Some Results on the Analytical Solution of Cylindrical Shells With Large Openings

1991 ◽  
Vol 113 (2) ◽  
pp. 297-307 ◽  
Author(s):  
M.-D. Xue ◽  
Y. Deng ◽  
K.-C. Hwang
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Stress Analysis ◽  
Shallow Shell ◽  
Cylindrical Shells ◽  
Geometric Description ◽  
Present Solution ◽  
Approximate Boundary Conditions ◽  
Shell Equation ◽  
Good Agreement

An analytical solution for cylindrical shells with large openings has been developed by the asymptotic method. In comparison with previous analytical solutions obtained by Eringen, Van Dyke and Lekkerkerker, the following three areas have been improved by the present method: 1) The modified Morley’s equation, which is applicable to ro/RT≫1, is used instead of Donnell’s shallow shell equation. 2) The accurate expression of boundary curve of hole is expanded in terms of powers of ρo = ro/R, while the previous approximate geometric description corresponds to the first term of the expansion. 3) The accurate boundary conditions for generalized forces are expanded in terms of powers of ρo and truncated after the terms of ρo3; the previous approximate boundary conditions correspond to the terms of order up to ρo, in the asymptotic expansions. The present solutions are in good agreement with Van Dyke’s solutions for small openings. The analytical results show that the error caused by the previous approximate boundary conditions is significant and has the order O(ρo); the error caused by the previous approximate geometric description of hole boundary has the order O(ρo2); and finally, the error caused by using Donnell’s shallow shell equation is very small for ρo ≤ 0.7. For openings with ρo > 0.25, say, noticeable differences exist between the present and the previous results. The stress analysis of cylindrical shells connected with nozzles has been developed by using the present solution. For increasing the accuracy of stress analysis in the nozzle, the exact description of the edge of nozzle is given and the near-edge boundary layer stress state in the nozzle is considered. The results obtained are in good agreement with those by Eringen for small openings and with those by F.E.M. and experiments for large openings.

Frequency and damping of non-axisymmetric surface oscillations of a viscous cylindrical liquid bridge

2011 ◽  
Vol 681 ◽  
pp. 597-621 ◽  
Author(s):  
RANGACHARI KIDAMBI
Keyword(s):  
Boundary Conditions ◽  
Liquid Bridge ◽  
Slenderness Ratio ◽  
Surface Boundary ◽  
Test Functions ◽  
Free Standing ◽  
Surface Boundary Conditions ◽  
Present Solution ◽  
Suitable Space ◽  
Good Agreement

We present a semi-analytic solution for the non-axisymmetric oscillations of a viscous cylindrical free-standing liquid bridge formed between two coaxial discs of radius R. Even though a streamfunction does not exist, a Helmholtz decomposition is used to obtain an analytic representation of the velocity field. An eigenvalue problem is formulated by projecting the free-surface boundary conditions onto a suitable space of test functions. This is then solved iteratively along with the dispersion relation obtained from the satisfaction of endwall boundary conditions. Extensive comparison with previous theoretical and numerical results, for a range of Reynolds number and bridge slenderness ratio, shows very good agreement in most cases. The present solution generalises that of Tsamopoulos, Chen & Borkar (J. Fluid Mech., vol. 235, 1992, p. 579), which employed a streamfunction formulation and was for the axisymmetric case.

scholarly journals Analytical solution for free vibrations of rotating cylindrical shells having free boundary conditions

2017 ◽  
Vol 132 ◽  
pp. 152-171 ◽  
Author(s):  
N. Alujević ◽  
N. Campillo-Davo ◽  
P. Kindt ◽  
W. Desmet ◽  
B. Pluymers ◽  
...  
Keyword(s):  
Free Boundary ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Free Boundary Conditions

scholarly journals An Experimental Investigation of Modal Densities of Composite Honeycomb Sandwich Cylindrical Shells

2020 ◽  
Vol 25 (1) ◽  
pp. 112-120
Author(s):  
K. Renji ◽  
S. Josephine Kelvina Florence ◽  
Sameer Deshpande
Keyword(s):  
Boundary Conditions ◽  
Cylindrical Shells ◽  
Sandwich Composite ◽  
Modal Density ◽  
Bending Mode ◽  
Honeycomb Sandwich ◽  
Sandwich Type ◽  
The Face ◽  
Honeycomb Sandwich Composite ◽  
Good Agreement

