Stresses in a Transversely Isotropic Half Space Having a Spherical Cavity

1974 ◽  
Vol 41 (3) ◽  
pp. 708-712 ◽  
Author(s):  
A. Atsumi ◽  
S. Itou
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Half Space ◽  
Spherical Cavity ◽  
Transversely Isotropic ◽  
Elastic Half Space ◽  
Numerical Calculations ◽  
Schmidt Method ◽  
Free Boundary Conditions ◽  
Hankel Transforms

In this paper, a solution is given for the stresses and displacements around a spherical cavity in a transversely isotropic homogeneous elastic half space under all-around tension. The traction-free boundary conditions on the faces of the plane and on the cavity are satisfied with the aid of Hankel transforms and the Schmidt method, respectively. Numerical calculations are carried out for some practical materials.

Stresses in a Transversely Isotropic Circular Cylinder Having a Spherical Cavity

1974 ◽  
Vol 41 (2) ◽  
pp. 507-511 ◽  
Author(s):  
A. Atsumi ◽  
S. Itou
Keyword(s):  
Stress Distribution ◽  
Circular Cylinder ◽  
Boundary Conditions ◽  
Spherical Cavity ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Hankel Transform ◽  
Numerical Calculations ◽  
Infinite Cylinder ◽  
Longitudinal Tension

This paper concerns the analysis of the stress distribution arising in a transversely isotropic infinite cylinder having a spherical cavity under longitudinal tension. Boundary conditions on the surface of the cylinder and the cavity are well satisfied by using the methods of Hankel transform and Schmidt-orthonormalization. Numerical calculations for some practical materials are carried out and the influence of transverse isotropy upon stress distribution is clarified.

scholarly journals Local Well-Posedness for Free Boundary Problem of Viscous Incompressible Magnetohydrodynamics

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 461
Author(s):  
Kenta Oishi ◽  
Yoshihiro Shibata
Keyword(s):  
Free Surface ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Mhd Flow ◽  
Transmission Conditions ◽  
Well Posedness ◽  
Anisotropic Space ◽  
Free Boundary Conditions ◽  
Incompressible Magnetohydrodynamics

In this paper, we consider the motion of incompressible magnetohydrodynamics (MHD) with resistivity in a domain bounded by a free surface. An electromagnetic field generated by some currents in an external domain keeps an MHD flow in a bounded domain. On the free surface, free boundary conditions for MHD flow and transmission conditions for electromagnetic fields are imposed. We proved the local well-posedness in the general setting of domains from a mathematical point of view. The solutions are obtained in an anisotropic space Hp1((0,T),Hq1)∩Lp((0,T),Hq3) for the velocity field and in an anisotropic space Hp1((0,T),Lq)∩Lp((0,T),Hq2) for the magnetic fields with 2<p<∞, N<q<∞ and 2/p+N/q<1. To prove our main result, we used the Lp-Lq maximal regularity theorem for the Stokes equations with free boundary conditions and for the magnetic field equations with transmission conditions, which have been obtained by Frolova and the second author.

scholarly journals Identification of Corrosion on a Hollow Tube Using Vibration

2014 ◽  
Vol 564 ◽  
pp. 176-181
Author(s):  
S.T. Cheng ◽  
Nawal Aswan Abdul Jalil ◽  
Zamir A. Zulkefli
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Impact Loading ◽  
Structural Damage ◽  
Natural Frequencies ◽  
Localized Corrosion ◽  
Free Boundary Conditions ◽  
The Impact ◽  
Impact Vibration

Vibration based technique have so far been focused on the identification of structural damage. However, not many studies have been conducted on the corrosion identification on pipes. The objective of this paper is to identify corrosion on pipes from vibration measurements. A hollow pipe, 500 mm in length with 63.5 mm in diameter was subjected to impact loading using an impact hammer to identify the natural frequency of the tube in two conditions i) without any corrosion and ii) with an induced localized 40 mm by 40 mm corrosion at the middle of the pipe. The shift of natural frequencies of the structures under free boundary conditions was examined for each node of excitation. The results showed that there is a shift in natural frequency of the pipe, between 3 and 4 Hz near to the corrosion area. It can suggested that that the impact vibration is capable of identifying of localized corrosion on a hollow tube.

Contact Stress Analysis of a Layered Transversely Isotropic Half-Space

1992 ◽  
Vol 114 (2) ◽  
pp. 253-261 ◽  
Author(s):  
C. H. Kuo ◽  
L. M. Keer
Keyword(s):  
Half Space ◽  
Mixed Boundary ◽  
Contact Region ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Contact Stresses ◽  
Stress Components ◽  
Contact Failure

The three-dimensional problem of contact between a spherical indenter and a multi-layered structure bonded to an elastic half-space is investigated. The layers and half-space are assumed to be composed of transversely isotropic materials. By the use of Hankel transforms, the mixed boundary value problem is reduced to an integral equation, which is solved numerically to determine the contact stresses and contact region. The interior displacement and stress fields in both the layer and half-space can be calculated from the inverse Hankel transform used with the solved contact stresses prescribed over the contact region. The stress components, which may be related to the contact failure of coatings, are discussed for various coating thicknesses.

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