The Stress Fields Caused by a Circular Cylindrical Inclusion

1992 ◽  
Vol 59 (2S) ◽  
pp. S107-S114 ◽  
Author(s):  
Hisao Hasegawa ◽  
Ven-Gen Lee ◽  
Toshio Mura
Keyword(s):  
Exact Solutions ◽  
Strain Energy ◽  
Elastic Solid ◽  
Cylindrical Inclusion ◽  
Stress Fields ◽  
Axisymmetric Stress ◽  
Displacement Fields ◽  
Elastic Fields ◽  
Stress And Displacement Fields ◽  
Interior Points

Exact solutions are presented in closed forms for the axisymmetric stress and displacement fields caused by a solid or hollow circular cylindrical inclusion (with uniform axial eigenstrain prescribed) in an infinite elastic solid. The same expressions are obtained for the elastic fields for interior and exterior points of the inclusion. Although Eshelby’s solutions for ellipsoidal inclusions are uniform in the interior points, the present solutions do not show the uniformity. When the length of inclusion becomes infinite, the present solutions agree with Eshelby ’s results. The strain energy is also shown. The method of Green’s function is used.

The Stress Field Caused by a Circular Cylindrical Inclusion in a Transversely Isotropic Elastic Solid

2003 ◽  
Vol 70 (6) ◽  
pp. 825-831 ◽  
Author(s):  
H. Hasegawa ◽  
M. Kisaki
Keyword(s):  
Stress Field ◽  
Strain Energy ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Cylindrical Inclusion ◽  
Stress Distributions ◽  
Axisymmetric Stress ◽  
Displacement Fields ◽  
Isotropic Solid ◽  
Stress And Displacement Fields

Exact solutions are presented in closed form for the axisymmetric stress and displacement fields caused by a circular solid cylindrical inclusion with uniform eigenstrain in a transversely isotropic elastic solid. This is an extension of a previous paper for an isotropic elastic solid to a transversely isotropic solid. The strain energy is also shown. The method of Green’s functions is used. The numerical results for stress distributions are compared with those for an isotropic elastic solid.

Hollow Circular Cylindrical Inclusion at the Surface of a Half-Space

1993 ◽  
Vol 60 (1) ◽  
pp. 33-40 ◽  
Author(s):  
Hisao Hasegawa ◽  
Ven-Gen Lee ◽  
Toshio Mura
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Half Space ◽  
Strain Energy ◽  
Analytical Form ◽  
Cylindrical Inclusion ◽  
Displacement Fields ◽  
Elastic Fields

Exact solutions are presented in closed form for the axisymmetric stresses and displacement fields caused by a solid or hollow circular cylindrical inclusion in the present of uniform eigenstrain in a half space. The elastic fields for interior and exterior points are expressed by one analytical form. The strain energy is also obtained in closed forms.

The Elastic Field of an Elliptic Cylindrical Inclusion in a Laminate With Multiple Isotropic Layers

1999 ◽  
Vol 66 (1) ◽  
pp. 165-171 ◽  
Author(s):  
H. G. Beom ◽  
Y. Y. Earmme
Keyword(s):  
Plate Theory ◽  
Elastic Field ◽  
Cylindrical Inclusion ◽  
Transverse Displacement ◽  
Laminated Plate ◽  
Displacement Fields ◽  
Elastic Fields ◽  
Closed Form Solutions ◽  
Main Plane ◽  
Interior Points

An elliptic cylindrical inclusion with an eigenstrain in an infinite laminate composed of multiple isotropic layers is analyzed. The problem is formulated by using the classical laminated plate theory in which displacement fields in the laminated plate are expressed in terms of in-plane displacements on the main plane and transverse displacement. Employing a method based on influence functions, an integral type solution to the equilibrium equation is expressed in terms of the eigenstrain. Closed-Form solutions for the elastic fields are obtained by evaluating the integrals explicitly for interior points and exterior points of the ellipse. The elastic fields caused by an elliptic cylindrical inhomogeneity with an eigenstrain in the infinite laminate are determined by the equivalent eigenstrain method. Solutions for a finite laminate with an eigenstrain in a circular cylindrical inhomogeneity are also obtained in terms of material and geometric parameters for each layer composing the laminate.

The Elastic Field Caused by a Circular Cylindrical Inclusion—Part I: Inside the Region x12+x22

1995 ◽  
Vol 62 (3) ◽  
pp. 579-584 ◽  
Author(s):  
Linzhi Wu ◽  
Shanyi Du
Keyword(s):  
Analytical Solutions ◽  
Elastic Field ◽  
Companion Paper ◽  
Elliptic Integrals ◽  
Cylindrical Inclusion ◽  
Stress Fields ◽  
Elastic Fields ◽  
Complete Elliptic Integrals ◽  
Nonsingular Surface ◽  
Surface Integrals

The displacement and stress fields caused by uniform eigenstrains in a circular cylindrical inclusion are analyzed inside the region x12+x22<a2,−∞<x3<∞ and are given in terms of nonsingular surface integrals. Analytical solutions can be expressed as functions of the complete elliptic integrals of the first, second and third kind. The corresponding elastic fields in the region x12+x22>a2,−∞<x3<∞ are solved by using the same technique (by Green’s functions) in the companion paper (Part II).

