples of partially coupled analysis, the accuracy and efficiency of the present theory are demonstrated. The present theory is suitable in the predictions of deformation and stresses of thick composite shell under mechanical and thermal loads combined.

• Structural Engineering and Mechanics
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• v.42 no.6
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• pp.867-882
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• 2012

Analytical (Rayleigh-Ritz method) and numerical studies are carried out and buckling interaction curves are developed for simply supported plates of varying aspect ratios ranging from 1 to 5, under the combined action of in-plane shear and tension. A multi-step buckling procedure is employed in the Finite Element (FE) model instead of a regular single step analysis in view of obtaining the buckling load under the combined forces. Both the analytical (classical) and FE studies confirm the delayed shear buckling characteristics of thin plate under the combined action of shear and tension. The interaction curves are found to be linear and are found to vary with plate aspect ratio. The interaction curve developed using Rayleigh-Ritz method is found to deviate in an increasing trend from that of validated FE model as plate aspect ratio is increased beyond value of 1. It is found that the observed deviation is due to the insufficient number of terms that is been considered in the assumed deflection function of Rayleigh-Ritz method and a convergence study is suggested as a solution.

• Structural Engineering and Mechanics
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• v.7 no.2
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• pp.147-157
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• 1999

An analytical methodology for solving antiplane problem of anisotropic materials is proposed and discussed in detail in this study. The material considered in this study possesses a symmetry plane at z=0. The relationship between the problems of anisotropic materials and the corresponding isotropic problems are established by Ma (1996) on the basis of the general solutions for the shear stresses and displacement in both the polar and Cartesian coordinate systems. This implies that any solution of an anisotropic problem can be obtained by solving a corresponding isotropic problem. In this study some examples and numerical results are presented as an explanation of how the complicated anisotropic problem could be solved by the associated simpler isotropic problem.

• Proceedings of the International Microelectronics And Packaging Society Conference
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• 2002.05a
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• pp.208-213
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• 2002

When a thermoset conductive adhesive joints are subjected to the thermal cycles, the thermal stresses are developed around the joints. Most of in-plane, hi-axial components of these residual stresses induces large tensile peel stresses and weakens adhesive joints. Also these stresses vary with thermal cycles, and result in thermal fatigue loading and debonding propagation. In this study, the thermal ratchetting effect in conductive adhesive joints are evaluated by the finite element analysis with the viscoelastic material model. In order to Investigate the relationship between thermal ratchetting and glass transition temperature, the mathematical material model has been developed experimentally by dynamic mechanical analysis. These material models are implemented to the finite element analysis with thermal loading cycles. And the stress profiles around the conductive adhesive joints are calculated. It has been observed that the thermal ratchetting occurs when the maximum temperature of thermal cycles is above the glass transition temperature. The peel and shear stress components increase as the thermal loading time increases. This will contributes to thermal fatigue fracture of the joints.

• Journal of the Korean Society of Safety
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• v.22 no.1 s.79
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• pp.47-53
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• 2007

A study is carried out to evaluate the stresses for steel box girder support diaphragm using finite elements method. This study includes the stress characteristic compared with experimental method for diaphragm design. The results from the finite elements method are compare with the results from experimental investigations and shown to give good agreement. The shear stresses were generally uniformed in the outer plane. increased rapidly above the bearing. The horizontal direct stresses were generally low except in the vicinity of the bearing and opening comer where a local increase in compressive stresses occured.

• Transactions of the Korean Society of Mechanical Engineers
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• v.13 no.2
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• pp.243-251
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• 1989

Assuming plastic zones spreading out on each slip plane of the two materials under out-of-plane shear loading, the size of each plastic zone is computed. The effect of the different frictional shear stresses in the two materials on the size of each plastic zone and the relative displacement at the crack tip are investigated. The relation between the J-integral in this model and the relative displacement at the crack tip is also obtained.