Analytical and fem methods for stress state estimation in a sheared plane with two identical circular holes

Florina Carmen Ciornei; Stelian Alaci; Dumitru Amarandei; Constantin Filote

Florina Carmen Ciornei Suceava University, Faculty of Mechanical Engineering, Mechatronics and Management
Stelian Alaci Suceava University, Faculty of Mechanical Engineering, Mechatronics and Management
Dumitru Amarandei Suceava University, Faculty of Mechanical Engineering, Mechatronics and Management
Constantin Filote Suceava University, Faculty of Electrical Engineering and Computer Science

Keywords: elastic plane, two similar holes, shear loading, stress concentration factor, Airy’s stress function

Abstract

Shear stresses occur in almost any applications during machining of mechanical parts. Inhomogeneities perturb the stress field in working pieces, meaning that they are responsible of a strong stress gradient and therefore cracks may occur in the regions in the vicinity of these inhomogeneities. The present paper presents some results concerning the stress state for a plane with two circular identical holes, subjected to pure shearing. To find the stress state the authors used analytical and numerical methods, on the basis of theory of elasticity hypothesis. The analytical method is based on the Airy’s stress function method, using bipolar coordinates. The stress fields (principal shearing and principal normal stresses), plotted using Mathcad application were compared with the stress fields obtained by FEA, using Catia application. An excellent agreement is found between the plotted stresses obtained by the mentioned methods.

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