Parametric analysis of analytical solutions to one‐ and two‐dimensional problems in couple‐stress theory of elasticity

Abstract

AbstractIn this paper the fundamentals of the asymmetric elasticity theory are used to consider one‐ and two‐dimensional boundary‐value problems: shear deformation of elastic infinite plane layer(plate); torsion of a ring rigidly fixed at the external contour due to rotation of the inner one; deformation of a plane washer caused by a rigid displacement of the internal contour relative to the external one; the Kirsch problem on unilateral extension of a plate loosened by a circular hole. The solution of each problem is compared with the corresponding solution obtained in the framework of the classical theory of elasticity. The comparison is made in terms of macro‐parameters introduced to characterize the degree of difference between these solutions. The analysis of the obtained results show that for each problem under consideration this difference is not essential. It is worthy of note that the macro‐parameters used for comparison can be constructively measured by experiment. The obtained results can be used to outline a key diagram of experiments enabling one to detect the effects of “couple” response of the examined medium.