• Bulletin of the Society of Naval Architects of Korea
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• v.13 no.4
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• pp.19-24
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• 1976

Some method of analysis of rectangular plates under distributed load of various intensity with all edges built in are presented in. Analysis of many structures such as bottom, side shell, and deck plate of ship hull, and flat slab, deck systems of bridges is a problem of plate with continuous supports or clamped edges. When the four edges of rectangular plate is simply supported, the double fourier series solution developed by Navier can represent an exact result of this problem. If two opposite edges are simply supported, Levy's method is available to give an "exact" solution. When the loading condition and boundary condition of a plate does not fall into these cases, no simple analytic method seems to be feasible. Analysis of a plate under distributed loads of various intensity with all edges built in is carried out by applying Navier solution and Levy's method as well as "Principle of Superposition" In discussing this problem we start with the solution of the problem for a simply supported rectangular plate and superpose on the deflection of such a plate the deflections of the plate by slopes distributed along the all edges. These slopes we adjust in such a manner as to satisfy the condition of no rotation at the boundary of the clamped plate. This method can be applied for the cases of plates under irregularly distributed loads of various intensity with two opposite edges simply supported and the other two edges clamped and all edges simply supported and this method can also be used to solve the influence values of deflection, moment and etc. at arbitrary position of plates under the live load.

• Journal of Korean Society of Steel Construction
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• v.20 no.3
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• pp.409-419
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• 2008

A co-rotational quasi-conforming formulation of four- node stress resultant shell elements using Ivanov-Ilyushin yield criteria are presented for the nonlinear analysis of plate and shell structure. The formulation of the geometrical stiffness is defined by the full definition of the Green strain tensor and it is efficient for analyzing stability problems of moderately thick plates and shells as it incorporates the bending moment and transverse shear resultant force. As a result of the explicit integration of the tangent stiffness matrix, this formulation is computationally very efficient in incremental nonlinear analysis. This formulation also integrates the elasto-plastic material behaviour using Ivanov Ilyushin yield condition with isotropic strain hardening and its asocia ted flow rules. The Ivanov Ilyushin plasticity, which avoids multi-layer integration, is computationally efficient in large-scale modeling of elasto-plastic shell structures. The numerical examples herein illustrate a satisfactory concordance with test ed and published references.

• Journal of the Korean Society of Safety
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• v.22 no.5
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• pp.41-49
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• 2007

In general, the curved structures have the engineering efficiency as well as a fine view compared with straight member. Also, composite materials are composed of two or more different materials to produce desirable properties for structural strength as compared to single ones. Shell structures with composite materials have many advantages in strength and weight reduction. Therefore, composite laminated conical shells are analyzed in this study. To solve differential equations of conical shells, this paper used finite difference method. Various parametric study according to the change of radius ratio, vertex angle and subtended angle are examined. The change of radius ratio, vertex angle and subtended angle mean the change from conical shells to cylindrical shells, conical shells to circular plates and open shells closed shells, respectively.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2005.05a
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• pp.130-133
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• 2005

Efficient finite element method has been introduced for metallic sandwich plates subject to 3-point bending. A full model 3-point bending FE-analysis shows that plastic behavior of inner structures appears only at the load point. So, Unit structures of sandwich plates are defined to numerically calculate the bending stiffness with recurrent boundary condition of pure bending. And then equivalent models with same bending stiffness and strength of full models are designed analytically. It is demonstrated that results of both models are almost same and FE analysis method with equivalent models can reduce analysis time effectively.

• Proceeding of KASS Symposium
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• 2006.05a
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• pp.191-204
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• 2006

This paper investigate the optimum thickness distribution of plate structure with different essential boundary conditions in the fundamental natural frequency maximization problem. In this study, the fundamental natural frequency is considered as the objective function to be maximized and the initial volume of structures is used as the constraint function. The computer-aided geometric design (CAGD) such as Coon's patch representation is used to represent the thickness distribution of plates. A reliable degenerated shell finite element is adopted calculate the accurate fundamental natural frequency of the plates. Robust optimization algorithms implemented in the optimizer DoT are adopted to search optimum thickness values during the optimization iteration. Finally, the optimum thickness distribution with respect to different boundary condition

• Journal of Ocean Engineering and Technology
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• v.34 no.1
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• pp.37-45
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• 2020

Unstiffened and stiffened cylindrically curved plates are often used in ship structures. For example, they can be found on a deck with a camber, a side shell at the fore and aft parts, and the circular bilge part of a ship structure. It is believed that such cylindrically curved plates can be fundamentally modelled using a portion of a circular cylinder. From estimations using cylindrically curved plate models, it is known that the curvature generally increases the buckling strength compared to a flat plate under axial compression. The existence of curvature is also expected to increase both the ultimate and buckling strengths. In the present study, a series of finite element analyses were conducted on stiffened curved plates with several varying parameters such as the curvature, panel slenderness ratio, and web height and type of stiffener applied. The results of numerical calculations on stiffened and unstiffened curved plates were examined to clarify the influences of such parameters on the characteristics of their buckling/plastic collapse behavior and strength under an axial compression.

