Stresses in a heavy half-space with a hole of arbitrary shape, arbitrarily oriented relative to the principal stresses at infinity

1972 ◽  
Vol 8 (6) ◽  
pp. 698-699 ◽  
Author(s):  
Zh. S. Erzhanov ◽  
V. Yu. Izakson ◽  
Yu. F. Glazkov
Keyword(s):  
Half Space ◽  
Arbitrary Shape ◽  
Principal Stresses

Inclined Flat Punch of Arbitrary Shape on an Elastic Half-Space

1986 ◽  
Vol 53 (4) ◽  
pp. 798-806 ◽  
Author(s):  
V. I. Fabrikant
Keyword(s):  
Integral Representation ◽  
Half Space ◽  
Arbitrary Shape ◽  
Contact Problems ◽  
Elastic Half Space ◽  
Elastic Contact ◽  
Circular Sector ◽  
Flat Punch ◽  
Circular Segment ◽  
Arbitrary Planform

A new method is proposed for the analysis of elastic contact problems for a flat inclined punch of arbitrary planform under the action of a normal noncentrally applied force. The method is based on an integral representation for the reciprocal distance between two points obtained by the author earlier. Some simple yet accurate relationships are established between the tilting moments and the angles of inclination of an arbitrary flat punch. Specific formulae are derived for a punch whose planform has a shape of a polygon, a triangle, a rectangle, a rhombus, a circular sector and a circular segment. All the formulae are checked against the solutions known in the literature, and their accuracy is confirmed.

The Half-Space Under Pressure Distributed Over an Elliptical Portion of Its Plane Boundary

1960 ◽  
Vol 27 (1) ◽  
pp. 111-119 ◽  
Author(s):  
H. Deresiewicz
Keyword(s):  
Pressure Distribution ◽  
Half Space ◽  
Principal Axis ◽  
Major Axis ◽  
Minor Axis ◽  
Plane Boundary ◽  
Uniform Pressure ◽  
Principal Stresses ◽  
The Difference ◽  
Normal Deflection

In determining the safety of foundations the assumption is usually made that the pressure distribution on the ground, in general unknown, is closely approximated by a constant one. Mathematically, the problem is thereby reduced to finding the components of stress and displacement in a half-space due to a uniform pressure on a portion of its plane boundary. The present paper contains an investigation of this problem for the case of loading over an area bounded by an ellipse. Two of the results are: (a) On the normal to the loading area through its center, the two principal stresses in planes parallel to the undeformed surface, compressive on and near the surface, become tensile within a depth smaller than the length of the corresponding principal axis of the loading area; (b) the normal deflection of the surface is greater at the extremity of the minor axis of the loading area than at the extremity of the major axis, the difference between the two values increasing with the ellipticity of the bounding curve.

Analysis of Stress in Half-Space Using Jacobian of Transformation and Gauss Numerical Integration

2013 ◽  
Vol 818 ◽  
pp. 178-186 ◽  
Author(s):  
Radim Čajka
Keyword(s):  
Numerical Integration ◽  
Half Space ◽  
Arbitrary Shape ◽  
Strain Analysis ◽  
Elastic Halfspace ◽  
Stress Strain ◽  
Numerical Examples ◽  
Nodal Points ◽  
Loaded Area ◽  
Isoparametric Elements

Stress strain analysis of elastic halfspace by means of Gauss numerical integration and Jacobean of transformation is presented. The arbitrary shape and general course of the loaded area in nodal points is allowed by use of 4-and 8-node isoparametric elements, numerical integration and Jacobean transformation. Results of numerical examples are compared with other solutions.

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