• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.10 no.3
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• pp.440-448
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• 1999

This paper describes a full wave analysis of the scattering from electromagnetic absorbers which can be approximated as infinite periodic structure using hybrid finite element method. By introducing fictitious boundaries, equivalent finite region is defined and proper boundary conditions of each boundary are obtained by Floquet theorem. Since higher-order Floquet modes are employed, the method presented in this paper can be readily applied to the periodic structure haying a relatively long period. To reduce difficulty in evaluating the surface integral, the normal component to the surface were represented with the tangential component to the surface. Comparisons of calculated results with analytical or published ones show the validation of the method.

• Steel and Composite Structures
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• v.30 no.1
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• pp.57-67
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• 2019

This paper deals with the static analysis of axially functionally graded rectangular plates. It is assumed that the flexural rigidity of the plate varies exponentially along one of the plate's in-plane dimensions. Both an analytical approach and a numerical method are utilized to solve the problem. The analytical solution is obtained by using the Green's function method. To employ this approach, the adjoint boundary value problem is established. Then, exact solutions for deflection of the plate for different boundary conditions are found. In another way, a finite element formulation for the problem is developed. In order to demonstrate the validity of the Authors' formulation, the results obtained via both mentioned schemes are compared with each other for functionally graded plates and with results of previously published works for homogeneous plates. The effect of plate parameters on the response of the plate is also investigated. To remind the research background, a brief review on the application of Green's function method in plates' analysis and functionally graded plates is also presented.

• Advances in nano research
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• v.12 no.2
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• pp.167-183
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• 2022

In this paper, the free and forced vibration analysis of rotating cantilever nanoscale cylindrical beams and tubes is investigated under the external dynamic load to examine the nonlocal effect. A couple of nonlocal strain gradient theories with different beams and tubes theories, involving the Euler-Bernoulli, Timoshenko, Reddy beam theory along with the higher-order tube theory, are assumed to the mathematic model of governing equations employing the Hamilton principle in order to derive the nonlocal governing equations related to the local and accurate nonlocal boundary conditions. The two-dimensional functional graded material (2D-FGM), made by the axially functionally graded (AFG) in conjunction with the porosity distribution in the radial direction, is considered material modeling. Finally, the derived Partial Differential Equations (PDE) are solved via a couple of the generalized differential quadrature element methods (GDQEM) with the Newmark-beta techniques for the time-dependent results. It is indicated that the boundary conditions equations play a crucial task in responding to nonlocal effects for the cantilever structures.

• Structural Engineering and Mechanics
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• v.85 no.2
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• pp.147-161
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• 2023

Based on the ideas of variational differential quadrature (VDQ) and finite element method (FEM), a numerical approach named as VDQFEM is applied herein to study the large deformations of plate-type structures under static loading with arbitrary shape hole made of functionally graded graphene platelet-reinforced composite (FG-GPLRC) in the context of higher-order shear deformation theory (HSDT). The material properties of composite are approximated based upon the modified Halpin-Tsai model and rule of mixture. Furthermore, various FG distribution patterns are considered along the thickness direction of plate for GPLs. Using novel vector/matrix relations, the governing equations are derived through a variational approach. The matricized formulation can be efficiently employed in the coding process of numerical methods. In VDQFEM, the space domain of structure is first transformed into a number of finite elements. Then, the VDQ discretization technique is implemented within each element. As the last step, the assemblage procedure is performed to derive the set of governing equations which is solved via the pseudo arc-length continuation algorithm. Also, since HSDT is used herein, the mixed formulation approach is proposed to accommodate the continuity of first-order derivatives on the common boundaries of elements. Rectangular and circular plates under various boundary conditions with circular/rectangular/elliptical cutout are selected to generate the numerical results. In the numerical examples, the effects of geometrical properties and reinforcement with GPL on the nonlinear maximum deflection-transverse load amplitude curve are studied.

