Orthotropic Half-plane Research Articles

The application of photo-orthotropic elasticity

A brief review of the recent developments in photo-orthotropic elasticity which covers methods of producing transparent, birefringent orthotropic model materials from glass fibres and plastics is presented. A classical form of the stress-optic law applicable in uniaxial-stress fields is given in which the orthotropic characteristics of the model material are treated by considering the material fringe value fu to be dependent upon fibre orientation. Limitations of the orthotropic model materials are identified and the effects of material non-linearities, fibre debonding and fibre distribution are described. The methods established were used to obtain a solution of the stresses in an orthotropic half-plane loaded with a concentrated force. The experimental results obtained were compared with theoretical results due to Green, and while the agreement was good, errors were considerably larger than those encountered in photo-isotropic elasticity. Finally the methods were applied to the solution of boundary stress on an elliptical hole in a finite-width tension strip.

The Indentation of an Orthotropic Half Plane Having Inclined Principal Axes

This Note concerns the calculation of the contact pressure when an orthotropic half plane is indented by a rigid frictionless indenter, the boundary of the half plane being inclined at an arbitrary angle to the principal axes of orthotropy. Specific results are given for an eccentrically loaded, flat-ended indenter.

The Affine Transformation for Orthotropic Plane-Stress and Plane-Strain Problems

Abstract It is demonstrated that a single affine transformation of the type x = ax′, y = by′ immediately extends the solution of any isotropic plane-stress or plane-strain problem to the solution of an orthotropic plane problem where the orthotropic material is characterized by three independent constants. Since orthotropy, defined as elastic symmetry with respect to two orthogonal axes, implies four independent elastic constants, the affine transformation introduces a restriction upon the orthotropic shear modulus. The orthotropic shear modulus differs from that used by previous investigators. This difference alters the equation which the orthotropic stress function must satisfy and, therefore, directly affects the solution to every plane-stress or plane-strain problem. Some arguments are advanced to favor the shear modulus, as here defined, whenever orthotropy must be restricted to three elastic constants. The two solutions of the orthotropic half plane subjected to a normal concentrated load are contrasted to illustrate the effect of the two definitions of orthotropic shear modulus.

The indentation of an orthotropic half plane

Der Verfasser findet eine allgemeine Losung fur die Verteilung des Druckes zwischen einem Block und einer orthotropen Halbebene. Es wird gezeigt, dass die Verteilung des Druckes fur den flachen Block mit allgemeiner Belastung un-abhangig ist von den elastischen Eigenschaften der Halbebene und auch genau dieselbe, als ob die Halbebene isotrop ware.

Note on the Orthotropic Half Plane Subjected to Concentrated Loads

Note on the Orthotropic Half Plane Subjected to Concentrated Loads

Discussion: “Some Problems of Orthotropic Plane Stress” (Conway, H. D., 1953, ASME J. Appl. Mech., 20, pp. 72–76) and “The Stress Distributions Induced by Concentrated Loads Acting in Isotropic and Orthotropic Half Planes” (Conway, H. D., 1953, ASME J. Appl. Mech., 20, pp. 82–86)

Discussion: “Some Problems of Orthotropic Plane Stress” (Conway, H. D., 1953, ASME J. Appl. Mech., 20, pp. 72–76) and “The Stress Distributions Induced by Concentrated Loads Acting in Isotropic and Orthotropic Half Planes” (Conway, H. D., 1953, ASME J. Appl. Mech., 20, pp. 82–86)

Closure to “Discussion of ‘Some Problems of Orthotropic Plane Stress’ and ‘The Stress Distributions Induced by Concentrated Loads Acting in Isotropic and Orthotropic Half Planes’” (1953, ASME J. Appl. Mech., 20, p. 446)

Closure to “Discussion of ‘Some Problems of Orthotropic Plane Stress’ and ‘The Stress Distributions Induced by Concentrated Loads Acting in Isotropic and Orthotropic Half Planes’” (1953, ASME J. Appl. Mech., 20, p. 446)

The Stress Distributions Induced by Concentrated Loads Acting in Isotropic and Orthotropic Half Planes

Abstract Using a Fourier integral method, the solution is obtained to an isotropic half plane subjected to a concentrated load acting at some distance from the straight edge. This problem was discussed previously by Melan, using a complex variable method of solution. The Fourier integral method is then extended to solve the corresponding problems of the orthotropic half plane.