Some Remarks on Spherical Shells

1965 ◽  
Vol 32 (1) ◽  
pp. 121-128
Author(s):  
C. N. DeSilva ◽  
H. Cohen
Keyword(s):  
Asymptotic Solution ◽  
Spherical Shell ◽  
Variable Thickness ◽  
Transverse Shear ◽  
Correction Term ◽  
Transverse Shear Deformation ◽  
Governing Equations ◽  
Spherical Shells ◽  
Annular Disk ◽  
Thickness Function

The present paper treats the deformation of a spherical shell within the framework of a linear bending theory which includes the effect of transverse-shear deformation. A two-term asymptotic solution of the governing equations is obtained which embraces all terms of an order retained in the formulation of the theory. The solution is valid within a physically important domain of the shell and reduces to the previously known one-term asymptotic solution of the classical bending theory. The problem of variable thickness is also discussed. The behavior of the thickness function may be such as to require in the solution a correction term which may contribute significantly to the deformation. This solution is applied to a treatment of the deformation of a rotating, completely closed spherical shell stiffened by an annular disk located normal to the axis of the spin.

Numerical Investigation of the Flutter of a Spherical Shell

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Mohamed Menaa ◽  
Aouni A. Lakis
Keyword(s):  
Finite Element ◽  
Spherical Shell ◽  
High Speed ◽  
Structural Model ◽  
Correction Term ◽  
Theoretical Data ◽  
Element Formulation ◽  
Spherical Shells ◽  
Flow Parameters ◽  
Nodal Displacements

In this study, aeroelastic analysis of a spherical shell subjected to external supersonic airflow is carried out. The structural model is based on a combination of the linear spherical shell theory and the classic finite element method (FEM). In this hybrid method, the nodal displacements are found from the exact solution of shell governing equations rather than approximated by polynomial functions. Therefore, the number of elements chosen is a function of the complexity of the structure. Convergence is rapid. It is not necessary to choose a large number of elements to obtain good results. Linearized first-order potential (piston) theory with the curvature correction term is coupled with the structural model to account for pressure loading. The linear mass, stiffness, and damping matrices are found using the hybrid finite element formulation. Aeroelastic equations are numerically derived and solved. The results are validated using the numerical and theoretical data available in literature. The analysis is accomplished for spherical shells with different boundary conditions, geometries, flow parameters, and radius to thickness ratios. the results show that the spherical shell loses its stability through coupled-mode flutter. This proposed hybrid FEM can be used efficiently for the design and analysis of spherical shells employed in high speed aircraft structures.

A Theory of Torsional and Coupled Bending Torsional Waves in Thin-Walled Open Section Beams

1967 ◽  
Vol 34 (2) ◽  
pp. 337-343 ◽  
Author(s):  
H. R. Aggarwal ◽  
E. T. Cranch
Keyword(s):  
Transverse Shear ◽  
Torsion Theory ◽  
Transverse Shear Deformation ◽  
Governing Equations ◽  
High Frequencies ◽  
Wave Velocities ◽  
Open Section ◽  
Torsional Waves ◽  
Torsion Theories ◽  
Thin Walled

An appropriate torsion or coupled bending torsion theory is developed for the dynamic behavior of thin-walled open section beams. A new, more accurate set of governing equations is established which eliminate the short-wavelength defects of both the Saint-Venant and Timoshenko torsion theories. This theory, which includes warping and associated effects of longitudinal inertia and transverse shear deformation, while agreeing with previous theories for large wavelengths, leads to satisfactory finite wave velocities for short wavelengths and high frequencies. Dispersion and group velocity curves for wide-flanged and channel sections are displayed.

scholarly journals Non-linear analysis of laminated plates

2002 ◽  
Vol 24 (4) ◽  
pp. 197-208
Author(s):  
Dao Huy Bich
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Large Deformation ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Linear Analysis ◽  
Laminated Plates ◽  
Transverse Shear Deformation ◽  
Governing Equations ◽  
Non Linear

The governing equations of laminates plates taking into account the transverse shear deformation effects for large deformation are given. The formulation of Ritsz method and finite element method for non-linear analysis of this problem is presented

Transient Solutions of a Longitudinally Impacted Conical Shell

1971 ◽  
Vol 38 (2) ◽  
pp. 545-547 ◽  
Author(s):  
R. W. Mortimer ◽  
A. Blum
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Conical Shell ◽  
Method Of Characteristics ◽  
Shell Theory ◽  
Experimental Results ◽  
Transverse Shear Deformation ◽  
Longitudinal Impact ◽  
Governing Equations ◽  
Transient Solutions

A thin conical shell theory, which includes the effects of transverse and rotary inertias and transverse shear deformation, is used to analyze the response of a conical shell to longitudinal impact. The governing equations of this theory are solved by the method of characteristics and the results are compared to published experimental results.

A Comparison of Theoretical and Experimental Results From Spherical Shells With a Single Radially Attached Nozzle

1967 ◽  
Vol 89 (3) ◽  
pp. 333-338 ◽  
Author(s):  
F. J. Witt ◽  
R. C. Gwaltney ◽  
R. L. Maxwell ◽  
R. W. Holland
Keyword(s):  
Spherical Shell ◽  
Internal Pressure ◽  
Experimental Results ◽  
Strain Gages ◽  
Spherical Shells ◽  
Axial Thrust ◽  
Outside Diameter ◽  
Theoretical Results

A series of steel models having single nozzles radially and nonradially attached to a spherical shell is presently being examined by means of strain gages. Parameters being studied are nozzle dimensions, length of internal nozzle protrusions, and angles of attachment. The loads are internal pressure and axial thrust and moment loadings on the nozzle. This paper presents both experimental and theoretical results from six of the configurations having radially attached nozzles for which the sphere dimensions are equal and the outside diameter of the attached nozzle is constant. In some instances the nozzle protrudes through the vessel.

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