A unified solution approach for a large variety of antiplane shear and torsion notch problems: Theory and examples. (15th December 2016)

• Record Type: Journal Article
• Authors: Salviato, Marco; Zappalorto, Michele
• Is Part Of: International journal of solids and structures. Volume 102/103(2016)
• Page Start: 10
• Page End: 20
• Publication Date: 2016-12-15
• Subjects: Antiplane shear -- Torsion -- Notch -- Stress distributions; Mechanics, Applied -- Periodicals; Structural analysis (Engineering) -- Periodicals; Elastic solids -- Periodicals; Mécanique appliquée -- Périodiques; Constructions, Théorie des -- Périodiques; Solides élastiques -- Périodiques; Elastic solids; Mechanics, Applied; Structural analysis (Engineering); Periodicals; 624.18
• DOI: 10.1016/j.ijsolstr.2016.10.022
• Languages: English
• ISSNs: 0020-7683

Abstract

Abstract: In this work, a unified solution approach is proposed for the analytical evaluation of the stress fields close to notches under antiplane shear and torsion loadings, which allows a large variety of notch problems to be tackled. The method is based on the complex potential approach for antiplane elasticity combined with the use of proper conformal mappings. In particular, it is shown that a well defined analytical link does exist between the complex potential to be used to determine stresses and the first derivative of the conformal mapping used to mathematically describe the notch profile. This makes some methodologies such as Schwarz-Christoffel transformation, which allows describing any polygonal domain automatically, very attractive for the direct solution of notch problems. A bulk of solutions are provided to support this finding, from cracks and pointed notches, to radiused notches. In addition, the accuracy of each proposed solution is discussed in detail taking advantage of a bulk of results from FE analyses.