The stress distribution due to a force in the interior of a semi-infinite elastic medium

1944 ◽  
Vol 40 (3) ◽  
pp. 229-238 ◽  
Author(s):  
Ian N. Sneddon
Keyword(s):  
Stress Distribution ◽  
Elastic Medium ◽  
Plane Strain ◽  
External Force ◽  
Displacement Vector ◽  
Not Given ◽  
Line Parallel ◽  
Infinite Line ◽  
Distribution Of Stress

1. In this paper an analysis is given of the distribution of stress in a semi-infinite elastic medium due to the action of an external force applied to the interior of the medium. It will be assumed throughout that the force acts in a direction perpendicular to that of the boundary of the solid; the analysis is similar when the line of action of the force is parallel to the boundary and is therefore not given here. The equations of plane strain parallel to the x-y plane are employed; physically this is equivalent to assuming that there is no component of the displacement vector in a direction normal to the x-y plane or, what is the same thing, that the external force is applied along are infinite line parallel to the axis of z.

scholarly journals Analysis of Disturbing Influence of Traffic Load on Soil Body

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Janat Musayev ◽  
Algazy Zhauyt
Keyword(s):  
Stress Distribution ◽  
Elastic Medium ◽  
Traffic Flow ◽  
Stress Waves ◽  
Point Sources ◽  
Traffic Load ◽  
Strength Evaluation ◽  
Propagating Waves ◽  
Waves Propagation ◽  
Distribution Of Stress

Stress waves propagate in soil in case of earthquake and man-made effects (traffic flow, buried explosions, shield-driven pipes and tunnels, etc.). The wave point-sources are those located at the distances equal to more than two waves lengths, which significantly simplifies solving of a problem of these waves’ strength evaluation. Distribution of stress and displacement by the stress waves propagation in elastic medium is a complex pattern. The stress distribution in propagating waves depends on the type and form of source, conditions of the source contact with medium, and properties of mediums in the vicinity of the source. The point-sources and their combinations are selected in such a way to model an influence of machines and processes on soil body in case of shield-driven pipes (tunnels).

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.

scholarly journals Stress distribution in a rectangular plate having two opposing edges sheared in opposite directions

1923 ◽  
Vol 103 (723) ◽  
pp. 598-610 ◽  
Keyword(s):  
Shear Stress ◽  
Stress Distribution ◽  
Rectangular Plate ◽  
Royal Society ◽  
External Stress ◽  
The Other ◽  
Optical Methods ◽  
Centre Line ◽  
Distribution Of Stress

The type of deformation under investigation is indicated by fig. 1. A rectangular plate ABCD is deformed into the shape A'B'C'D'. The two opposing edges AB, CD are shifted horizontally without alteration of length into the position A'B', C'D', the other boundaries AD, BC being kept free from external stress. In a paper which appeared in the 'Proc. Royal Society', December 28, 1911, Prof. E. G. Coker investigated this same type of deformation using optical methods to determine the distribution of stress along the centre line OX. He found that if the plate was square the shear stress along OX was distributed in a munner which was approximately parabolic. As the ratio of AD to AB decreased the curve of distribution first of all became flat-topped, and for yet smaller ratios two distinct humps made their appearance.

Settlement of a strip footing on a confined clay layer

1983 ◽  
Vol 20 (3) ◽  
pp. 535-542
Author(s):  
Brian B. Taylor ◽  
Elmer L. Matyas
Keyword(s):  
Stress Distribution ◽  
Plane Strain ◽  
Poisson’S Ratio ◽  
Ground Surface ◽  
Finite Depth ◽  
Strip Footing ◽  
Poisson's Ratio ◽  
Clay Layer ◽  
Line Load ◽  
Settlement Analysis

A procedure is described that permits an estimation of either consolidation or immediate settlements of a uniformly loaded, flexible strip footing founded below the ground surface. The soil above the base of the footing is sand, and the soil below the base consists of clay, which extends to a finite depth. The procedure is based on a solution of Kelvin's equations for a line load acting within an infinite solid. Charts are presented which permit an estimate of settlement for various compression moduli, Poisson's ratio, and clay thickness.The proposed method predicts consolidation settlements that are generally slightly greater than those predicted from Boussinesq theory. Consolidation settlements increase as Poisson's ratio increases. Immediate settlements are slightly greater than those reported previously. Keywords: consolidation, elasticity, footings, plane strain, settlement analysis, stress distribution.

Evaluation of the Bonding Strength at the Three-Dimensional Vertex in Silicon-Resin Joints

2009 ◽  
Author(s):  
Hideo Koguchi ◽  
Masato Nakajima
Keyword(s):  
Stress Distribution ◽  
Stress Field ◽  
Boundary Element ◽  
External Force ◽  
Thermal Stresses ◽  
Three Dimensional ◽  
Singular Stress ◽  
Singular Stress Field ◽  
Element Method ◽  
Silicon Resin

Portable electric devices such as mobile phone and portable music player become compact and also their performance improves. High density packaging technology such as CSP (Chip Size Package) and Stacked-CSP is needed to realize advanced functions. CSP is a bonded structure composed of materials with different properties. A mismatch of material properties may cause stress singularity at the edge of interface, which lead to the failure of bonding part in structures. Singular stress field in residual thermal stresses occurs in a cooling process after bonding the joints at a high temperature. In the present paper, the strength of interface in CSP consisted of silicon and resin is investigated. Boundary element method and an eigen value analysis based on finite element method are used for evaluating the intensity of singularity of residual thermal stresses at a vertex in a three-dimensional joint. Three-dimensional boundary element program based on the fundamental solution for two-phase isotropic body is used for calculating the stress distribution in the three-dimensional joint. Angular function in the singular stress field at the vertex in the three-dimensional joint is calculated using eigen vector determined from eigen analysis. The strength of bonding at the interface in several silicon-resin specimens with different thickness of resin is investigated analytically and experimentally. Stress singular analysis applying an external force for the joints is firstly carried out. After that, singular stress field for the residual thermal stresses varying material property of resin with temperature is calculated. Combining singular stress fields for the external force and the residual thermal stress yields a final stress distribution for evaluating the strength of interface. A relationship between the external force for delamination in joints and the thickness of resin is derived. Finally, a critical intensity of singularity for delamination between silicon and resin is determined.

Boussinesq's problem for a flat-ended cylinder

1946 ◽  
Vol 42 (1) ◽  
pp. 29-39 ◽  
Author(s):  
Ian N. Sneddon
Keyword(s):  
Free Surface ◽  
Rigid Body ◽  
Elastic Medium ◽  
Normal Displacement ◽  
Full Account ◽  
Elastic Stresses ◽  
Special Cases ◽  
Cylindrical Punch ◽  
Distribution Of Stress ◽  
Boussinesq’S Problem

1. In a recent paper(1) expressions were found for the elastic stresses produced in a semi-infinite elastic medium when its boundary is deformed by the pressure against it of a perfectly rigid body. In deriving the solution of this problem—the ‘Boussinesq’ problem—it was assumed that the normal displacement of a point within the area of contact between the elastic medium and the rigid body is prescribed and that the distribution of pressure over that area is determined subsequently. The solutions for the special cases in which the free surface was indented by a cone, a sphere and a flat-ended cylindrical punch were derived, but no attempt was made to give a full account of the distribution of stress in the interior of the medium in any of these cases.

Sign in / Sign up

Export Citation Format

Share Document