Thermal Stresses in Thick-Walled Circular Cylinders Under Axisymmetric Temperature Distribution

1971 ◽  
Vol 93 (4) ◽  
pp. 969-975 ◽  
Author(s):  
K. W. Yang ◽  
C. W. Lee
Keyword(s):  
Temperature Distribution ◽  
Thin Shell ◽  
Shell Theory ◽  
Thermal Stresses ◽  
Three Dimensional ◽  
Circular Cylinders ◽  
Curved Surfaces ◽  
Present Solution ◽  
Axisymmetric Temperature ◽  
Thin Shell Theory

A series solution is obtained for thick-walled cylinders subjected to a temperature distribution which varies both radially and axially. The solution is based on three-dimensional linear theory of thermoelasticity, with appropriate approximations by neglecting small terms and using St. Venant’s principle. The internal and external curved surfaces are assumed traction-free. In each series of the solution the first term is identical to the thin shell theory and the subsequent correcting terms are expressed in increasing powers of the thickness-to-radius ratio. An illustrative example problem is solved by using the present solution, and the numerical results are compared with those based on the thin shell theory.

Comparisons of Paraboloidal Shells and Sinusoidal-Shaped Shells in Natural Frequencies

2019 ◽  
Vol 24 (3) ◽  
pp. 451-457
Author(s):  
Yeong-Bin Yang ◽  
Jae-Hoon Kang
Keyword(s):  
Thin Shell ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Thin Shells ◽  
Thick Shell ◽  
Cylindrical Coordinates ◽  
Thin Shell Theory

Natural frequencies and mode shapes are obtained for a sinusoidal-shaped shell of revolution by using the Ritz method from a three-dimensional (3-D) analysis instead of a mathematically two-dimensional (2-D) thin shell theory or high order thick shell theory. The present analysis uses circular cylindrical coordinates instead of 3-D shell coordinates, which have been used in traditional shell analyses. Convergence studies can analyze the first five frequencies to four-digit exactitude. Results are given for a variety of shallow and deep sinusoidal-shaped shells with different boundary conditions. The sinusoidal-shaped shells are very similar to paraboloidal shells in shape. The frequencies of the sinusoidal-shaped shells from the present 3-D method are compared with those from 2-D thin shell theories for paraboloidal shells. The present 3-D method is applicable to very thick as well as thin shells.

Comparisons of Paraboloidal Shells and Sinusoidal-Shaped Shells in Natural Frequencies

2019 ◽  
Vol 24 (2) ◽  
pp. 451-457
Author(s):  
Yeong-Bin Yang ◽  
Jae-Hoon Kang
Keyword(s):  
Thin Shell ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Thin Shells ◽  
Thick Shell ◽  
Cylindrical Coordinates ◽  
Thin Shell Theory

Natural frequencies and mode shapes are obtained for a sinusoidal-shaped shell of revolution by using the Ritz method from a three-dimensional (3-D) analysis instead of a mathematically two-dimensional (2-D) thin shell theory or high order thick shell theory. The present analysis uses circular cylindrical coordinates instead of 3-D shell coordinates, which have been used in traditional shell analyses. Convergence studies can analyze the first five frequencies to four-digit exactitude. Results are given for a variety of shallow and deep sinusoidal-shaped shells with different boundary conditions. The sinusoidal-shaped shells are very similar to paraboloidal shells in shape. The frequencies of the sinusoidal-shaped shells from the present 3-D method are compared with those from 2-D thin shell theories for paraboloidal shells. The present 3-D method is applicable to very thick as well as thin shells.

