Combined Loading of a Fully Plastic Ligament Ahead of an Edge-Crack

1986 ◽  
Vol 53 (2) ◽  
pp. 271-277 ◽  
Author(s):  
C. F. Shih ◽  
J. W. Hutchinson
Keyword(s):  
Plane Strain ◽  
Half Space ◽  
Power Law ◽  
Edge Crack ◽  
Deformation Theory ◽  
Approximate Solutions ◽  
Free Edge ◽  
Numerical Results ◽  
Combined Loading

Complete, accurate numerical results are given for the solution to the problem of a semi-infinite crack aligned perpendicularly to the free-edge of a semi-infinite half space in which the ligament is subject to arbitrary combinations of bending and tension or compression. The material is an incompressible, pure power-law deformation theory solid. Conditions of plane strain are assumed. Approximate solutions are proposed for predominantly bending loadings and also for predominantly stretching loadings.

The Stress Field Due to a Line Load Acting on a Half Space of a Power-Law Hardening Material (A Comparison Between Plane Strain and Plane Stress)

1973 ◽  
Vol 40 (1) ◽  
pp. 288-290 ◽  
Author(s):  
C. Atkinson
Keyword(s):  
Exact Solution ◽  
Stress Field ◽  
Plane Strain ◽  
Half Space ◽  
Power Law ◽  
Elastic Material ◽  
Plane Stress ◽  
Strain Fields ◽  
Line Load ◽  
Hardening Material

The exact solution is given for a line load acting on a half space of a power-law elastic material under conditions of plane stress. This solution is compared with the corresponding solution under plane-strain conditions; see Aruliunian [1]. A marked difference is found between the plane-stress and plane-strain fields for different values of the hardening exponent.

scholarly journals The Penny-Shaped Crack and the Plane Strain Crack in an Infinite Body of Power-Law Material

1981 ◽  
Vol 48 (4) ◽  
pp. 830-840 ◽  
Author(s):  
M. Y. He ◽  
J. W. Hutchinson
Keyword(s):  
Plane Strain ◽  
Power Law ◽  
Deformation Theory ◽  
Small Strain ◽  
Stress And Strain ◽  
Infinite Body ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Remote Stress ◽  
Plane Strain Crack

A study is carried out of the problem of a penny-shaped crack in an infinite body of power-law material subject to general remote axisymmetric stressing conditions. The plane strain version of the problem is also examined. The material is incompressible and is characterized by small strain deformation theory with a pure power relation between stress and strain. The solutions presented also apply to power-law creeping materials and to a class of strain-rate sensitive hardening materials. Both numerical and analytical procedures are employed to obtain the main results. A perturbation solution obtained by expanding about the trivial state in which the stress is everywhere parallel to the crack leads to simple formulas which are highly accurate even when the remote stress is perpendicular to the crack.

scholarly journals Wave propagation in micropolar monoclinic thermoelastic half space

2013 ◽  
Vol 18 (4) ◽  
pp. 1013-1023
Author(s):  
R.R. Gupta
Keyword(s):  
Wave Propagation ◽  
Quality Factor ◽  
Plane Strain ◽  
Half Space ◽  
Numerical Results ◽  
Plane Strain Problem ◽  
Phase Velocities ◽  
Propagation Of Waves

Abstract Propagation of waves in a micropolar monoclinic medium possessing hermoelastic properties based on the Lord- Shulman (L-S),Green and Lindsay (G-L) and Coupled thermoelasticty (C-T) theories is discussed. The investigation is divided into two sections, viz., plane strain and anti-plane strain problem. After developing the solution, the phase velocities and attenuation quality factor have been derived and computed numerically. The numerical results have been plotted graphically.

Solution of Navier’s Equation in Cylindrical Curvilinear Coordinates

1978 ◽  
Vol 45 (4) ◽  
pp. 812-816 ◽  
Author(s):  
B. S. Berger ◽  
B. Alabi
Keyword(s):  
Fourier Transform ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Half Space ◽  
Coordinate Transformation ◽  
Numerical Results ◽  
Three Dimensions ◽  
Curvilinear Coordinates ◽  
Rectangular Region

A solution has been derived for the Navier equations in orthogonal cylindrical curvilinear coordinates in which the axial variable, X3, is suppressed through a Fourier transform. The necessary coordinate transformation may be found either analytically or numerically for given geometries. The finite-difference forms of the mapped Navier equations and boundary conditions are solved in a rectangular region in the curvilinear coordinaties. Numerical results are given for the half space with various surface shapes and boundary conditions in two and three dimensions.

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.

