Stress analysis of an infinite plate containing two unequal collinear elliptical holes under in-plane stresses at infinity

Abstract

<span style="font-size:11.0pt;line-height:115%; font-family:" calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-fareast-font-family:="" "times="" new="" roman";mso-fareast-theme-font:minor-fareast;mso-hansi-theme-font:="" minor-latin;mso-bidi-font-family:"times="" roman";mso-ansi-language:en-us;="" mso-fareast-language:en-us;mso-bidi-language:ar-sa"="">A closed form analytical solution to the problem of an infinite plate containing collinear unequal elliptical holes subjected to in-plane loadings at an angle <i style="mso-bidi-font-style:normal">β</i> with respect to x or y-axis on infinite boundary of the plate is presented. The problem is formulated in the complex plane using the Kolo-soff- Muskhellshvili's complex stress functions and further the Schwarz's Alternating Method is used to solve the problem of doubly connected region. The stress concentration factor for holes and stress intensity factors at all crack tips for varying sizes and centre to centre distances are evaluated. Some displacement formulation and the checked by Finite Element Method using displacement formulation and the two solutions are in good agreement The present results are compared with reported ones obtained by other methods. An analytical method for locating point in the vicinity of ellipses where the local and global strain energy density are equal is also presented.</span>