• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2002년도 춘계학술대회논문집
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• pp.1177-1184
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• 2002

In this paper, power flow analysis method on the various types of thin shell has been developed to solve vibrational Problems in the medium to high frequency ranges. Energy governing equations have been derived both for out-of plane and in-plane waves in thin shell. These results have been numerically applied to predict the vibrational energy density and intensity distributions of cylindrical, spherical and doubly-curved shells.

• 대한조선학회논문집
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• 제44권5호
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• pp.517-525
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• 2007

This paper presents how to approximate an optimal shape of roll bending process in the fabrication of a curved shell plate. The roll bending process usually makes the cylindrical or conic shape from an initial flat plate. It means that the final shape is developable or its surface representation has zero Gaussian curvature. The fabrication shape is important in order to find process parameters of roil bending. An optimal concept is used to determine the developable fabrication shape which is in the closest proximity to the design surface or the given shell plate and is subject to developability. The results and the efficiency of this algorithm are evaluated by applying to some shell plates. Furthermore, the fabrication shape will be fundamental information for other process parameters of roll bending such as the vertical displacement of the center roller and the rolling directions.

• Steel and Composite Structures
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• 제15권4호
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• pp.379-397
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• 2013

Conoidal shells are doubly curved stiff surfaces which are easy to cast and fabricate due to their singly ruled property. Application of laminated composites in fabrication of conoidal shells reduces gravity forces and mass induced forces compared to the isotropic constructions due to the high strength to weight ratio of the material. These light weight shells are preferred in the industry to cover large column free open spaces. To ensure design reliability under service conditions, detailed knowledge about different behavioral aspects of conoidal shell is necessary. Hence, in this paper, static bending, free and forced vibration responses of composite conoidal shells are studied. Lagrange's equation of motion is used in conjunction with Hamilton's principle to derive governing equations of the shell. A finite element code using eight noded curved quadratic isoparametric elements is developed to get the solutions. Uniformly distributed load for static bending analysis and three different load time histories for solution of forced vibration problems are considered. Eight different stacking sequences of graphite-epoxy composite and two different boundary conditions are taken up in the present study. The study shows that relative performances of different shell combinations in terms of static behaviour cannot provide an idea about how they will relatively behave under dynamic loads and also the fact that the points of occurrence of maximum static and dynamic displacement may not be same on a shell surface.

• 대한조선학회논문집
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• 제36권3호
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• pp.134-143
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• 1999

선박의 선미부와 선수부는 복잡한 곡을 가진 블록들의 조립으로 만들어진다. 이러한 복잡한 곡률 분포를 가진 이중 곡면을 성형하기 위해서 조선소에서는 롤러 굽힘 가공과 선상 가열을 이용하고 있다. 일차적으로는 롤러 굽힘에 의한 가공으로 실린더 형상이나 원추 형상의 곡면을 만들고 난 후, 선상 가열을 수행하여 목적 형상으로 이차 가공을 한다. 본 논문은 곡면 가공에서 선행되는 일차 가공의 정보로서 가공 방향과 가공 후 형상을 결정하는데 목적이 있다. 목적 형상의 가우스 변환(Gauss mapping)으로부터 가공 방향에 관한 정보를 결정하고 목적 형상과 롤러 굽힘 가공에 의해 변형된 판 사이의 기하학적 관계를 이용하여 롤러 굽힘 가공의 모양을 결정하는 알고리즘을 제시하였다.

• Earthquakes and Structures
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• 제16권1호
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• pp.55-67
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• 2019

The finite solutions of deflection and the corresponding in-plane stress values of the graded sandwich shallow shell structure are computed in this research article via a higher-order polynomial shear deformation kinematics. The shell structural equilibrium equation is derived using the variational principle in association with a nine noded isoprametric element (nine degrees of freedom per node). The deflection values are computed via an own customized MATLAB code including the current formulation. The stability of the current finite element solutions including their accuracies have been demonstrated by solving different kind of numerical examples. Additionally, a few numerical experimentations have been conducted to show the influence of different design input parameters (geometrical and material) on the flexural strength of the graded sandwich shell panel including the geometrical configurations.

• Steel and Composite Structures
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• 제44권2호
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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%.

• Steel and Composite Structures
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• 제25권3호
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• pp.337-346
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• 2017

Sandwich shells made of composite materials are the main focus on recent literature parallel to the requirements of industry. They are commonly chosen for the modern engineering applications which require moderate strength to weight ratio without dependence on conventional manufacturing techniques. The investigations on hyperbolic paraboloidal formed sandwich composite shells are limited in the literature contrary to shells that have a number of studies, consisting of doubly curved surfaces, arbitrary boundaries and laminations. Because of the lack of contributive data in the literature, the aim of this study is to present the effects of curvature on hyperbolic paraboloidal formed, layered sandwich composite surfaces that have arbitrary boundary conditions. Analytical solution methodology for the analyses of stresses and deformations is based on Third Order Shear Deformation Theory (TSDT). Double Fourier series, which are specialized for boundary discontinuity, are used to solve highly coupled linear partial differential equations. Numerical solutions showing the effects of shell geometry are presented to provide benchmark results.

• Steel and Composite Structures
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• 제28권3호
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• pp.389-401
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• 2018

An isoparametric six-node triangular element is utilized for geometrically nonlinear analysis of functionally graded (FG) shells. To overcome the shear and membrane locking, the element is improved by using strain interpolation functions. The Total Lagrangian formulation is employed to include the large displacements and rotations. Finding the nonlinear behavior of FG shells via laminated modeling is also the goal. A power function is employed to formulate the variation of elastic modulus through the thickness of shells. The results are presented in two ways, including the general FGM formulation and the laminated modeling. The equilibrium path is obtained by using the Generalized Displacement Control Method. Some popular benchmarks, including hyperbolical shell structures are solved to declare the correctness and accuracy of proposed formulations.

• 대한기계학회논문집A
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• 제31권12호
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• pp.1180-1187
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• 2007

In the present work, topology optimization method using adaptive inner-front level set method is presented. In the conventional level set based topology optimization method, there exists an incapability for inner-front creation during optimization process. In this regard, as a new attempt to avoid and to overcome the limitation, an inner-front creation algorithm is proposed. In the inner-front creation algorithm, the strain energy density of a structure along with volume constraint is considered. Especially, to facilitate the inner-front creation process during the optimization process, the inner-front creation map which corresponds to the discrete valued function of strain energy density is constructed. In the evolution of the level set function during the optimization process, the least-squares finite element method (LSFEM) is employed. As an application to shell structures, the lightweight design of doubly curved shell and segmented mirror is carried out.

• Structural Engineering and Mechanics
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• 제13권5호
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• pp.533-542
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• 2002

This paper considers the buckling and post-buckling behavior of empty metal storage tanks under wind load. The structures of such tanks may be idealized as cantilever cylindrical shells, and the structural response is investigated using a computational model. The modeling employs a doubly curved finite element based on a theory by Simo and coworkers, which is capable of handling large displacements and plasticity. Buckling results for tanks with four different geometric relations are presented to consider the influence of the ratios between the radius and the height of the shell (R/L), and between the radius and the thickness (R/t). The studies aim to clarify the differences in the shells regarding their imperfection-sensitivity. The results show that thin-walled short tanks, with R/L = 3, display high imperfection sensitivity, while tanks with R/L = 0.5 are almost insensitive to imperfections. Changes in the total potential energy of tanks that would buckle under the same high wind pressures are also considered.