A Mixed Boundary Value Problem for a Finite Isotropic Wedge Under Antiplane Deformation

Abstract

This study investigates the behavior of singularities in a finite isotropic wedge subjected to antiplane deformation, focusing on how varying angles influence the strength of these singularities. Employing the finite Mellin transform technique, we derive solutions to the boundary value problems associated with the wedge configuration. The analysis reveals that as the angle α\alphaα approaches critical values of 2π/3,3π/4 and π. the strength of the singularity exhibits significant variations, specifically decreasing to ¾, 2/3 and ½, respectively. These findings underscore the critical relationship between the geometric configuration of the wedge and the resultant stress distribution around singularities. Furthermore, the implications of this research extend to practical engineering applications, highlighting the importance of understanding singularities in the design and analysis of structures under similar deformation conditions. Recommendations for further research include exploring additional geometric configurations, conducting experimental validations, and implementing numerical simulations to enhance the understanding of singular behavior in isotropic materials. This work contributes to the existing literature on boundary value problems and provides valuable insights for both theoretical and applied mechanics.