Force in the Plane of Two Joined Semi-Infinite Plates

1957 ◽  
Vol 24 (4) ◽  
pp. 582-584
Author(s):  
J. T. Frasier ◽  
Leif Rongved
Keyword(s):  
Three Dimensional ◽  
Aluminum Plate ◽  
Elastic Solids ◽  
State Of Stress ◽  
Point Interior

Abstract The stress due to a force parallel to the plane of two joined semi-infinite plates is obtained from the three-dimensional state of stress produced by a force operative at a point interior to one of two joined semi-infinite elastic solids. The variation in the traction on the interface of a steel and aluminum plate is shown graphically.

scholarly journals Photoelastic Analysis of Three-Dimensional Stress Systems using Scattered Light

1940 ◽  
Vol 44 (349) ◽  
pp. 74-88 ◽  
Author(s):  
R. Weller ◽  
J. K. Bussey
Keyword(s):  
Elementary Theory ◽  
Scattered Light ◽  
Three Dimensional ◽  
Plane Section ◽  
Stress System ◽  
Principal Stresses ◽  
State Of Stress ◽  
Polarised Light ◽  
Photoelastic Analysis ◽  
Good Agreement

SummaryA method has been developed for making photoelastic analyses of threedimensional stress systems by utilising the polarisation phenomena associated with the scattering of light. By this method, the maximum shear and the directions of the three principal stresses at any point within a model can be determined, and the two principal stresses at a free-bounding surface can be separately evaluated. Polarised light is projected into the model through a slit so that it illuminates a plane section. The light is continuously analysed along its path by scattering and the state of stress in the illuminated section is obtained. By means of a series of such sections, the entire stress field may be explored. The method was used to analyse the stress system of a simple beam in bending. The results were found to be in good agreement with those expected from elementary theory.

The influence of near face behaviour on monitoring of deep tunnels

1991 ◽  
Vol 28 (2) ◽  
pp. 226-238 ◽  
Author(s):  
F. Pelli ◽  
P. K. Kaiser ◽  
N. R. Morgenstern
Keyword(s):  
Numerical Modelling ◽  
Numerical Simulations ◽  
Three Dimensional ◽  
Back Analysis ◽  
Total Change ◽  
State Of Stress ◽  
Stress Changes ◽  
The Face ◽  
Tunnel Design

Convergence, radial displacements, and stress changes are often recorded during the advance of a tunnel for the observational tunnel design approach. In deep tunnels, instruments must be installed from underground and can seldom be placed in undisturbed ground. Consequently, observations are only partial records of the total change induced by an excavation and the influence of the three-dimensional state near the face must be considered. This paper presents results from numerical simulations to assess face effects on monitoring data. The influence of such aspects as in situ state of stress, anisotropy, nonlinearity, and plasticity (yielding ground) are evaluated. Guidelines for underground monitoring of deformations are given. Key words: tunnelling, monitoring, back-analysis, convergence, extensometers, numerical modelling.

scholarly journals A Distortion Energy Failure Theory for Orthotropic Materials

1972 ◽  
Vol 94 (4) ◽  
pp. 1073-1076 ◽  
Author(s):  
G. W. Forman
Keyword(s):  
Experimental Studies ◽  
Three Dimensional ◽  
Algebraic Method ◽  
Orthotropic Materials ◽  
Rational Basis ◽  
State Of Stress ◽  
Failure Theory ◽  
Distortion Energy ◽  
Energy Theory ◽  
Energy Failure

Of the numerous methods developed to predict failure of isotropic materials exposed to a three-dimensional state of stress, experimental studies tend to confirm the validity of the distortional energy theory. To date no rational basis of predicting inelastic action in an orthotropic material exposed to principle stresses coincident with the material axes has been proposed. This study assumes that distortion energy may be used to predict failure of orthotropic materials, and a usable algebraic method of predicting failure is developed.

A Variational Boundary Integral Method for the Analysis of Three-Dimensional Cracks of Arbitrary Geometry in Anisotropic Elastic Solids

1999 ◽  
Vol 67 (2) ◽  
pp. 403-408 ◽  
Author(s):  
G. Xu
Keyword(s):  
Integral Method ◽  
Three Dimensional ◽  
Continuous Distribution ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Symmetric System ◽  
Dislocation Loops ◽  
Elastic Solids ◽  
Arbitrary Geometry ◽  
Anisotropic Elastic

A variational boundary integral method is developed for the analysis of three-dimensional cracks of arbitrary geometry in general anisotropic elastic solids. The crack is modeled as a continuous distribution of dislocation loops. The elastic energy of the solid is obtained from the known expression of the interaction energy of a pair of dislocation loops. The crack-opening displacements, which are related to the geometry of loops and their Burgers vectors, are then determined by minimizing the corresponding potential energy of the solid. In contrast to previous methods, this approach results in the symmetric system of equations with milder singularities of the type 1/R, which facilitate their numerical treatment. By employing six-noded triangular elements and displacing midside nodes to quarter-point positions, the opening profile near the front is endowed with the accurate asymptotic behavior. This enables the direct computation of stress intensity factors from the opening displacements. The performance of the method is assessed by the analysis of an elliptical crack in the transversely isotropic solid. It also illustrates that the conventional average schemes of elastic constants furnish quite inaccurate results when the material is significantly anisotropic. [S0021-8936(00)02702-1]

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