Concentrated Couple in a Plane and in a Half-Plane in the Framework of Fractional Nonlocal Elasticity

Abstract

In nonlocal elasticity, the constitutive equation for the stress tensor is written in an integral form, with the weight function, referred to as the nonlocality kernel, often being the Green’s function for the partial differential equation. In this paper, we obtain solutions to elasticity problems for a concentrated couple in a plane and on the boundary of a half-plane within framework of a new theory of nonlocal elasticity, where the nonlocal kernel is the Green’s function of the Cauchy problem for the fractional diffusion equation. The obtained solutions are free from nonphysical singularities that appear in the classical local elasticity solutions.

Keywords

• fractional calculus
• nonlocal elasticity
• concentrated couple
• Caputo fractional derivative
• fractional diffusion equation
• Mittag-Leffler function