There is stress concentration in the crack tip.It has apparent effect on the stress field of the crack tip and the fracture behavior of the material.The stress concentration factor of a finite plate in a uniform tension field with the element-free method was calculated based on the couple stress theory,and the influence of couple stress on the stress field in crack tip was analyzed.The result shows the feasibility and efficiency of this method.

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.

By applying mobility and modal approach to a familiar vibration isolat ion model of machine in the engineering, the expression of the power flow input into basic beam is obtained. And the equivalent damp of super-elastic effect o f TiNi Shape Memory Alloy is calculated by simulating its cycle curve using experimen t data. According to super-elastic effect of TiNi shape memory alloy, the allo y threads are applied in the model as a kind of equivalent damp material. Differe nt figures are drawn by the simulation in case of SMA thread as damp material as well as using generic damp material equivalent to the damp of SMA thread under diffrent frequencies. From the figu res, the eff ect of vibration isolation is analyzed in case of SMA thread as damp materia l and the superiority of SMA thread as damp material is revealed.