• Steel and Composite Structures
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• v.44 no.2
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• pp.155-169
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• 2022

In the present paper an analytical model was developed to study the non-linear vibrations of Functionally Graded Carbon Nanotube (FG-CNT) reinforced doubly-curved shallow shells using the Multiple Scales Method (MSM). The nonlinear partial differential equations of motion are based on the FGM shallow shell hypothesis, the non-linear geometric Von-Karman relationships, and the Galerkin method to reduce the partial differential equations associated with simply supported boundary conditions. The novelty of the present model is the simultaneous prediction of the natural frequencies and their mode shapes versus different curvatures (cylindrical, spherical, conical, and plate) and the different types of FG-CNTs. In addition to combining the vibration analysis with optimization algorithms based on the genetic algorithm, a design optimization methode was developed to maximize the natural frequencies. By considering the expression of the non-dimensional frequency as an objective optimization function, a genetic algorithm program was developed by valuing the mechanical properties, the geometric properties and the FG-CNT configuration of shallow double curvature shells. The results obtained show that the curvature, the volume fraction and the types of NTC distribution have considerable effects on the variation of the Dimensionless Fundamental Linear Frequency (DFLF). The frequency response of the shallow shells of the FG-CNTRC showed two types of nonlinear hardening and softening which are strongly influenced by the change in the fundamental vibration mode. In GA optimization, the mechanical properties and geometric properties in the transverse direction, the volume fraction, and types of distribution of CNTs have a considerable effect on the fundamental frequencies of shallow double-curvature shells. Where the difference between optimized and not optimized DFLF can reach 13.26%.

• Journal of the Korean Society of Hazard Mitigation
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• v.7 no.5
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• pp.61-71
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• 2007

Navier's and Finite element solutions based on the first-order shear deformation theory are presented for the analysis of through-thickness functionally graded plates and shells. The functionally graded materials are considered: a sigmoid function is utilized for the mechanical properties through the thickness of the isotropic structure which varies smoothly through the plate and shell thickness. The formulation of a nonlinear 9-node Element-based Lagrangian shell element is presented for the geometrically nonlinear analysis. Natural-coordinate-based strains are used in present shell element. Numerical results of the linear and nonlinear analysis are presented to show the effect of the different top/bottom elastic modulus, loading conditions, aspect ratios and side-to-thickness ratios on the mechanical behaviors. Besides, the result according to the variation of the power-law index of isotropic functionally graded structures is investigated.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.04a
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• pp.263-270
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• 1996

Noise control of a plate structure with multiple disk shaped piezoelectric actuators is studied. The plate is excited by an acoustic pressure field produced by a noise source located below the plate. Finite element modeling is used for the plate structure that supports a combination of three dimensional solid, flat shell and transition elements. The objective function, in the optimization procedure, is to minimize the sound energy radiated onto a hemispherical surface of given radius and the design parameters are the locations and sizes of the piezoelectric actuators as well as the amplitudes of the voltages applied to them. Automatic mesh generation is addressed as part of the modeling procedure. Numerical results for both resonance and off resonance frequencies show remarkable noise reduction and the optimal locations of the actuators are found to be close to the edges of the plate structure. The optimized result is robust such that when the acoustic pressure pattern is changed, reduction of radiated sound is still maintained. The robustness of an optimally designed structure is also tested by changing the frequency of the noise source using only the actuator voltages as design parameters.

• Bulletin of the Society of Naval Architects of Korea
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• v.13 no.1
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• pp.17-23
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• 1976

Some methods of analysis of rectangular plates under distributed load of various intensity with interior supports are presented herein. Analysis of many structures such as bottom, side shell, and deck plate of ship hull and flat slab, with or without internal supports, Floor systems of bridges, included crthotropic bridges is a problem of plate with elastic supports or continuous edges. When the four edges of rectangular plate is simply supported, the double Fourier series solution developed by Navier can represent an exact result of this problem. If two opposite edges are simply supported, Levy's method is available to give an "exact" solution. When the loading condition and supporting condition of a plate does not fall into these cases, no simple analytic method seems to be feasible. Analysis of a simply supported rectangular plate under irregularly distributed loads of various intensity with internal supports is carried out by applying Navier solution well as the "Principle of Superposition." Finite difference technique is used to solve plates under irregularly distributed loads of various intensity with internal supports and with various boundary conditions. When finite difference technique is applied to the Lagrange's plate bending equation, any of fourth order derivative term in this equation produces at least five pivotal points leading to some troubles when the resulting linear algebraic equations are to be solved. This problem was solved by reducing the order of the derivatives to two: the fourth order partial differential equation with one dependent variable, namely deflection, is changed to an equivalent pair of second order partial differential equations with two dependent variables. Finite difference technique is then applied to transform these equations to a set of simultaneous linear algebraic equations. Principle of Superposition is then applied to handle the problems caused by concentrated loads and interior supports. This method can be used for the cases of plates under irregularly distributed loads of various intensity with arbitrary conditions such as elastic supports, or continuous edges with or without interior supports, and this method can also be solve the influence values of deflection, moment and etc. at arbitrary position of plates under the live load.