Turbulence-Induced Vibration Analysis of an Open Curved Thin Shell

2010 ◽  
Author(s):  
Mitra Esmailzadeh ◽  
Aouni A. Lakis
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Root Mean Square ◽  
Thin Shell ◽  
Shell Theory ◽  
Pressure Field ◽  
Mean Square Displacement ◽  
Mean Square ◽  
Cross Spectral Density ◽  
Thin Shell Theory

A method is presented to predict the root mean square displacement response of an open curved thin shell structure subjected to a turbulent boundary-layer-induced random pressure field. The basic formulation of the dynamic problem is an efficient approach combining classic thin shell theory and the finite element method. The displacement functions are derived from Sanders’ thin shell theory. A numerical approach is proposed to obtain the total root mean square displacements of the structure in terms of the cross-spectral density of random pressure fields. The cross-spectral density of pressure fluctuations in the turbulent pressure field is described using the Corcos formulation. Exact integrations over surface and frequency lead to an expression for the total root mean square displacement response in terms of the characteristics of the structure and flow. An in-house program based on the presented method was developed. The total root mean square displacements of a curved thin blade subjected to turbulent boundary layers were calculated and illustrated as a function of free stream velocity and damping ratio. A numerical implementation for the vibration of a cylinder excited by fully developed turbulent boundary layer flow was presented. The results compared favorably with those obtained using software developed by Lakis et al.

A NEW KIND OF SINGULAR STIFF PROBLEMS AND APPLICATION TO THIN ELASTIC SHELLS

1995 ◽  
Vol 05 (01) ◽  
pp. 47-66 ◽  
Author(s):  
D. CAILLERIE ◽  
E. SANCHEZ-PALENCIA
Keyword(s):  
Asymptotic Behavior ◽  
Local Structure ◽  
Thin Shell ◽  
Spectral Properties ◽  
Shell Theory ◽  
Stiff Problems ◽  
Medium Frequency ◽  
Limit Solution ◽  
General Configuration ◽  
Thin Shell Theory

We consider the asymptotic behavior of the solution of a class of problems involving a small parameter ε and ε2. This generalizes the “singular stiff” problems arising in classical thin shell theory. The new problems appear in theory of composite shells, when the local structure implies coupling between membrane stresses and flexions. According to specific hypotheses, this kind of problems contains singular perturbations and penalty problems where the limit solution belongs to a subspace G1 of the general configuration space V. In addition to the coercive problem, spectral properties are considered in the small and medium frequency ranges, including spectral families in the case without compactness.

Free vibration of bi-material cylindrical shells

2016 ◽  
Vol 230 (15) ◽  
pp. 2637-2649 ◽  
Author(s):  
Saeed Sarkheil ◽  
Mahmud S Foumani ◽  
Hossein M Navazi
Keyword(s):  
Exact Solution ◽  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
State Space ◽  
Thin Shell ◽  
Shell Theory ◽  
Circular Cylindrical Shell ◽  
Space Technique ◽  
Thin Shell Theory

Based on the Sanders thin shell theory, this paper presents an exact solution for the vibration of circular cylindrical shell made of two different materials. The shell is sub-divided into two segments and the state-space technique is employed to derive the homogenous differential equations. Then continuity conditions are applied where the material of the cylindrical shell changes. Shells with various combinations of end boundary conditions are analyzed by the proposed method. Finally, solving different examples, the effect of geometric parameters as well as BCs on the vibration of the bi-material shell is studied.

Vibration of Shallow Shells: A Review With Bibliography

1997 ◽  
Vol 50 (8) ◽  
pp. 431-444 ◽  
Author(s):  
K. M. Liew ◽  
C. W. Lim ◽  
S. Kitipornchai
Keyword(s):  
Thin Shell ◽  
Shell Theory ◽  
Free Vibration Analysis ◽  
Review Article ◽  
Shallow Shells ◽  
First Order ◽  
Recent Developments ◽  
Thick Shells ◽  
Thin Shell Theory ◽  
Introductory Review

This review article documents recent developments in the free vibration analysis of thin, moderately thick, and thick shallow shells. An introductory review of the studies in Kirchhoff-Love classical thin shell theory is given. The development of studies in moderately thick shells incorporating the effects of transverse shear deformation and rotary inertia is detailed. This review article mainly focuses on research advances in vibration studies since the 1970s using the classical Kirchhoff-Love, first-order, and higher-order theories. The validity and range of applicability of these theories are examined. There are 163 references listed at the end of the article.

