Stresses in Spherical Shells Due to Local Loadings Over a Rectangular Area

1985 ◽  
Vol 107 (2) ◽  
pp. 205-207 ◽  
Author(s):  
T. L. Chao
Keyword(s):  
Analytical Solutions ◽  
Shear Load ◽  
Radial Load ◽  
Spherical Shells ◽  
Rectangular Area ◽  
Bending Stresses ◽  
Overturning Moment ◽  
Moment Load

Analytical solutions for displacements, membrane stresses, and bending stresses in spherical shells due to local loadings over a rectangular area were developed. The three types of loading considered are radial load, overturning moment load, and tangential shear load.

Stress Concentrations in Thin Spherical Shells

1966 ◽  
Vol 88 (2) ◽  
pp. 231-236 ◽  
Author(s):  
Egor P. Popov ◽  
Joseph Penzien ◽  
Mandayam K. S. Rajan
Keyword(s):  
Axial Load ◽  
Shear Load ◽  
Stress Distributions ◽  
Stress Concentrations ◽  
Spherical Shells ◽  
Practical Applications ◽  
Small Deflection ◽  
External Moment ◽  
Rigid Insert ◽  
Deflection Theory

Stress distributions occurring in the proximity of rigid circular inserts attached to thin spherical shells are reported in this paper. The solutions are achieved by employing conical coordinates tangent to the sphere at its intersection with the insert. A small-deflection theory is used and results are stated in terms of readily available functions. For convenience in practical applications, solutions for several loading conditions are carried through to completion. Specifically, the paper gives formulas for stress distributions occurring in a spherical shell when provided with a rigid insert and when subjected to (a) internal pressurization in the shell; (b) axial load on the insert; (c) external moment on the insert; and (d) tangential shear load on the insert. The necessary constants of integration are given in tables and the procedure developed is illustrated by a comprehensive example.

A Boundary Integral Approach to Attachment/Spherical Shell Interaction

1997 ◽  
Vol 119 (4) ◽  
pp. 407-413
Author(s):  
N. Simos ◽  
C. Chassapis
Keyword(s):  
Finite Element ◽  
Integral Equations ◽  
Analytical Solutions ◽  
Structural Integrity ◽  
Computational Cost ◽  
Boundary Integral ◽  
Integral Approach ◽  
Computational Techniques ◽  
Attractive Alternative ◽  
Spherical Shells

In pressure vessel applications, the accurate evaluation of the state of stress in the vicinity of nozzles or rigid attachments is of vital importance to the structural integrity of the vessel. Consequently, a number of investigations have paid attention to the problem and, through analytical and numerical approaches, provided information concerning the effect of system parameters, such as shell curvature and attachment geometry, on stress concentration and effective shell stiffness. While analytical solutions have only been able to provide information to axisymmetric problems, finite element approaches have been widely used as an attractive alternative. In evaluating the latter, one can identify the high computational cost that accompanies analyses dealing with complex systems. In this study, the performance of a boundary integral scheme is assessed as a possible analytical and/or numerical tool in dealing with spherical shells interacting with attachments. Such method hopes to achieve a close to analytical solutions representation of the stress state in the vicinity of the attachment that is accompanied by significant reduction in the computational cost. To achieve this, a set of integral equations, which satisfy the edge constraints, are reduced to a system of algebraic equations. These integral equations utilize singular solutions obtained for deep (nonshallow) spherical shells, which in turn are more representative of the shell domain. Explicit comparisons, on the basis of representative shell-attachment interaction problems, between the finite element and boundary integral computational techniques are conducted in order to assess the performance and efficiency of the new method. Finally, shell stiffnesses in the form of insert translations and rotations are presented in dimensionless form.

scholarly journals In-Plane Instability of Fixed Arches under Linear Temperature Gradient Field and Uniformly Distributed Radial Load

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaochun Song ◽  
Hanwen Lu ◽  
Airong Liu ◽  
Yonghui Huang
Keyword(s):  
Temperature Gradient ◽  
Analytical Solutions ◽  
Bending Moment ◽  
Internal Force ◽  
Gradient Field ◽  
Radial Load ◽  
Temperature Differential ◽  
Instability Analysis ◽  
Linear Temperature ◽  
Linear Temperature Gradient

This paper focuses on an in-plane instability analysis of fixed arches under a linear temperature gradient field and a uniformly distributed radial load, which has not been reported in the literature. Combining a linear temperature gradient field and uniformly distributed radial load leads to the changes in axial expansion and curvature of arches, producing the complex in-plane nonuniform bending moment and axial force. Therefore, it is necessary to explore the in-plane thermoelastic mechanism behavior of fixed arches under a linear temperature gradient field and a uniformly distributed radial load in the in-plane instability analysis. Based on the energy method and the exact solutions of internal force before instability, the analytical solutions of the critical uniformly distributed radial load considering the linear temperature gradient field associated with in-plane thermoelastic instability of arches are derived. Comparisons show that agreements of analytical solutions against FE (finite element) results are excellent. Influences of various factors on in-plane instability are also studied. It is found that the change of the linear temperature gradient field has significant influences on the in-plane instability load. The in-plane instability load decreases as the temperature differential of the linear temperature gradient field increases.

Application of the Point-Matching Method to Shallow-Spherical-Shell Theory

1962 ◽  
Vol 29 (4) ◽  
pp. 745-747 ◽  
Author(s):  
H. D. Conway ◽  
A. W. Leissa
Keyword(s):  
Spherical Shell ◽  
Shell Theory ◽  
Shallow Spherical Shell ◽  
Circular Pipe ◽  
Radial Load ◽  
Matching Method ◽  
Spherical Shells ◽  
Point Matching ◽  
Circular Base

Using Reissner’s [1] theory of the bending of shallow spherical shells, two unsymmetrical problems are investigated by the method of point-matching. The first is a uniformly loaded spherical shell clamped on a square base, numerical values of the moments and membrane forces being obtained and compared with the corresponding values for the case of a clamped circular base. The second problem is a spherical shell with a rigid elliptical insert, the latter carrying a central radial load. This gives information concerning the problem of a spherical shell which is pierced at an angle by a relatively rigid circular pipe.

Uniform Oval Reinforcing Rings—Power-Series Expansions

1965 ◽  
Vol 9 (03) ◽  
pp. 105-121
Author(s):  
William P. Vafakos ◽  
Louis Rostand
Keyword(s):  
Power Series ◽  
Cross Section ◽  
Analytical Solutions ◽  
Minor Axis ◽  
Series Expansions ◽  
Radial Load ◽  
Axis Ratio ◽  
Graphical Comparison ◽  
Power Series Expansions ◽  
Oval Cylindrical Shells

Power-series expansions are employed in the analysis of oval reinforcing rings which are arbitrarily located on the inside or outside of oval cylindrical shells of prescribed cross section. The expansions are in terms of two small geometric parameters which are fixed by specifying the cross section of the ring and the major and minor-axis lengths of the oval. Analytical solutions are presented for the case of a uniform radial load. A graphical comparison is made with the results of a relatively lengthy energy solution. In addition, the effect of inside or outside rings is displayed in graphs, where the results are plotted versus the major-to-minor axis ratio.

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