• Structural Engineering and Mechanics
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• v.6 no.6
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• pp.583-612
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• 1998

A unified third-order laminate plate theory that contains classical, first-order and third-order theories as special cases is presented. Analytical solutions using the Navier and L$\acute{e}$vy solution procedures are presented. The Navier solutions are limited to simply supported rectangular plates while the L$\acute{e}$vy solutions are restricted to rectangular plates with two parallel edges simply supported and other two edges having arbitrary combination of simply supported, clamped, and free boundary conditions. Numerical results of bending and vibration for a number of problems are discussed in the second part of the paper.

• Structural Engineering and Mechanics
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• v.74 no.2
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• pp.227-241
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• 2020

The bi-axial and shear buckling behavior of laminated hypar shells having rhombic planforms are studied for various boundary conditions using the present mathematical model. In the present mathematical model, the variation of transverse shear stresses is represented by a second-order function across the thickness and the cross curvature effect in hypar shells is also included via strain relations. The transverse shear stresses free condition at the shell top and bottom surfaces are also satisfied. In this mathematical model having a realistic second-order distribution of transverse shear strains across the thickness of the shell requires unknown parameters only at the reference plane. For generality in the present analysis, nine nodes curved isoparametric element is used. So far, there exists no solution for the bi-axial and shear buckling problem of laminated composite rhombic (skew) hypar shells. As no result is available for the present problem, the present model is compared with suitable published results (experimental, FEM, analytical and 3D elasticity) and then it is extended to analyze bi-axial and shear buckling of laminated composite rhombic hypar shells. A C⁰ finite element (FE) coding in FORTRAN is developed to generate many new results for different boundary conditions, skew angles, lamination schemes, etc. It is seen that the dimensionless buckling load of rhombic hypar increases with an increase in c/a ratio (curvature). Between symmetric and anti-symmetric laminations, the symmetric laminates have a relatively higher value of dimensionless buckling load. The dimensionless buckling load of the hypar shell increases with an increase in skew angle.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.941-948
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• 2006

In this paper, the effect of stiffness on hydroelastic responses of plate-like floating structure under wave loads are studied. Direct method is used for the numerical analysis. In the numerical analysis, structural equation is formulated by finite element method(FEM) and higher order boundary element method(HOBEM) is employed for the analysis of fluid flow. A 1000m-long VLFS(Very Large Floating Structure) is considered in numerical analyses. By analyzing VLFS for various cases of stiffness, the characteristics of hydroelastic responses with the variation of stiffness are investigated.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.2 s.107
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• pp.132-140
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• 2006

This paper investigates the characteristics of dynamic responses of floating structures with connections under sea wave loads. Direct method using higher order boundary element method (HOBEM) and finite element method (FEM) is adopted for numerical analysis. A 500 m-long and 250-m width very large floating structure (VLFS) with four units are considered in numerical analysis. Hinge connection and spring connection with various strength are considered as connection types. Displacements and stresses of VLFS according to the connection types are compared considering wave period and heading angle reduction.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.895-902
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• 2005

This paper investigates the characteristics of dynamic responses of floating structures with connections under sea wave loads. Direct method using higher order boundary element method and finite element method is adopted for numerical analysis. 500 m-long VLFS with four units are considered in numerical analysis. Hinge connection and spring connection with various strength are considered as connection types. Displacements and stresses of VLFS according to the connection types are compared considering wave period and heading angle.

• Advances in aircraft and spacecraft science
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• v.1 no.3
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• pp.253-271
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• 2014

A linearised buckling analysis of thin-walled beams is addressed in this paper. Beam theories formulated according to a unified approach are presented. The displacement unknown variables on the cross-section of the beam are approximated via Mac Laurin's polynomials. The governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the expansion order. Classical beam theories such as Euler-Bernoulli's and Timoshenko's can be retrieved as particular cases. Slender and deep beams are investigated. Flexural, torsional and mixed buckling modes are considered. Results are assessed toward three-dimensional finite element solutions. The numerical investigations show that classical and lower-order theories are accurate for flexural buckling modes of slender beams only. When deep beams or torsional buckling modes are considered, higher-order theories are required.