Incompatible finite element constrained by Lagrange multiplier on couple-stress theory

There is a constraint condition that macro rotation equal to the micro rotation in couple-stress theory. In recent studying, the constraint condition is introduced by a penalty function technique mostly, the penalty function technique has some disadvantages that make the couple-stress theory difficult to use. In this paper the constraint condition is introduced by Lagrange multiplier method to overcome these disadvantages of the penalty function technique. As the couple-stress theory has special demand of c(1) continuity, four nodes incompatible element is introduced to meet this demand The good accuracy and high efficiency of this method is proved by numerical example.