• Title/Summary/Keyword: shell theories

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Vibrations of Complete Paraboloidal Shells with Variable Thickness form a Three-Dimensional Theory

  • Chang, Kyong-Ho;Shim, Hyun-Ju;Kang, Jae-Hoon
    • Journal of Korean Association for Spatial Structures
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    • v.4 no.4 s.14
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    • pp.113-128
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    • 2004
  • A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of solid paraboloidal and complete (that is, without a top opening) paraboloidal shells of revolution with variable wall thickness. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. The ends of the shell may be free or may be subjected to any degree of constraint. Displacement components $u_r,\;u_{\theta},\;and\;u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in ${\theta}$, and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the paraboloidal shells of revolution are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four digit exactitude is demonstrated for the first five frequencies of the complete, shallow and deep paraboloidal shells of revolution with variable thickness. Numerical results are presented for a variety of paraboloidal shells having uniform or variable thickness, and being either shallow or deep. Frequencies for five solid paraboloids of different depth are also given. Comparisons are made between the frequencies from the present 3-D Ritz method and a 2-D thin shell theory.

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A cylindrical shell model for nonlocal buckling behavior of CNTs embedded in an elastic foundation under the simultaneous effects of magnetic field, temperature change, and number of walls

  • Timesli, Abdelaziz
    • Advances in nano research
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    • v.11 no.6
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    • pp.581-593
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    • 2021
  • This model is proposed to describe the buckling behavior of Carbon Nanotubes (CNTs) embedded in an elastic medium taking into account the combined effects of the magnetic field, the temperature, the nonlocal parameter, the number of walls. Using Eringen's nonlocal elasticity theory, thin cylindrical shell theory and Van der Waal force (VdW) interactions, we develop a system of partial differential equations governing the buckling response of CNTs embedded on Winkler, Pasternak, and Kerr foundations in a thermal-magnetic environment. The pre-buckling stresses are obtained by applying airy's stress function and an adjacent equilibrium criterion. To estimate the nonlocal critical buckling load of CNTs under the simultaneous effects of the magnetic field, the temperature change, and the number of walls, an optimization technique is proposed. Furthermore, analytical formulas are developed to obtain the buckling behavior of SWCNTs embedded in an elastic medium without taking into account the effects of the nonlocal parameter. These formulas take into account VdW interactions between adjacent tubes and the effect of terms involving differences in tube radii generally neglected in the derived expressions of the critical buckling load published in the literature. Most scientific research on modeling the effects of magnetic fields is based on beam theories, this motivation pushes me to develop a cylindrical shell model for studying the effect of the magnetic field on the static behavior of CNTs. The results show that the magnetic field has significant effects on the static behavior of CNTs and can lead to slow buckling. On the other hand, thermal effects reduce the critical buckling load. The findings in this work can help us design of CNTs for various applications (e.g. structural, electrical, mechanical and biological applications) in a thermal and magnetic environment.

Free vibration analysis of orthotropic and laminated composite circular cylindrical shells (직교이방성 복합재료 원통셀의 자유진동 해석)

  • 이영신;문홍기
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.10 no.5
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    • pp.758-769
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    • 1986
  • A general analytical procedure is developed for evaluating the free vibration characteristics of orthotropic and laminated composite circular cylindrical shells. The solution is obtained through a direct solution procedure with axial mode displacements presented as simple Fourier series expressions. On the basis of the various thin shell theories most commonly used, the frequency equation is derived and is expressed in a unified form. The present analysis can deal with shells which are made of an arbitrary number of bonded layers each with a different thickness and different elastic orthotropic properties, and have classical boundary conditions of any kind. Several examples are shown with the consideration of the effects of fiber orientations and boundary conditions as well as different shell geometries and material properties. To verify the validity and accuracy of this analysis, the results are compared with the experimental and analytical results of other workers. Agreement among the various results is found to be fairly good.

Human Error Analysis Technique and Its Application to Marine Accidents

  • Na, Seong;Kim, Hong-Tae;Kim, Hye-Jin;Ha, Wook-Hyun
    • Journal of Navigation and Port Research
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    • v.34 no.2
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    • pp.145-152
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    • 2010
  • The management of safety at sea is based on a set of internationally accepted regulations and codes, governing or guiding the design and operation of ships. The regulations most directly concerned with human safety and protection of the environment are, in general, agreed internationally through the International Maritime Organization(IMO). IMO has continuously dealt with safety problems and, recognized that the human element is a key factor in both safety and pollution prevention issues(IMO, 2010). This paper proposes a human error analysis methodology which is based on the human error taxonomy and theories (SHELL model, GEMS model and etc.) that were discussed in the IMO guidelines for the investigation of human factors in marine casualties and incidents. In this paper, a cognitive process model, a human error analysis technique and a marine accident causal chains focused on human factors are discussed, and towing vessel collision accidents are analyzed as a case study in order to examine the applicability of the human error analysis technique to marine accidents. Also human errors related to those towing vessel collision accidents and their underlying factors are discussed in detail.

