Analysis of Stresses in Shallow Spherical Shells With Periodically Spaced Holes

1970 ◽  
Vol 92 (4) ◽  
pp. 834-840 ◽  
Author(s):  
L. E. Hulbert ◽  
F. A. Simonen
Keyword(s):  
Computer Program ◽  
Spherical Shell ◽  
Numerical Solution ◽  
Least Squares ◽  
Boundary Point ◽  
Numerical Results ◽  
Series Solutions ◽  
Spherical Shells ◽  
Perforated Plates ◽  
Circular Holes

This paper concerns the numerical solution of shallow spherical shell problems by the method of boundary-point-least-squares. The analysis forms the basis of a computer program for the calculation of stresses in curved perforated plates. Multiple-pole series solutions are used, and recursion methods for generating the required Bessel-Kelvin functions are discussed. Numerical results are given for previously unsolved problems involving an array of seven circular holes and for an array of four noncircular holes.

On the Influence of Uniform Stress States on the Natural Frequencies of Spherical Shells

1962 ◽  
Vol 29 (3) ◽  
pp. 502-505 ◽  
Author(s):  
R. R. Archer
Keyword(s):  
Spherical Shell ◽  
Compressive Stress ◽  
Shallow Shell ◽  
Natural Frequencies ◽  
Numerical Results ◽  
Uniform Stress ◽  
Spherical Shells ◽  
Transverse Vibrations ◽  
Stress States ◽  
General Frequency

The influence of uniform tensile and compressive stress states on the natural frequencies of transverse vibrations for shallow spherical shell segments is determined from the general equations for elastokinetic shallow shell problems with longitudinal inertia terms neglected. General frequency determinants are derived and detailed numerical results obtained for a range of shell geometries and stress states.

Analysis of Multiholed Orthotropic Laminated Plates by the Boundary-Point-Least-Squares Method

1975 ◽  
Vol 97 (2) ◽  
pp. 118-122 ◽  
Author(s):  
S. G. Sampath ◽  
L. E. Hulbert
Keyword(s):  
Least Squares ◽  
Boundary Point ◽  
Numerical Solutions ◽  
Least Squares Method ◽  
Elliptical Hole ◽  
Laminated Plates ◽  
Series Solutions ◽  
Orthotropic Plates ◽  
Multiply Connected

The paper describes the application of boundary-point-least-squares method (BPLS) for the determination of stresses in multiply connected finite orthotropic plates under plane stress. Series solutions composed of mapping functions are employed. Numerical solutions presented include the case of an orthotropic plate with an elliptical hole with orientation noncoincident with the material axes.

Thermal Stress Analysis of Multiholed Composite Plates and Cylinders by the Boundary-Point-Least-Squares Method

1974 ◽  
Vol 96 (3) ◽  
pp. 214-219 ◽  
Author(s):  
L. E. Hulbert ◽  
S. G. Sampath
Keyword(s):  
Least Squares ◽  
Boundary Point ◽  
Thermal Stresses ◽  
Least Squares Method ◽  
Composite Plates ◽  
Multiply Connected Domains ◽  
Series Solutions ◽  
Thermally Induced ◽  
Multiply Connected

The paper describes the application of the boundary-point-least-squares method (BPLS) to the determination of the two-dimensional temperatures and thermal stresses in composite multiply connected domains. Series solutions are first determined for the steady-state temperatures. Using these temperature solutions, the solution to the thermally-induced stresses is automatically found in terms of Airy stress function series. Applications are described which illustrate use of the method in specific problems.

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.

scholarly journals Splitting least squares and collocation procedures for two-point boundary value problems

1985 ◽  
Vol 27 (2) ◽  
pp. 167-193
Author(s):  
John Locker ◽  
P. M. Prenter
Keyword(s):  
Linear System ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Least Squares ◽  
Boundary Value ◽  
Linear Operators ◽  
Point Boundary ◽  
System Error ◽  
Densely Defined ◽  
Split System

AbstractLet L, T, S, and R be closed densely defined linear operators from a Hubert space X into X where L can be factored as L = TS + R. The equation Lu = f is equivalent to the linear system Tv + Ru = f and Su = v. If Lu = f is a two-point boundary value problem, numerical solution of the split system admits cruder approximations than the unsplit equations. This paper develops the theory of such splittings together with the theory of the Methods of Least Squares and of Collocation for the split system. Error estimates in both L2 and L∞ norms are obtained for both methods.

