The aim of this paper is to study the problem of stress concentration in an infinite plate with an elliptic hole reinforced by a functionally graded layer based on the complex variable method combined with the technique of conformal mapping. With using the method of piece-wise homogeneous layers, the general solution for the functionally graded layer having normal arbitrary elastic properties is derived when the plate is subjected to arbitrary constant loads at infinity, and then numerical results are presented for several special examples. It is found that the existence of the functionally graded layer can influence the stress distribution in the plate, and thus choosing proper variations of the normal elastic properties and proper thicknesses of the layer can effectively reduce the stress concentration around the elliptic hole.

Reduction of the stress concentration around an elliptic hole by using a functionally graded layer

Analytical solution for a reinforcement layer bonded to an elliptic hole under a remote uniform load

Interaction of an edge dislocation with a coated elliptic inclusion

The purpose of this study is to evaluate stress distribution around a non-circular hole in an infinite metallic plate subjected to a uniform heat flux. The development of the Goodier and Florence’s method is used for the stress analysis of perforated plates subjected to a uniform heat flux. Goodier and Florence used their solution for the stress analysis of infinite isotropic plates with circular and elliptical holes. In order to expand their method to study non-circular holes, by means of conformal mapping, the infinite area external to the hole can be presented by the area outside the unit circle. In this study, thermal-insulated condition along the hole boundary is assumed. The rotation angle of hole, bluntness and the angle of heat flux as important parameters are considered in this study. Results showed that the effects of these parameters on stress distribution around various shaped holes are very significant and by the correct selection of these parameters, a lower amount of thermal stress compare to that of a circular hole can be achieved.

Thermal stress analysis in metallic plates with a non-circular hole subjected to uniform heat flux

Lekhnitskii’s complex variable method was developed to investigate the effect of uniform heat flux on perforated anisotropic plate with elliptical hole. The Cauchy’s integral formula was simplified by conformal mapping, and infinite area external to the hole was represented by the area outside the unit circle. In this article, Neumann boundary conditions and thermal-insulated condition along with the hole boundary were considered. Important parameters affecting stress distribution and displacement were those of rotation angle of hole, aspect ratio of hole size, and fiber angle. Results determined in this article were verified by finite element analysis.

Thermal stress analysis of infinite anisotropic plate with elliptical hole under uniform heat flux

A thermoelastic solution to a coated elliptic hole embedded in an infinite matrix subjected to a remote uniform heat flow is provided in this article. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, the general expressions of the temperature and stresses in the coated layer and the matrix are derived explicitly in a series form. Some numerical results are provided to investigate the effects of the material combinations and geometric configurations on the interfacial stresses. It is found that a coated layer has a strong effect on thermal stresses of the problem with an elliptic hole embedded in an infinite plate.

F. M. Chen

Papers

Stress Analysis of an Infinite Plate with a Coated Elliptic Hole Under a Remote Uniform Heat Flow