Shear deformation theory using logarithmic function for thick circular beams and analytical solution for bi-directional functionally graded circular beams

摘要

A shear deformation theory including a logarithmic function in the postulated expression for the circumferential displacement is developed for thick circular beams and is used to analytically solve static deformations of bi-directional functionally graded circular beams. The consideration of a logarithmic term is motivated by the displacement field in the analytical solution of the plane strain elasticity problem of a hollow circular cylindrical shell. The non-zero shear traction boundary conditions at the two major surfaces of the beam are a priori satisfied by the assumed displacement field. The material properties are assumed to vary according to exponential and power laws, respectively, in the tangential and the thickness directions. Parametric studies conducted for the variation of stresses and displacements indicate that material properties can be tailored to satisfy several structural constraints. For the bending of a sandwich beam with a bi-directionally graded core and homogeneous isotropic facesheets, it is found that the maximum interfacial bending stress, the peak interfacial shear stress and the maximum interfacial peeling stress can be reduced, respectively, by 20%, 44% and 42%. (C) 2017 Elsevier Ltd. All rights reserved.