A general solution of axisymmetric problem of arbitrary thick spherical shell and solid sphere

1992 ◽  
Vol 13 (6) ◽  
pp. 515-521
Author(s):  
Bu Xiao-ming ◽  
Yan Zong-da
Keyword(s):  
General Solution ◽  
Spherical Shell ◽  
Axisymmetric Problem ◽  
Solid Sphere

The Onset of Plastic Yielding in a Spherical Shell Compressed by a Rigid Flat

2010 ◽  
Vol 78 (1) ◽  
Author(s):  
Longqiu Li ◽  
Izhak Etsion ◽  
Andrey Ovcharenko ◽  
Frank E. Talke
Keyword(s):  
Spherical Shell ◽  
Normal Load ◽  
Empirical Relation ◽  
Solid Sphere ◽  
Plastic Yielding ◽  
Element Analysis ◽  
Shell Parameter ◽  
Shell Geometry ◽  
Limiting Value ◽  
Critical Contact

The onset of plastic yielding in a spherical shell loaded by a rigid flat is analyzed using finite element analysis. The effect of spherical shell geometry and material properties on the critical normal load, critical interference, and critical contact area, at the onset of plastic yielding, is investigated and the location where plastic yielding first occurs is determined. A universal dimensionless shell parameter, which controls the behavior of the spherical shell, is identified. An empirical relation is found for the load-interference behavior of the spherical shell prior to its plastic yielding. A limiting value of the dimensionless shell parameter is identified above which the shell behaves like a solid sphere.

Axisymmetric Thermal Stresses in a Spherical Shell of Arbitrary Thickness

1957 ◽  
Vol 24 (3) ◽  
pp. 376-380
Author(s):  
E. L. McDowell ◽  
E. Sternberg
Keyword(s):  
Steady State ◽  
Spherical Shell ◽  
Spherical Cavity ◽  
Series Solution ◽  
Thermal Stresses ◽  
Solid Sphere ◽  
Theory Of Elasticity ◽  
Infinite Medium ◽  
Series Solutions ◽  
Arbitrary Thickness

Abstract This paper contains an explicit series solution, exact within the classical theory of elasticity, for the steady-state thermal stresses and displacements induced in a spherical shell by an arbitrary axisymmetric distribution of surface temperatures. The corresponding solutions for a solid sphere and for a spherical cavity in an infinite medium are obtained as limiting cases. The convergence of the series solutions obtained is discussed. Numerical results are presented appropriate to a solid sphere if two hemispherical caps of its boundary are maintained at distinct uniform temperatures.

scholarly journals A New Form of the General Solution of the Elastic Space Axisymmetric Problem in Pavement Mechanics

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Jia Liang ◽  
Guo Jian ◽  
He Shikai
Keyword(s):  
General Solution ◽  
Axisymmetric Problem ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Displacement Function ◽  
Winkler Foundation ◽  
Elastic Space ◽  
Equilibrium Equations ◽  
Present Solution ◽  
New Form

In order to analyze the stress and displacement of pavement, a new form of the general solution of the elastic space axisymmetric problem is proposed by the method of mathematics reasoning. Depending on the displacement function put forward by Southwell, displacement function is derived based on Hankel transform and inverse Hankel transform. A new form of the general solution of the elastic space axisymmetric problem has been set up according to a few basic equations as the geometric equations, constitutive equations, and equilibrium equations. The present solution applies to elastic half-space foundation and Winkler foundation; the stress and displacement of pavement are obtained by mathematical deduction. The example results show that the proposed method is practically feasible.

2D Axisymmetric Problem for a Sphere with Heat Sources in the Theory of Generalized Thermoviscoelasticity

2017 ◽  
Vol 09 (02) ◽  
pp. 1750028
Author(s):  
Hany H. Sherief ◽  
Allam A. Allam
Keyword(s):  
Temperature Distribution ◽  
Heat Source ◽  
Axisymmetric Problem ◽  
Solid Sphere ◽  
Heat Sources ◽  
Inner Sphere ◽  
Axisymmetric Temperature

A solid sphere composed of a thermoviscoelastic material is subjected to an axisymmetric temperature distribution on its surface that is traction free. A distributed heat source acts inside an inner sphere. The problem is solved analytically and numerically. The solutions are represented graphically for different cases.

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