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.

Stresses in a Transversely Isotropic Slab Having a Spherical Cavity

1973 ◽  
Vol 40 (3) ◽  
pp. 752-758 ◽  
Author(s):  
A. Atsumi ◽  
S. Itou
Keyword(s):  
Stress Distribution ◽  
Boundary Conditions ◽  
Spherical Cavity ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Hankel Transform ◽  
Isotropic Slab ◽  
Infinite Slab

This paper deals with the analysis of the stress distribution arising in a transversely isotropic infinite slab with a symmetrically located spherical cavity under all-around tension. Difficulties in satisfying both boundary conditions on the surfaces of the slab and the surface of the cavity are successfully overcome by using the methods of Hankel transform and Schmidt-orthogonormalization. For some practical materials the influence of transverse isotropy upon stress distribution is presented in the form of curves.

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.

Wrinkling of a Fiber-Reinforced Membrane

2008 ◽  
Vol 76 (1) ◽  
Author(s):  
E. Shmoylova ◽  
A. Dorfmann
Keyword(s):  
Boundary Conditions ◽  
Energy Function ◽  
Mechanical Response ◽  
Transverse Isotropy ◽  
Base Material ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
Incompressible Material ◽  
Fiber Reinforced ◽  
Relaxed Energy

In this paper we investigate the response of fiber-reinforced cylindrical membranes subject to axisymmetric deformations. The membrane is considered as an incompressible material, and the phenomenon of wrinkling is taken into account by means of the relaxed energy function. Two cases are considered: transversely isotropic membranes, characterized by one family of fibers oriented in one direction, and orthotropic membranes, characterized by two family of fibers oriented in orthogonal directions. The strain-energy function is considered as the sum of two terms: The first term is associated with the isotropic properties of the base material, and the second term is used to introduce transverse isotropy or orthotropy in the mechanical response. We determine the mechanical response of the membrane as a function of fiber orientations for given boundary conditions. The objective is to find possible fiber orientations that make the membrane as stiff as possible for the given boundary conditions. Specifically, it is shown that for transversely isotropic membranes a unique fiber orientation exists, which does not affect the mechanical response, i.e., the overall behavior is identical to a nonreinforced membrane.

Stresses in a Stretched Slab Having a Spherical Cavity

1959 ◽  
Vol 26 (2) ◽  
pp. 235-240
Author(s):  
Chih-Bing Ling
Keyword(s):  
Boundary Conditions ◽  
Stress Function ◽  
Spherical Cavity ◽  
Analytic Solution ◽  
Linear Equations ◽  
Hankel Transform ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Biharmonic Functions ◽  
Infinite Slab

Abstract This paper presents an analytic solution for an infinite slab having a symmetrically located spherical cavity when it is stretched by an all-round tension. The required stress function is constructed by combining linearly two sets of periodic biharmonic functions and a biharmonic integral. The sets of biharmonic functions are derived from two fundamental functions specially built up for the purpose. The arbitrary functions involved in the biharmonic integral are first adjusted to satisfy the boundary conditions on the surfaces of the slab by applying the Hankel transform of zero order. Then the stress function is expanded in spherical co-ordinates and the boundary conditions on the surface of the cavity are satisfied by adjusting the coefficients of superposition attached to the sets of biharmonic functions. The resulting system of linear equations is solved by the method of successive approximations. The solution is finally illustrated by numerical examples for two radii of the cavity.