Elastic Design Methods for Perforated Plates

1978 ◽  
Vol 100 (2) ◽  
pp. 356-362 ◽  
Author(s):  
J. S. Porowski ◽  
W. J. O’Donnell
Keyword(s):  
Finite Element ◽  
Thermal Loading ◽  
Solid Material ◽  
Perforated Plates ◽  
Finite Element Stress Analysis ◽  
Effective Elastic Constants ◽  
New Methods ◽  
Circular Holes ◽  
Elastic Design ◽  
Generalized Plane Strain

Methods for performing finite element stress analysis of perforated plates under pressure and complex thermal loading conditions are described. The concept of the equivalent solid material of anisotropic properties is employed to define the elasticity matrices to be used for axisymmetric analysis of plates containing triangular and square patterns of circular holes. Generalized plane strain effective elastic constants are used for better approximation of the overall plate behavior. New methods and curves for obtaining local ligament stresses from the nominal stresses in the equivalent solid material are given.

Using the generalized Adams-Bashforth-Moulton method for obtaining the numerical solution of some variable-order fractional dynamical models

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohamed M. Khader
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Numerical Solution ◽  
Numerical Results ◽  
Convergence Order ◽  
Variable Order ◽  
Numerical Treatment ◽  
Dynamical Models ◽  
Fractional Modeling ◽  
Dynamics Problems

AbstractThis paper is devoted to introduce a numerical treatment using the generalized Adams-Bashforth-Moulton method for some of the variable-order fractional modeling dynamics problems, such as Riccati and Logistic differential equations. The fractional derivative is described in Caputo variable-order fractional sense. The obtained numerical results of the proposed models show the simplicity and efficiency of the proposed method. Moreover, the convergence order of the method is also estimated numerically.

A fast approach for acoustic source localization on a thin spherical shell

2021 ◽  
pp. 147592172110419
Author(s):  
Zixian Zhou ◽  
Zhiwen Cui ◽  
Tribikram Kundu
Keyword(s):  
Velocity Profile ◽  
Spherical Shell ◽  
Source Localization ◽  
Pressure Vessels ◽  
Solution Technique ◽  
Acoustic Source ◽  
Spherical Shells ◽  
Fast Approach ◽  
Acoustic Source Localization ◽  
Thin Spherical Shell

Thin spherical shell structures are wildly used as pressure vessels in the industry because of their property of having equal in-plane normal stresses in all directions. Since very large pressure difference between the inside and outside of the wall exists, any formation of defects in the pressure vessel wall has a huge safety risk. Therefore, it is necessary to quickly locate the area where the defect maybe located in the early stage of defect formation and make repair on time. The conventional acoustic source localization techniques for spherical shells require either direction-dependent velocity profile knowledge or a large number of sensors to form an array. In this study, we propose a fast approach for acoustic source localization on thin isotropic and anisotropic spherical shells. A solution technique based on the time difference of arrival on a thin spherical shell without the prior knowledge of direction-dependent velocity profile is provided. With the help of “L”-shaped sensor clusters, only 6 sensors are required to quickly predict the acoustic source location for anisotropic spherical shells. For isotropic spherical shells, only 4 sensors are required. Simulation and experimental results show that this technique works well for both isotropic and anisotropic spherical shells.

Rods falling near a vertical wall

1977 ◽  
Vol 83 (2) ◽  
pp. 273-287 ◽  
Author(s):  
W. B. Russel ◽  
E. J. Hinch ◽  
L. G. Leal ◽  
G. Tieffenbruck
Keyword(s):  
Integral Equation ◽  
Viscous Fluid ◽  
Numerical Solution ◽  
Vertical Wall ◽  
Numerical Results ◽  
Slender Body ◽  
Asymptotic Results ◽  
Slender Body Theory ◽  
Friction Coefficients ◽  
Body Theory

As an inclined rod sediments in an unbounded viscous fluid it will drift horizontally but will not rotate. When it approaches a vertical wall, the rod rotates and so turns away from the wall. Illustrative experiments and a slender-body theory of this phenomenon are presented. In an incidental study the friction coefficients for an isolated rod are found by numerical solution of the slender-body integral equation. These friction coefficients are compared with the asymptotic results of Batchelor (1970) and the numerical results of Youngren ' Acrivos (1975), who did not make a slender-body approximation.

Numerical solution of a source identification problem: Almost coercivity

2019 ◽  
Vol 27 (4) ◽  
pp. 457-468 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Abdullah Said Erdogan ◽  
Ali Ugur Sazaklioglu
Keyword(s):  
Numerical Solution ◽  
Source Identification ◽  
Identification Problem ◽  
Second Order ◽  
Numerical Results ◽  
Difference Schemes ◽  
Stability Estimates ◽  
Order Of Accuracy ◽  
Accuracy Difference ◽  
Coercive Stability

Abstract The present paper is devoted to the investigation of a source identification problem that describes the flow in capillaries in the case when an unknown pressure acts on the system. First and second order of accuracy difference schemes are presented for the numerical solution of this problem. Almost coercive stability estimates for these difference schemes are established. Additionally, some numerical results are provided by testing the proposed methods on an example.

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