scholarly journals Calculation method of locking torque based on elastic thin shell theory for hydraulic locking sleeve

2017 ◽  
Vol 9 (2) ◽  
pp. 168781401769269
Author(s):  
Ming Yan ◽  
Hai-Chao Liu
Keyword(s):  
Thin Shell ◽  
Shell Theory ◽  
Calculation Model ◽  
Thin Cylindrical Shell ◽  
Deformation Equation ◽  
Test Platform ◽  
Large Elastic Deformation ◽  
Five Axis ◽  
Thin Shell Theory ◽  
Rotational Freedom

The hydraulic locking sleeve is a key component of precision instruments such as five-axis machine tools, giant astronomical telescope, and satellite antenna. This is subjected to the action of pressure load causing large elastic deformation and locking the rotational freedom of feed shaft at any angle. The maximum locking torque is an important parameter for designing the hydraulic locking sleeve. First, the hydraulic locking sleeve is simplified as elastic thin cylindrical shell structure. Neglecting the bending and twisting effects, the calculation equations describing the deformation and stress state between the hydraulic locking sleeve and rotary shaft are derived by applying the theory of elastic thin shell. Then, taking into account that one end of the hydraulic lock sleeve is fixed to the shaft sleeve seat by the end face flange; the calculating formula of the maximum locking torque of the hydraulic locking sleeve is obtained by modifying the deformation equation based on moment model. Finally, a test platform of hydraulic locking sleeve is designed, which can measure the maximum locking torque of the hydraulic locking sleeve. The error between the calculation result of locking torque theoretical calculation model and the experimental measured value is <15%. As a result, the causes of the error are analyzed, and the effects of the shaft sleeve length, wall thickness, and radius on the maximum locking torque are calculated.

Three-Dimensional Vibration Analysis of Thick, Complete Conical Shells

2004 ◽  
Vol 71 (4) ◽  
pp. 502-507 ◽  
Author(s):  
Jae-Hoon Kang ◽  
Arthur W. Leissa
Keyword(s):  
Present Method ◽  
Shell Theory ◽  
Ritz Method ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Algebraic Polynomials ◽  
Shells Of Revolution ◽  
Conical Shells ◽  
Thin Shell Theory ◽  
Time Periodic

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution. Unlike conventional shell theories, which are mathematically two-dimensional (2D), the present method is based upon the 3D dynamic equations of elasticity. Displacement components ur,uz, and uθ in the radial, axial, and circumferential directions, respectively, are 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 conical shells are formulated, 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 conical shells. Novel numerical results are presented for thick, complete conical shells of revolution based upon the 3D theory. Comparisons are also made between the frequencies from the present 3D Ritz method and a 2D thin shell theory.

A Study on Gas Pressure for Superplastic Forming of Titanium Alloy Bellows

2005 ◽  
Vol 475-479 ◽  
pp. 3051-3054 ◽  
Author(s):  
Gang Wang ◽  
Jun Chen ◽  
X.Y. Ruan
Keyword(s):  
Titanium Alloy ◽  
Thin Shell ◽  
Deformation Theory ◽  
Shell Theory ◽  
Superplastic Forming ◽  
Gas Pressure ◽  
Forming Process ◽  
Compressive Axial Load ◽  
Thin Shell Theory ◽  
Gas Pressures

The complex superplastic forming (SPF) technology applying gas pressure and compressive axial load is an advanced forming method for bellows made of titanium alloy, which forming process consists of the three main forming phases namely bulging, clamping and calibrating phase. The influence of forming gas pressure in various phases on the forming process are analyzed and models of forming gas pressure for bellows made of titanium alloy are derived according to the thin shell theory and plasticity deformation theory. Using model values, taking a two-convolution DN250 bellows made of Ti-6Al-4V titanium alloy as an example, a series of superplastic forming tests are performed to evaluate the influence of the variation of forming gas pressure on the forming process. According to the experimental results models are corrected to make the forming gas pressures prediction more accurate.

Sign in / Sign up

Export Citation Format

Share Document