The Meshless Method With General Couple Stress Theory

The micromation of the mechanical devices and electronic devices is a trend of the development of industry .However,the beahavior of material in the scale of micron meters is different from what the theory in macro meters has predicted .Therefore the couple stress theory theory was developped and had beed 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.There are two kinds of couple stress theories, Cosserat theory with constrained rotations (simpled couple stress theory )and Cosserat theory (the general couple stress theory).They both considered the infulence of strain gradient by couple stress and curvature.The difference of the two theories lies in there are three freedoms of motion in the Cosserat theory, the micro-rotation is treated as an independent kinematic quantity with no direct dependence upon the displacement vector.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 neccesary with the development of computer. The finite element method has the difficuty of displacement commutium to solve couple stress problem.The element free method based on the message of nodes has many advantages in crack propagation and elastic-plastic problems. Therefore,based on the element free method with simpled couple stress theory,we solved the problems of crack mechnics ,and developped a new element free mehod with general couple stress theory,through the numerical example ,the high accuracy,and high efficiency of the method were proved.Because of the difference of the two theories,the numerical stimulations are different.It is neccesary to study the difference in order to give advice to the engineering.In this paper ,we studied these from the theorical analysis and numerical analysis. The classical numerical example proved that the difference of the two theories on stress concertration,at last we find the relationship of the two theories.