Thermostatics of micropolar elastic thin beams with a circular axis with independent fields of displacements and rotations and the finite element method

Abstract

In the present paper, on the basis of the previously developed system of hypotheses, the applied (one-dimensional) theory of thermostatic bending of micropolar (with independent fields of displacements and rotations) elastic thin beams with a circular axis is constructed, energy theorems are proved and the corresponding variational principles are established. To solve specific boundary-value problems of the applied theory of thermostatic bending of micropolar thin beams with a circular axis, ways of analytical solutions are considered as well as a variant of the finite element method is developed. On the basis of numerical results and parametric analysis of the problems, it is stated that the micropolar properties of the material, in case of other equal conditions, increase the rigidity of the beams in comparison with the classical case.