On a heat flow problem in a hollow circular cylinder

1968 ◽  
Vol 64 (1) ◽  
pp. 193-202
Author(s):  
Nuretti̇n Y. Ölçer
Keyword(s):  
Circular Cylinder ◽  
Boundary Conditions ◽  
Hollow Cylinder ◽  
Eigenvalue Problems ◽  
Integral Transforms ◽  
Hankel Transform ◽  
Frequency Equation ◽  
Hollow Circular Cylinder ◽  
New Ideas ◽  
Finite Integral

Recently, through a repeated application of one-dimensional finite integral transforms, Cinelli(1) gave a solution for the temperature distribution in a hollow circular cylinder of finite length. Since no new ideas or techniques are introduced, the extension claimed in (1) with regard to the finite Hankel transform technique employed in the transformation of the radial space variable in the hollow cylinder problem is trivial, in view of well-known works by Sneddon(2) and Tranter (3), to mention a few. The list of the finite Hankel transforms given in (1) for a variety of boundary conditions at r = a and r = b is the result of routine, algebraic manipulations well known from the general theory of eigenvalue problems specialized for the hollow cylinder. In this list a set of seemingly different series expansions is given for the inverse Hankel transform for each combination of boundary conditions at the two radial surfaces. In each case, the two expressions for inversion can readily be shown to be identical to each other when use is made of the frequency equation. One of the inversion forms is therefore unnecessary once the other is given. Furthermore, the general solution as given by equation (54) of Cinelli(1)does not satisfy his boundary conditions (27), (28), (29) and (30), unless these latter are homogeneous.

Using the Multi-Parameter Fracture Mechanics for more Accurate Description of Stress/Displacement Crack Tip Fields

2013 ◽  
Vol 586 ◽  
pp. 237-240 ◽  
Author(s):  
Lucie Šestáková
Keyword(s):  
Stress Distribution ◽  
Fracture Mechanics ◽  
Boundary Conditions ◽  
Displacement Field ◽  
Singular Term ◽  
Crack Tip ◽  
Higher Order ◽  
Precise Description ◽  
Accurate Knowledge ◽  
Higher Order Terms

Most of fracture analyses often require an accurate knowledge of the stress/displacement field over the investigated body. However, this can be sometimes problematic when only one (singular) term of the Williams expansion is considered. Therefore, also other terms should be taken into account. Such an approach, referred to as multi-parameter fracture mechanics is used and investigated in this paper. Its importance for short/long cracks and the influence of different boundary conditions are studied. It has been found out that higher-order terms of the Williams expansion can contribute to more precise description of the stress distribution near the crack tip especially for long cracks. Unfortunately, the dependences obtained from the analyses presented are not unambiguous and it cannot be strictly derived how many of the higher-order terms are sufficient.

Spherical waves in a simple locking medium

1964 ◽  
Vol 54 (2) ◽  
pp. 737-754
Author(s):  
Sathyanarayana Hanagud
Keyword(s):  
Shock Wave ◽  
Stress Distribution ◽  
Mechanical Behavior ◽  
Spherical Cavity ◽  
Shear Resistance ◽  
Finite Deformations ◽  
Spherical Shock Wave ◽  
Spherical Waves ◽  
Spherical Shock ◽  
Elastic Shear

ABSTRACT The mechanical behavior of some types of soils can be idealized by that of a “Locking Solid.” This paper investigates the spherical shock wave and the stress distribution behind the wave in a simple locking solid due to a sudden explosion at the surface of a small spherical cavity. The cases of infinitesimal and finite deformations are considered. The effect of an elastic shear resistance and the consequent phenomenon of “unlocking” are also studied.

Stress Distribution in a Uniformly Rotating Equilateral Triangular Shaft

1955 ◽  
Vol 22 (2) ◽  
pp. 255-259
Author(s):  
H. T. Johnson
Keyword(s):  
Approximate Solution ◽  
Stress Distribution ◽  
Boundary Conditions ◽  
Plane Strain ◽  
Cross Section ◽  
Plane Stress ◽  
Biharmonic Equation ◽  
Approximate Solutions ◽  
Distribution Of Stresses ◽  
General Method

Abstract An approximate solution for the distribution of stresses in a rotating prismatic shaft, of triangular cross section, is presented in this paper. A general method is employed which may be applied in obtaining approximate solutions for the stress distribution for rotating prismatic shapes, for the cases of either generalized plane stress or plane strain. Polynomials are used which exactly satisfy the biharmonic equation and the symmetry conditions, and which approximately satisfy the boundary conditions.

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