Honeycomb sandwich composite cylindrical shells are widely used in aerospace structures. Experimentally observed modal densities of such shells are not reported. In this work, modal densities of a typical honeycomb sandwich composite cylinder are obtained experimentally by measuring the drive point admittance. The results are in good agreement with those estimated theoretically that incorporated transverse shear deformation. Its limitations at higher frequencies are investigated and the frequency beyond which the estimation is in error is determined. The results provide an example to prove the need for measuring the imaginary part of the driving point admittance and using it in the determination of the modal densities of honeycomb sandwich-type structures. Experiments are carried out with two boundary conditions for the cylinder and the results provide experimental evidence for the fact that the modal densities at high frequencies do not depend on the boundary conditions. At higher frequencies, it is expected that both of the face sheets vibrate independently. This frequency can be approximately estimated as the fundamental bending mode frequency of the wall of the honeycomb core. The modal density determined through the measured driving point admittance will have a sharp reduction at this frequency and this feature can be used in identifying this phenomenon. The experimental results are in very good agreement with the above results.

Stress analysis of cylindrical shells with nozzles due to external run pipe moments

2000 ◽  
Vol 35 (3) ◽  
pp. 159-170 ◽  
Author(s):  
M. D Xue ◽  
H. H Wang ◽  
K. C Hwang
Keyword(s):  
Thin Shell ◽  
Cylindrical Shells ◽  
Large Diameter ◽  
Three Dimensional ◽  
Diameter Ratio ◽  
Test Results ◽  
Present Solution ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element ◽  
Good Agreement

In this paper the analytical results of two normally intersecting cylindrical shells subjected to external moments on the ends of main shells are presented. The thin shell theoretical solutions are obtained on the basis of the modified Morley equation for the main shell with a cut out with large diameter ratio and of the Goldenveizer equation for the branch tube with a nonplaner end. The results are in good agreement with the previous test results and with Moffat's three-dimensional finite element method results. The design curves based on the present solution can be applied to d/D ≤ 0.8 successfully.

scholarly journals Analytical Solution for Free Vibrations of a Moderately Thick Rectangular Plate

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Ivo Senjanović ◽  
Marko Tomić ◽  
Nikola Vladimir ◽  
Dae Seung Cho
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Thick Plate ◽  
Mixed Boundary ◽  
Separation Of Variables ◽  
Equations Of Motion ◽  
Mixed Boundary Conditions ◽  
Free Vibrations ◽  
Force Displacement ◽  
Good Agreement

In the present thick plate vibration theory, governing equations of force-displacement relations and equilibrium of forces are reduced to the system of three partial differential equations of motion with total deflection, which consists of bending and shear contribution, and angles of rotation as the basic unknown functions. The system is starting one for the application of any analytical or numerical method. Most of the analytical methods deal with those three equations, some of them with two (total and bending deflection), and recently a solution based on one equation related to total deflection has been proposed. In this paper, a system of three equations is reduced to one equation with bending deflection acting as a potential function. Method of separation of variables is applied and analytical solution of differential equation is obtained in closed form. Any combination of boundary conditions can be considered. However, the exact solution of boundary value problem is achieved for a plate with two opposite simply supported edges, while for mixed boundary conditions, an approximate solution is derived. Numerical results of illustrative examples are compared with those known in the literature, and very good agreement is achieved.

An Analytical Method for Cylindrical Shells With Nozzles Due to Internal Pressure and External Loads—Part I: Theoretical Foundation

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Ming-De Xue ◽  
Qing-Hai Du ◽  
Keh-Chih Hwang ◽  
Zhi-Hai Xiang
Keyword(s):  
Analytical Solution ◽  
Internal Pressure ◽  
Stress Analysis ◽  
Pressure Vessel ◽  
Cylindrical Shells ◽  
Branch Pipe ◽  
Theoretical Solution ◽  
External Branch ◽  
Complex Valued ◽  
External Loads

