Deformation of a two-dimensional, shear deformable cantilever beam using gradient elasticity and finite differences

© 2016 Praise Worthy Prize S.r.l. - All rights reserved. In the paper it has been studied the deformation of a cantilever beam using gradient elasticity and the finite difference method. The basic equilibrium equations are derived for an infinitesimal area for linear and gradient elasticity. Higher order expressions for the strain are considered, and from the differential equilibrium equation for gradient elasticity separate differential equations for the displacements, in terms of the linear solution, were formulated. Subsequently, recursive formulas are derived by replacing the derivatives with difference expressions over points. Computer implementation is performed and the deformation of a cantilever beam (tension, bending, through-the-thickness) is studied with the finite difference method. Solutions of exponential and periodic type are obtained