A study of dietetic on the gastric & duodenal ulcer (위.십이지장궤양의 식요방법(食療方法)에 관한 연구)

  • Baek Tae-Hyeun
    • The Journal of Internal Korean Medicine
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    • v.24 no.2
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    • pp.233-248
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    • 2003
  • Objectives : This research examined about dietary therapy on the gastric & duodenal ulcer based on the literary findings, for clinical treatment and prevention of the gastric & duodenal ulcer. Methods : This Research examined on histories, compositions, applications, and effects of dietetic on about 200 cases of dietary therapy of the gastric & duodenal ulcer from recent Chinese literatures Results : 1. Various vegetables, animals and mineral materials including herbs, grains, vegetables, fruits, food and drink were used for the dietary therapy. 2. Methods of the preparation for use as therapeutics were decoction, pulvis, gruel, medicinal wine, cake, tea, paste and gelatin and etc. 3. Frequently used materials were cuttle fish bone, Bletillae rhizoma, oyster shell, egg shell, sugar, aloe, licorice, lily, red jujube, and pig stomach. 4. Four properties of cold, warm, cool and hot were equal in frequencies. Most common tastes were sweet and bitter. Conclusion : Though dietary therapy for the gastric & duodenal ulcer is not based on clinical or experimental data, but through experience. It is mostly based on Yin-Yang and five elements, visceral manifestation, channels and their collateral channels and chinese herbal medicine theories. If we use them properly according to oriental medicine method, it will be effective on treating and preventing the gastric & duodenal ulcer.

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A Coupled Analysis of Smart Plate Under Electro-Mechanical Loading Using Enhanced Lower-Order Shear Deformation Theory (개선된 저차 전단 변형 이론을 이용한 전기, 기계 하중을 받는 스마트 복합재 구조물의 연성 해석)

  • Oh, Jin-Ho;Cho, Maeng-Hyo;Kim, Jun-Sik
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.31 no.1 s.256
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    • pp.121-128
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    • 2007
  • Enhanced lower order shear deformation theory is developed in this study. Generally, lower order theories are not adequate to predict accurate deformation and stress distribution through the thickness of laminated plate. For the accurate prediction of detailed stress and deformation distributions through the thickness, higher order zigzag theories have been proposed. However, in most cases, simplified zigzag higher order theory requires $C_1$, shape functions in finite element implementation. In commercial FE softwares, $C_1$, shape functions are not so common in plate and shell analysis. Thus zigzag theories are useful for the highly accurate prediction of thick composite behaviors but they are not practical in the sense that they cannot be used conveniently in the commercial package. In practice, iso-parametric $C_0$ plate model is the standard model for the analysis and design of composite laminated plates and shells. Thus in the present study, an enhanced lower order shear deformation theory is developed. The proposed theory requires only $C_0$ shape function in FE implementation. The least-squared energy error between the lower order theory and higher order theory is minimized. An enhanced lower order shear deformation theory(ELSDT) in this paper is proposed for smart structure under complex loadings. The ELSDT is constructed by the strain energy transformation and fully coupled mechanical, electric loading cases are studied. In order to obtain accurate prediction, zigzag in-plane displacement and transverse normal deformation are considered in the deformation Held. In the electric behavior, open-circuit condition as well as closed-circuit condition is considered. Through the numerous examples, the accuracy and robustness of present theory are demonstrated.

A Study of Literature Review on Chinese Pediatrics (중국(中國) 소아과학(小兒科學)의 사적(史的) 고찰(考察)(고대(古代)부터 청대(淸代)까지))