An improved version of the analytical solutions by Xue, Hwang and co-workers (1991, “Some Results on Analytical Solution of Cylindrical Shells With Large Opening,” ASME J. Pressure Vessel Technol., 113, 297–307; 1991, “The Stress Analysis of Cylindrical Shells With Rigid Inclusions Having a Large Ratio of Radii,” SMiRT 11 Transactions F, F05/2, 85–90; 1995, “The Thin Theoretical Solution for Cylindrical Shells With Large Openings,” Acta Mech. Sin., 27(4), pp. 482–488; 1995, “Stresses at the Intersection of Two Cylindrical Shells,” Nucl. Eng. Des., 154, 231–238; 1996, “A Reinforcement Design Method Based on Analysis of Large Openings in Cylindrical Pressure Vessels,” ASME J. Pressure Vessel Technol., 118, 502–506; 1999, “Analytical Solution for Cylindrical Thin Shells With Normally Intersecting Nozzles Due to External Moments on the Ends of Shells,” Sci. China, Ser. A: Math., Phys., Astron., 42(3), 293–304; 2000, “Stress Analysis of Cylindrical Shells With Nozzles Due to External Run Pipe Moments,” J. Strain Anal. Eng. Des., 35, 159–170; 2004, “Analytical Solution of Two Intersecting Cylindrical Shells Subjected to Transverse Moment on Nozzle,” Int. J. Solids Struct., 41(24–25), 6949–6962; 2005, “A Thin Shell Theoretical Solution for Two Intersecting Cylindrical Shells Due to External Branch Pipe Moments,” ASME J. Pressure Vessel Technol., 127(4), 357–368; 2005, “Theoretical Stress Analysis of Two Intersecting Cylindrical Shells Subjected to External Loads Transmitted Through Branch Pipes,” Int. J. Solids Struct., 42, 3299–3319) for two normally intersecting cylindrical shells is presented, and the applicable ranges of the theoretical solutions are successfully extended from d/D≤0.8 and λ=d/(DT)1/2≤8 to d/D≤0.9 and λ≤12. The thin shell theoretical solution is obtained by solving a complex boundary value problem for a pair of fourth-order complex-valued partial differential equations (exact Morley equations (Morley, 1959, “An Improvement on Donnell’s Approximation for Thin Walled Circular Cylinders,” Q. J. Mech. Appl. Math. 12, 89–91; Simmonds, 1966, “A Set of Simple, Accurate Equations for Circular Cylindrical Elastic Shells,” Int. J. Solids Struct., 2, 525–541)) for the shell and the nozzle. The accuracy of results is improved by some additional terms to the expressions for resultant forces and moments in terms of complex-valued displacement-stress function. The theoretical stress concentration factors due to internal pressure obtained by the improved expressions are in agreement with previously published test results. The theoretical results discussed and presented herein are in sufficient agreement with those obtained from three dimensional finite element analyses for all the seven load cases, i.e., internal pressure and six external branch pipe load components involving three orthogonal forces and the respective three orthogonal moments.

An Exact Solution for Transient Anisotropic Heat Conduction in Composite Cylindrical Shells

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Hossein Rahmani ◽  
Mahmood Norouzi ◽  
Alireza Komeili Birjandi ◽  
Amir Komeili Birjandi
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Analytical Solution ◽  
Cylindrical Shells ◽  
Cylindrical Vessel ◽  
Conductive Heat ◽  
Composite Shells ◽  
Fiber Angle ◽  
Present Solution ◽  
Composite Cylindrical Shells

Abstract In this study, an analytical solution is proposed for the problem of transient anisotropic conductive heat transfer in composite cylindrical shells. The composite shells are considered to have directional heat transfer properties, which is due to the existence of fibers which can be winded in any direction. The composite shells usually show high conductivity in the direction parallel to fiber direction and low conductivity in other two orthogonal directions. To solve the heat transfer partial differential equation, finite Fourier transform and separation of variables method are used. The present solution is used to find the temperature distribution in a composite cylindrical vessel for which the composite material is graphite/epoxy and the vessel is prone to an external heat flux and also ambient flow. The analytical solution is verified perfectly by the data obtained from a second-order finite difference solution. The solution is used to investigate the effects of values of fiber angle and material conductivity coefficients on temperature distribution of the composite cylindrical vessel. The results show the important role of fiber angle values on the temperature distribution of vessel.

Buckling of Circular Cylindrical Shells Using a Displacement Function

1974 ◽  
Vol 96 (4) ◽  
pp. 1322-1327
Author(s):  
Shun Cheng ◽  
C. K. Chang
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Displacement Function ◽  
Combined Loading ◽  
Trial Solution ◽  
Governing Differential Equation ◽  
Circular Cylindrical Shells ◽  
The Stability

The buckling problem of circular cylindrical shells under axial compression, external pressure, and torsion is investigated using a displacement function φ. A governing differential equation for the stability of thin cylindrical shells under combined loading of axial compression, external pressure, and torsion is derived. A method for the solutions of this equation is also presented. The advantage in using the present equation over the customary three differential equations for displacements is that only one trial solution is needed in solving the buckling problems as shown in the paper. Four possible combinations of boundary conditions for a simply supported edge are treated. The case of a cylinder under axial compression is carried out in detail. For two types of simple supported boundary conditions, SS1 and SS2, the minimum critical axial buckling stress is found to be 43.5 percent of the well-known classical value Eh/R3(1−ν2) against the 50 percent of the classical value presently known.

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