The Mesh-Free Method With Couple Stress Theory For Vibration Analysis Of Micro-Structure

The micromation of the mechanical devices and electronic devices is a trend of the development of industry.However, the behavior of material in the scale of micron meters is different from what the theory in macro meters has predicted.Therefore the theory for size effect was developed and had been used in the analysis of stress and strain of granular material, composite material, and the characteristic length of material was introduced in the constitutive relations of the theory.The mechanics character of the couple stress theory is analyzed systemically. The equilibrium relations and the constitutive relations are derived for the general couple stress. Strain gradient deformation theory was developed in order to explain such size effect for materials in the scale of micron meters. The general couple stress theory is one of the strain gradient theories. There are many material constants in the coupled elastic body than the classic elastic body, it is difficult to obtain the analytic solutions, the numerical solution is necessary with the development of computer.The mesh-free method based on the message of nodes has many advantages in analysis of micro-structure. A new mesh-free method for vibration analysis of micro-structure is developed, with couple stress theory combined with mesh-free method. The equilibrium relations and the constitutive relations are derived for the mesh-free method with couple stress theory.Based on the mesh-free method with couple stress theory, the range of parameters in mesh-free method which have great impact on the result had been discussed. Solved the problems in vibration analysis of micro-structure, through the numerical example, the high accuracy, and high efficiency of the method were proved.Lastly, the development of the mesh-free method in vibration analysis based on couple stress theory is forecasted.