Keywords: micropolar solid, anisotropy, linear elasticity, cylinder, pressure, torsion.

The paper deals with two special linear elastic problems for axisymmetric orthotropic micropolar solids with central symmetry [1]. The first one is a hollow circular cylinder of unlimited length, subjected to internal and external uniform pressure. The second one is a hollow or solid circular cylinder of finite length, subjected to twisting moments acting on its bases. In both cases, one of the axes of elastic symmetry is parallel to the cylinder axis; the other two are arbitrarily oriented in the plane of any cross-section of the solid. The elastic properties are invariant along the cylinder axis.

The solution of both problems is sought in terms of unknown displacement and microrotation functions. Special kinematic fields (in-plane displacements and microrotations) are proposed for each problem, taking account of the solid geometry and the solutions previously obtained by other authors for micropolar isotropic elastic bodies [2]. The two problems are found to be governed by formally similar sets of ordinary differential equations in the kinematic fields.

Numerical solutions of the governing equations of both problems are obtained using the commercial code Matlab©, which solves boundary value problems for systems of differential equations using finite differences. These solutions are critically discussed, putting special emphasis on the comparison between 'classical' Cauchy solution and micropolar solution.

A sensitivity analysis for the problem of the hollow cylinder subjected to radial external pressure showed that the solution is very similar to that of a Cauchy solid with comparable equivalent elastic properties, as far as the radial and hoop force stresses are concerned, regardless of the value of the micropolar material internal length.

Regarding the problem of a solid cylinder subjected to torques at the end bases, the shear stresses acting on any section of the cylinder were found to be sensibly different from those computed according to the Cauchy model for certain values of the elasticities, and can underestimate or overestimate those in the non-polar solid for a given angle of twist.

The results obtained are intended to be preliminary to the problem of optimally designing axisymmetric micropolar bodies, taking the orientation of the material symmetry axes as design variable.

1

A.C. Eringen, "Linear theory of micropolar elasticity", J. Math. Mech, 15(6), 909-923, 1966.

2

D. Iesan, "Torsion of micropolar elastic beams", Int. J. Engng. Sci., 9, 1047-1060, 1971. doi:10.1016/0020-7225(71)90001-2

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