• 한국정밀공학회지
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• 제9권4호
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• pp.118-125
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• 1992

Theoretical equations for hoop stress, longitudinal or meridian stress and Von Mises stress of an axismmetric conical pressure vessel and a frustum of conical pressure velle, both of which are pressuized by hydrostatic loading, are derived from equilibrium equations. The membrane stresses conputed by theoretical equations for a conical pressure vessel and a frustum of conical pressure vessel are compared with the values obtained from finite elelment method. Based on the fact that the computational values by theoretical equations are well agreed with the finite element results, derived equations are proved to be valid and it is possible for those equations to be conveniently used for structural analysis or design of frustum of conical pressure vessel which is a part of silo body.

• Journal of Mechanical Science and Technology
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• 제20권11호
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• pp.1848-1862
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• 2006

As a basic study on the fluid-structure interaction of the shell structure, a theoretical formulation has been suggested on the free vibration of a thin-walled conical frustum shell filled with an ideal fluid, where the shell is assumed to be fixed at both ends. The motion of fluid coupled with the shell is determined by means of the velocity potential flow theory. In order to calculate the normalized natural frequencies that represent the fluid effect on a fluid-coupled system, finite element analyses for a fluid-filled conical frustum shell are carried out. Also, the effect of apex angle on the frequencies is investigated.

• 한국자동차공학회논문집
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• 제3권6호
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• pp.96-111
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• 1995

A bellows is a component installed in the automobile exhaust system to reduce the impact from an engine. It's stiffness has a great influence on the natural frequency of the system. Therefore, it must be designed to keep the specified stiffness that requires in the system. This study present the finite element analysis of U-typed bellows using a curved conical frustum element and the shape optimal design with specified stiffness. The finite element analysis is verified by comparing with the experimental results. In the shape optimal design, the weight is considered as the cost function. The specified stiffness from the system design is transformed to equality constraints. The formulation has inequality constraints imposed on the fatigue limit, the natural frequencies, the buckling load and the manufacturing conditions. A procedure for shape optimization adopts a thickness, a corrugation radius, and a length of annular plate as optimal design variables. The external loading conditions include the axial and lateral loads with a boundary condition fixed at an end of the bellows. The recursive quadratic programming algorithm is selected to solve the problem. The result are compared with the existing bellows, and the characteristics of the bellows is investigated through the optimal design process. The optimized shape of the bellows are expected to give quite a good guideline to the practical design.

• Journal of Advanced Marine Engineering and Technology
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• 제23권5호
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• pp.702-710
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• 1999

U-shaped bellows are usually used to piping system pressure sensor and controller for refriger-ator. Bellows subjected to internal pressure are designed for the purpose of absorbing deformation. Internal pressure on the convolution sidewall and end collar will be applied to an axial load tend-ing to push the collar away from the convolutions. To find out deformation behavior of bellow sub-jected to internal pressure the axisymmetric shell theory using the finite element method is adopted in this paper. U-shaped bellows can be idealized by series of conical frustum-shaped ele-ments because it is axisymmetric shell structure. The displacements of nodal points due to small increment of force are calculated by the finite element method and the calculated nodal displace-ments are added to r-z cylindrical coordinates of nodal points. The new stiffness matrix of the sys-tem using the new coordinates of nodal points is adopted to calculate the another increments of nodal displacement that is the step by step method is used in this paper. The force required to deflect bellows axially is a function of the dimensions of the bellows and the materials from which they are made. Spring constant is analyzed according to the changing geometric factors of U-shaped bellows. The FEM results were agreed with experiment. Using developed FORTRAN PROGRAM the internal pressure vs. deflection characteristics of a particu-lar bellows can be predicted by input of a few factors.

