Stress concentration around a hole in bending of micropolar plates

A finite element approach to the analysis of stresses in micropolar media is developed. The stress concentration around a circular hole in a micropolar medium in a state of plane stress has been studied by Kaloni and Ariman using a stress function approach and the results have been compared with the solution of the problem obtained by Mindlin using couple-stress theory. It appears that the problem of stress concentration around a circular hole in a thin plate of micropolar material under transverse loading has not been studied previously. This problem is presently treated using a triangular micropolar plate bending element, assumption being made of a circular hole in a rectangular plate under uniform transverse loading. The results are compared with exact and finite element solutions of the corresponding problem of classical elasticity. It may be expected that the microelastic constants of relevant materials will be established in the relatively near future. The results of the present study will become particularly useful at that time for the calculation of stresses and deformations in the neighborrhood of penetrations, either circular or non-circular, in the head or in the body of reactor vessels and other pressure vessels, especially when the affected region is relatively shallow