Size effects of micropolar medium in problem on the cylindrical body torsion

A. V. Romanov

Čebyševskij sbornik, Tome 25 (2024) no. 5, pp. 262-276

Résumé

In this paper, a variational principle of Lagrange of micropolar theory of elasticity is formulated for a some boundary-value problems. Anisotropic, isotropic and centrally symmetric material are considered. The Ritz method is used to obtain a system of linear algebraic equations in a form of the tensor-block stiffness matrices. The macro-displacement and the micro-rotation are expressed as a sum of products of shape functions and the generalized kinematic nodal fields. For effective approximation of the nearly incompressible micropolar material the generalized method of reduced and selective integration is used. For testing of described variational model the cylinder torsion problem of the classical and micropolar media is considered. Micropolar continuum exhibit substantial size effects in torsion(and bending) [18]: slender specimens are more rigid than anticipated via classical elasticity. Analytical solution which satisfy integral condition of torsion on the end faces is used.

Détail

Mots-clés : torsion problem, rotation gradient tensor
Keywords: micropolar continuum, Cosserat continuum, couple stress theory, variational principle, couple stress tensor, finite element method, stiffness matrix, reduced and selective integration, size effect of torsion, relative stiffness.