Based On The Couple Stress Theory Of Non-grid Method

In order to explain the size effect for materials in the scale of micron meters, the strain gradient theory was developed. Based on the analysis and arrangement of present strain gradient theories and element-free methods, the elasticity couple stress theory is combined with EFGM (Element-Free Galerkin Method) in this paper, and developed a new element-free method. MATLAB programs are compiled on this method, together with some experiments, proved its feasibility and efficiency.The main research content and conclusion are stated as followed:The mechanics character of couple stress theory is analyzed systemically. Equation of balance, equation of motion, equation of compatibility and constitution equation of couple stress theory are derived in both plane strain deformation and plane stress deformation. For the convenience of discussing, elasticity couple stress theory in plane stress deformation is studied in the paper.A n ew element-free method is derived, with the elasticity couple s tress theory combined with EFGM. The development of the element-free methods during recent years is studied, and the research progress in element-free methods is discussed in detail in this paper. EFGM, which is based on the moving least squares method, is not constrained by the connectivity between nodes and elements in the finite element method. It can freely distribute nodes and integration subdomains according to the actual geometry, and it can apply the proper basis function according to the possible displacement function, have a good computational precision. MATLAB programs arecompiled to validate some experiments.To deal with stress concentration problems, the problems of the circular hole in a field of uniform tension or in a field of tension or compressions in two perpendicular directions are solved. The computational precision of MLS (Moving Least Squares)-based element-free method is analyzed, some commonly used weight functions are studied. At the same time, the effect of the compact support on the computational precision is studied. When couple stress must be considered, the stress concentration factor decreases and increases with a/l (hole radius/characteristic length) increases, and finally it approaches classical answer. The stress concentrationfactor a lso d epends o n Poisson's r ation, d ecreasing w ith P oisson's r ation. All t hese show that the new method possesses several advantages, such as high accuracy, high stability, and high efficiency.Lastly, the development of element-free method based on strain gradient theories is forecasted.