Multiple Region Contact Solutions for a Flat Indenter on a Layered Elastic Half Space: Plane-Strain Case

1989 ◽  
Vol 56 (2) ◽  
pp. 251-262 ◽  
Author(s):  
T. W. Shield ◽  
D. B. Bogy
Keyword(s):  
Plane Strain ◽  
Half Space ◽  
Contact Region ◽  
Integral Transforms ◽  
Elastic Half Space ◽  
Geometrical Parameters ◽  
Restricted Range ◽  
Complete Contact ◽  
The One ◽  
Layered Half Space

The plane-strain problem of a smooth, flat rigid indenter contacting a layered elastic half space is examined. It is mathematically formulated using integral transforms to derive a singular integral equation for the contact pressure, which is solved by expansion in orthogonal polynomials. The solution predicts complete contact between the indenter and the surface of the layered half space only for a restricted range of the material and geometrical parameters. Outside of this range, solutions exist with two or three contact regions. The parameter space divisions between the one, two, or three contact region solutions depend on the material and geometrical parameters and they are found for both the one and two layer cases. As the modulus of the substrate decreases to zero, the two contact region solution predicts the expected result that contact occurs only at the corners of the indenter. The three contact region solution provides an explanation for the nonuniform approach to the half space solution as the layer thickness vanishes.

Approximate Solutions in Linear, Coupled Thermoelasticity

1968 ◽  
Vol 35 (2) ◽  
pp. 255-266 ◽  
Author(s):  
R. E. Nickell ◽  
J. L. Sackman
Keyword(s):  
Half Space ◽  
Rapid Heating ◽  
Ritz Method ◽  
Gaussian Quadrature ◽  
Boundary Surface ◽  
Initial Boundary ◽  
Approximate Solutions ◽  
Coupled Thermoelasticity ◽  
Initial Boundary Value ◽  
Thermally Conducting

A method for obtaining approximate solutions to initial-boundary-value problems in the linear theory of coupled thermoelasticity is developed. This procedure is a direct variational method representing an extension of the Ritz method. As an illustration of the procedure, it is applied to a class of one-dimensional, transient problems involving weak thermal shocks. The problems considered are: (a) Rapid heating of a half space through a thermally conducting boundary layer, and (b) gradual heating of the boundary surface of a half space. The solutions generated by the extended Ritz method are compared, for accuracy, to solutions obtained from a numerical inversion scheme for the Laplace transform based on Gaussian quadrature. These comparisons indicate that the variational procedure developed here can yield accurate results.

Thermal post-buckling of laminated and isotropic rectangular plates with fixed edges: Comparison of experimental and numerical results

2012 ◽  
Vol 226 (10) ◽  
pp. 2393-2401 ◽  
Author(s):  
Marco Amabili ◽  
Mohammad Reza Sareban Tajahmadi
Keyword(s):  
Deformation Theory ◽  
Laboratory Experiments ◽  
Continuation Method ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Numerical Results ◽  
Rectangular Plates ◽  
Arc Length ◽  
Thermal Changes ◽  
Post Buckling

Post-buckling behaviors of laminated composite and isotropic rectangular plates subjected to various thermal changes are studied. Geometric imperfections are taken into account since they play a fundamental role. The plate is modeled using a nonlinear, higher order shear deformation theory. Plates with clamped edges are considered. A pseudo-arc length continuation method is used to obtain numerical results. Laboratory experiments have been performed in order to compare to the numerical calculations.

Subsurface and Surface Cracking Due to Hertzian Contact

1982 ◽  
Vol 104 (3) ◽  
pp. 347-351 ◽  
Author(s):  
L. M. Keer ◽  
M. D. Bryant ◽  
G. K. Haritos
Keyword(s):  
Crack Propagation ◽  
Half Space ◽  
Elastic Half Space ◽  
Contact Stresses ◽  
Numerical Results ◽  
Hertzian Contact ◽  
Vertical Crack ◽  
Subsurface Crack ◽  
Surface Cracking ◽  
Crack Geometry

Numerical results are presented for a cracked elastic half-space surface-loaded by Hertzian contact stresses. A horizontal subsurface crack and a surface breaking vertical crack are contained within the half-space. An attempt to correlate crack geometry to fracture is made and possible mechanisms for crack propagation are introduced.

On the Torsion of Elastic Half Spaces With Embedded Penny-Shaped Flaws

1972 ◽  
Vol 39 (3) ◽  
pp. 786-790 ◽  
Author(s):  
R. D. Low
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Rigid Inclusion ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Fredholm Integral Equations ◽  
Graphical Displays ◽  
Penny Shaped Crack ◽  
Shaped Crack

The investigation is concerned with some of the effects of embedded flaws in an elastic half space subjected to torsional deformations. Specifically two types of flaws are considered: (a) a penny-shaped rigid inclusion, and (b) a penny-shaped crack. In each case the problem is reduced to a system of Fredholm integral equations. Graphical displays of the numerical results are included.

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