The Problem of Minimizing Stress Concentration at a Rigid Inclusion

1985 ◽  
Vol 52 (1) ◽  
pp. 83-86 ◽  
Author(s):  
L. Wheeler
Keyword(s):  
Stress Concentration ◽  
Variational Problem ◽  
Plane Strain ◽  
Rigid Inclusion ◽  
Elastic Matrix ◽  
Optimum Shape ◽  
Plane Strain Problem ◽  
Elementary Problem ◽  
Conventional Methods

With the objective of minimizing stress concentration, the plane-strain problem of the optimum shape for a rigid inclusion in an elastic matrix of unbounded extent is investigated. It is shown rigorously that the underlying variational problem is reducible to a more elementary problem which can be solved by conventional methods to arrive at the optimum shape, which is a suitably proportioned ellipse.

The Contact Problem for a Rigid Inclusion Pressed Between Two Dissimilar Elastic Half Planes

1981 ◽  
Vol 48 (1) ◽  
pp. 104-108
Author(s):  
G. M. L. Gladwell
Keyword(s):  
Contact Problem ◽  
Plane Strain ◽  
Integral Equations ◽  
Elastic Constants ◽  
Contact Stress ◽  
Rigid Inclusion ◽  
Numerical Results ◽  
Stress Distributions ◽  
Plane Strain Problem

Paper concerns the plane-strain problem of a rigid, thin, rounded inclusion pressed between two isotropic elastic half planes with different elastic constants. Required to find the extents of the contact regions between each plane and the inclusion, and the contact stress distributions. The governing integral equations are solved approximately by using Chebyshev expansions. Numerical results are presented.

Equilibrium equations and boundary conditions of strain gradient theory in arbitrary curvilinear coordinates

2014 ◽  
Vol 23 (5-6) ◽  
pp. 169-176
Author(s):  
Mikhail Guzev ◽  
Chengzhi Qi ◽  
Jiping Bai ◽  
Kairui Li
Keyword(s):  
Boundary Conditions ◽  
Plane Strain ◽  
Strain Gradient ◽  
Special Form ◽  
Curvilinear Coordinates ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Equilibrium Equations ◽  
Plane Strain Problem

AbstractEquilibrium equations and boundary conditions of the strain gradient theory in arbitrary curvilinear coordinates have been obtained. Their special form for an axisymmetric plane strain problem is also given.

The Comparison of the Loess Mechanical Properties under Plane Strain and Conventional Triaxial Experiments

2014 ◽  
Vol 919-921 ◽  
pp. 791-794
Author(s):  
Lin Ma
Keyword(s):  
Mechanical Properties ◽  
Moisture Content ◽  
Plane Strain ◽  
Confining Pressure ◽  
Test Method ◽  
The Other ◽  
Strain Condition ◽  
Plane Strain Problem ◽  
Plain Strain ◽  
The Impact

Plane strain problem is currently prevalent in the loess engineering. However, this problem still using conventional triaxial test method for processing. So the paper conducted the plain strain test, analyze differences in plane strain experiments with conventional triaxial experiments under different moisture content and confining pressure. Research shows two points, the first one is the impact on the strength of the soil is more under moisture content than confining pressure, the other is that the soil strength under the plane strain condition is significantly greater than conventional triaxial conditions. It shows that the results were conservative under the plane strain problem at past. It played a certain role in guiding the engineering.

Three-Dimensional Elastic Stress Fields of Finite Thickness Plates with Elliptical Hole

2007 ◽  
Vol 353-358 ◽  
pp. 74-77
Author(s):  
Zheng Yang ◽  
Chong Du Cho ◽  
Ting Ya Su ◽  
Chang Boo Kim ◽  
Hyeon Gyu Beom
Keyword(s):  
Stress Concentration ◽  
Plane Strain ◽  
Plane Stress ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Maximum Stress ◽  
Elastic Stress ◽  
Finite Thickness ◽  
Plate Thickness ◽  
Three Dimensional

Based on detailed three-dimensional finite element analyses, elastic stress and strain field of ellipse major axis end in plates with different thickness and ellipse configurations subjected to uniaxial tension have been investigated. The plate thickness and ellipse configuration have obvious effects on the stress concentration factor, which is higher in finite thickness plates than in plane stress and plane strain cases. The out-of-plane stress constraint factor tends the maximum on the mid-plane and approaches to zero on the free plane. Stress concentration factors distribute ununiformly through the plate thickness, the value and location of maximum stress concentration factor depend on the plate thickness and the ellipse configurations. Both stress concentration factor in the middle plane and the maximum stress concentration factor are greater than that under plane stress or plane strain states, so it is unsafe to suppose a tensioned plate with finite thickness as one undergone plane stress or plane strain. For the sharper notch, the influence of three-dimensional stress state on the SCF must be considered.

Sign in / Sign up

Export Citation Format

Share Document