基于偶应力理论的拉格朗日乘子约束的四结点杂交元法

在约束转动的偶应力理论中，有微转动和宏观转动相等的约束条件，目前的研究对于此约束条件的引入大都是采用罚函数法，罚函数法与其他引入约束条件的方法相比要求相对弱一点，容易实现，但罚函数值的选择有一定的困难，不利于偶应力理论的推广应用，以拉格朗日乘子来引入此约束条件，避免了罚函数法的缺点.为了满足偶应力问题对单元位移试解的c1连续性要求，采用四结点杂交元来构造有限单元法的基本单元.数值算例验证了本文方法具有精度高和稳定性好的特点.

Hybrid finite element method constrained by Lagrange multiplier in couple-stress theory

There is a constrained condition,in which macro rotation is equal to the micro rotation in couple-stress theory.The constraint condition has been introduced by a penalty function technique in recent research,which has not only some advantages but also some disadvantages making couple-stress theory use difficult.The constrained condition was introduced by the Lagrange multiplier method to overcome these disadvantages of the penalty function technique.To meet the special demand of c1 continuity of the couple-stress theory,a four-node hybrid element was introduced.A numerical example validates the good accuracy and high efficiency of this method.