Penetration of a Half Space by a Rectangular Cylinder

1979 ◽  
Vol 46 (3) ◽  
pp. 587-591 ◽  
Author(s):  
A. Cemal Eringen ◽  
F. Balta
Keyword(s):  
Half Space ◽  
Stress Singularity ◽  
Elastic Solid ◽  
Interatomic Interaction ◽  
Elastic Half Space ◽  
Rigid Block ◽  
Field Equations ◽  
Displacement Fields ◽  
Rectangular Cylinder ◽  
Stress And Displacement Fields

The stress and displacement fields are determined in an elastic half space loaded by a rectangular frictionless, rigid block normally at its surface. The semi-infinite solid is considered to be an elastic solid with nonlocal interatomic interaction. The field equations of the nonlocal elasticity and boundary conditions are employed to treat this contact problem. Interestingly the classical stress singularity at the edges of the block are not present in the nonlocal solutions. Consequently the critical applied load for the initiation of penetration of the rigid cylinder into the semi-infinite solid can be determined without recourse to any criterion foreign to the theory. The stress field obtained is valid even for penetrators of submicroscopic width.

Elastodynamic Local Fields for a Crack Running in an Orthotopic Medium

1991 ◽  
Vol 58 (4) ◽  
pp. 982-987 ◽  
Author(s):  
A. Piva ◽  
E. Radi
Keyword(s):  
Dynamic Stress ◽  
Equations Of Motion ◽  
Local Fields ◽  
Stress Fields ◽  
Orthotropic Materials ◽  
Displacement Fields ◽  
First Order ◽  
Stress And Displacement Fields ◽  
Order Elliptic System ◽  
Separated Variables

The dynamic stress and displacement fields in the neighborhood of the tip of a crack propagating in an orthotropic medium are obtained. The approach deals with the methods of linear algebra to transform the equations of motion into a first-order elliptic system whose solution is sought under the assumption that the local displacement field may be represented under a scheme of separated variables. The analytical approach has enabled the distinction between two kinds of orthotropic materials for which explicit espressions of the near-tip stress fields are obtained. Some results are presented graphically also in order to compare them with the numerical solution given in a quoted reference.

The Elastic Field in a Half-Space With a Circular Cylindrical Inclusion

1996 ◽  
Vol 63 (4) ◽  
pp. 925-932 ◽  
Author(s):  
L. Z. Wu ◽  
S. Y. Du
Keyword(s):  
Half Space ◽  
Elastic Field ◽  
Elastic Half Space ◽  
Elliptic Integrals ◽  
Cylindrical Inclusion ◽  
Stress Fields ◽  
Function Technique ◽  
Explicit Solutions ◽  
Elastic Fields ◽  
Complete Elliptic Integrals

The problem of a circular cylindrical inclusion with uniform eigenstrain in an elastic half-space is studied by using the Green’s function technique. Explicit solutions are obtained for the displacement and stress fields. It is shown that the present elastic fields can be expressed as functions of the complete elliptic integrals of the first, second, and third kind. Finally, numerical results are shown for the displacement and stress fields.

scholarly journals Strain-energy bounds in finite-element analysis by slab analogy

1967 ◽  
Vol 2 (4) ◽  
pp. 265-271 ◽  
Author(s):  
B Fraeijs De Veubeke ◽  
O C Zienkiewicz
Keyword(s):  
Strain Energy ◽  
Energy Content ◽  
True Strain ◽  
Plane Elasticity ◽  
Stress Fields ◽  
Lower And Upper Bounds ◽  
Displacement Fields ◽  
Element Analysis ◽  
Energy Bounds ◽  
Elasticity Problems

It is well known that in approximate analysis of elasticity problems lower and upper bounds to the true strain-energy content can be obtained by the alternative assumptions of compatible displacement fields or of equilibrating stress fields. While formulations based on the first are relatively easy to achieve those based on the second present many difficulties. In this paper it is shown how by virtue of the analogy between plane-elasticity and slab-deflection problems compatible-displacement formulations in either one can be used to generate equilibrating formulations in the other. This should result in a direct application of existing programmes to a wider range of problems.

Elastic Fields Around the Cohesive Zone of a Mode III Crack Perpendicular to a Bimaterial Interface

2007 ◽  
Vol 74 (5) ◽  
pp. 1049-1052 ◽  
Author(s):  
W. Zhang ◽  
X. Deng
Keyword(s):  
Cohesive Zone ◽  
Bimaterial Interface ◽  
Mode Iii ◽  
Displacement Fields ◽  
Mode Iii Crack ◽  
Elliptic Coordinates ◽  
Elastic Fields ◽  
Stress And Displacement Fields

Asymptotic stress and displacement fields near the cohesive zone ahead of a semi-infinite Mode III crack normal to a bimaterial interface are derived using elliptic coordinates.

Stress and Displacement Fields at a Transient Crack Tip Propagating in Functionally Graded Materials

2007 ◽  
Vol 345-346 ◽  
pp. 481-484
Author(s):  
Kwang Ho Lee ◽  
Gap Su Ban
Keyword(s):  
Functionally Graded Materials ◽  
Crack Tip ◽  
Functionally Graded ◽  
Stress Fields ◽  
Displacement Fields ◽  
Graded Materials ◽  
Transient Motion ◽  
Stress And Displacement Fields ◽  
Displacement Potentials ◽  
Nonhomogeneous Materials

Stress and displacement fields for a transient crack tip propagating along gradient in functionally graded materials (FGMs) with an exponential variation of shear modulus and density under a constant Poisson's ratio are developed. The equations of transient motion in nonhomogeneous materials are developed using displacement potentials and the solution to the displacement fields and the stress fields for a transient crack propagating at nonuniform speed though an asymptotic analysis.

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