• 대한기계학회논문집A
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• 제21권8호
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• pp.1195-1208
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• 1997

Bellows is a component in piping systems which absorbs mechanical deformation with flexibility. Its geometry is an axial symmetric shell which consists of two toroidal shells and one annular plate or conical shell. In order to analyze bellows, this study presents the finite element analysis using a conical frustum shell element. A finite element analysis is developed to analyze various bellows. The validity of the developed program is verified by the experimental results for axial and lateral stiffness. The formula for calculating the natural frequency of bellows is made by the simple beam theory. The formula for fatigue life is also derived by experiments. The shape optimal design problem is formulated using multiple objective optimization. The multiple objective functions are transformed to a scalar function by weighting factors. The stiffness, strength and specified stiffness are considered as the multiple objective function. The formulation has inequality constraints imposed on the fatigue limit, the natural frequencies, and the manufacturing conditions. Geometric parameters of bellows are the design variables. The recursive quadratic programming algorithm is selected to solve the problem. The results are compared to existing bellows, and the characteristics of bellows is investigated through optimal design process. The optimized shape of bellows is expected to give quite a good guideline to practical design.

• 대한기계학회논문집
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• 제12권6호
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• pp.1273-1281
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• 1988

본 연구에서는 복합 셸구조에 유리한 축대칭 원추대 요소(axisymmetric coni- cal frustum element)의 유한 요소법을 이용하였고, 고유 진동수와 진동 모우드를 구 하여 벨로우즈의 동특성을 규명하였다. 또한, 벨로우즈의 기하학적인 형상을 변수로 한 동특성의 변화를 검토하여 벨로우즈의 동적인 안정성에 관한 설계 자료를 제시하고 자 하였다.

• 오토저널
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• 제9권4호
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• pp.61-68
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• 1987

The Bellows Joint which was used as a absorber or safety equipment to prevent the deformation or fracture of a structure, have been analyzed by the F.E.M using axi-symmetric conical frustum element. Using the F.E.M the general behavior of Bellows Joint corrugation can be investigated easily, and the stability of the analysis be guaranteed. In annular type corrugation, the F.E.M results were agreed with those of other theoretical analyses, but in the U type corrugation, the F.E.M results were more acceptable than those of others.

• 기계저널
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• 제16권2호
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• pp.100-107
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• 1976

Stress analysis of tapered cylinder of reactor vessels is investigated by means of the intersection method. The tapered cylinder is approximated into three models-average cylinder, conical frustum, and ring. The results are compared with those of the finite element method program and an experiment. In this paper, the following results are obtained: (1) the best aproximation has been obtained by the ring model analysis: (2) the intersection analysis of the tapered cylinder by the ring model shows a sufficient accuracy for the stress analysis of reactor vessels.

• 대한기계학회논문집
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• 제19권6호
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• pp.1439-1450
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• 1995

Bellows is a familiar component in piping systems as it provides a relatively simple means of absorbing thermal expansion and providing system flexibility. In routine piping flexibility analysis by finite element methods, bellows is usually considered to be straight pipe runs modified by an appropriate flexibility factor; maximum stresses are evaluated using a corresponding stress concentration factor. The aim of this study is to develop a bellows finite element, which similarly includes more complex shell type deformation patterns. This element also does not require flexibility or stress factors, but evaluates more detailed deformation and stress patterns. The proposed bellows element is a 3-D, 2-noded line element, with three degrees of freedom per node and no bending. It is formulated by including additional 'internal' degrees of freedom to account for the deformation of the bellows corrugation; specifically a quarter toroidal section of the bellows, loaded by axial force, is considered and the shell type deformation of this is include by way of an approximating trigonometric series. The stiffness of each half bellows section may be found by minimising the potential energy of the section for a chosen deformation shape function. An experiment on the flexibility is performed to verify the reliability for bellows finite element.

• 한국공작기계학회논문집
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• 제13권6호
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• pp.102-106
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• 2004

The purpose of the study is to perform structual analysis of 9 type bellows for automotive. The bellows joint which was used as a absorber or safety equipment to prevent the deformation or fracture of a structure, has been analyzed by the FEM modeling using axi-symmetric conical frustum element. Using FEM the general behavior of bellows analysis can be investigate easily, as well as the stability of the analysis can be guarantee. The results of finite element structual analysis and actual result gave a good agreement.