  • Lee Hoon;Lee Jin-Yong
    • The Journal of Pediatrics of Korean Medicine
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    • v.13 no.1
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    • pp.63-138
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    • 1999
  • From all possible chinese medical literatures, I studied the history of chinese pediatrics by dividing into Chunqiu Zhanguo, QinHan dynasties, LiangJin, SuiTang five dynasties, Song Dynasty, Jin and Yuan dynasties, Ming Qing dynasties. The conclusions are summarized as followings 1. The mentions related with pediatrics existed already in Yan ruins turtle shell letters, and 〈Yellow Emperor's classic of internal medicine> in Chunqiu Zhanguo time formed the system of medicine, established the theoretical foundation. 2. Chang Ji established the system of diagnosis and treatment based on overall analysis of symptoms and signs in , and later pediatricians commonly applied his prescriptions to the febrile diseases. 3. The period from LiangJin to SuiTang, Pediatrics was established as special department then in , Chao Yuanfang stated the etiology, pathogenesis, symptomatology of pediatric diseases. 4. In Song dynasty. pediatric 4 major, symptoms that had been mentioned from SuiTang dynasties, were clearly established, pediatrical special books were published, and written by Qian Yi who is considered as the founder of chinese pediatrics, established the foundation of pediatrical division formation in distinction from adult fields. 5. In Jin and Yuan dynasties, four eminent physicians established the actual relationship between the theories and practical applications and insisted various and creative theories based on the classical medicine, for example, the theory that fire and heat in the body was the main cause of diseases of Liu Wansu purgation theory of Zhang Congzheng, qi regulating theory of Liu Gao, ministerial fire theory and the theory that yang is ever in excess while Yin is ever deficient of Zhu Zhenheng, etc, and they applied those theories to pediatrical various sides. 6, In Ming Qing dynasties, pediatrical specialists and pediatrical publications had increased, eg, father and son Xue Kai Xue Ji, Wan Quan, Lu Bai-si, etc in Ming dynasty, Ye Gui, Chen Fuzheng, Xia Ding, etc in Qing dynasty were famous as pediatricians. Specially, the doctrine of epidemic febrile diseases at that time showed prominent effects to children's epidemic febrile diseases.

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Vibration Analysis of Thick Hyperboloidal Shells of Revolution from a Three-Dimensional Analysis (두꺼운 축대칭 쌍곡형 쉘의 3차원 진동해석)

  • 심현주;강재훈
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.16 no.4
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    • pp.419-429
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    • 2003
  • A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies of thick, hyperboloidal shells of revolution. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components u/sub r/, u/sub θ/, u/sub z/ in the radial, circumferential, and axial directions, respectively, we taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the r and z directions. Potential(strain) and kinetic energies of the hyperboloidal shells are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four digit exactitude is demonstrated for the first five frequencies of the hyperboloidal shells of revolution. Numerical results are tabulated for eighteen configurations of completely free hyperboloidal shells of revolution having two different shell thickness ratios, three variant axis ratios, and three types of shell height ratios. Poisson's ratio (ν) is fixed at 0.3. Comparisons we made among the frequencies for these hyperboloidal shells and ones which ate cylindrical or nearly cylindrical( small meridional curvature. ) The method is applicable to thin hyperboloidal shells, as well as thick and very thick ones.

Structural behavior of aluminum reticulated shell structures considering semi-rigid and skin effect

  • Liu, Hongbo;Chen, Zhihua;Xu, Shuai;Bu, Yidu
    • Structural Engineering and Mechanics
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    • v.54 no.1
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    • pp.121-133
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    • 2015
  • The aluminum dome has been widely used in natatorium, oil storage tank, power plant, coal, as well as other industrial buildings and structures. However, few research has focused on the structural behavior and design method of this dome. At present, most designs of aluminum alloy domes have referred to theories and methods of steel spatial structures. However, aluminum domes and steel domes have many differences, such as elasticity moduli, roof structures, and joint rigidities, which make the design and analysis method of steel spatial structures not fully suitable for aluminum alloy dome structures. In this study, a stability analysis method, which can consider structural imperfection, member initial curvature, semi-rigid joint, and skin effect, was presented and used to study the stability behavior of aluminum dome structures. In addition, some meaningful conclusions were obtained, which could be used in future designs and analyses of aluminum domes.

Free vibration and elastic analysis of shear-deformable non-symmetric thin-walled curved beams: A centroid-shear center formulation

  • Kim, Nam-Il;Kim, Moon-Young
    • Structural Engineering and Mechanics
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    • v.21 no.1
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    • pp.19-33
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    • 2005
  • An improved shear deformable thin-walled curved beam theory to overcome the drawback of currently available beam theories is newly proposed for the spatially coupled free vibration and elastic analysis. For this, the displacement field considering the shear deformation effects is presented by introducing displacement parameters defined at the centroid and shear center axes. Next the elastic strain and kinetic energies considering the shear effects due to the shear forces and the restrained warping torsion are rigorously derived. Then the equilibrium equations are consistently derived for curved beams with non-symmetric thin-walled sections. It should be noticed that this formulation can be easily reduced to the warping-free beam theory by simply putting the sectional properties associated with warping to zero for curved beams with L- or T-shaped sections. Finally in order to illustrate the validity and the accuracy of this study, finite element solutions using the isoparametric curved beam elements are presented and compared with those in available references and ABAQUS's shell elements.