Finite Element Method Based On The Couple Stress Theory And Its Application To Fracture Mechanics

The foundation of couple stress finite element method is based on the combine of couple stress theory and finite element method. It has been applied to line elastic fracture problem in this thesis. Fundamental of fracture mechanics theory and couple stress theory is been introduced. The form function of eight-node quadrilateral element and the fundamental of finite element method based on couple stress theory is been derived.the MATLAB language has been used to compile programs about the finite element method based on couple stress theory. The method is been checked by two example:cantilever with uniform load, infinite board with small hole. When the effect of couple stress is been included, the result is smaller than theory result. If the characteristic length is close to the characteristic size, the scale effect is clearly, otherwise, the consequent is close to the theory consequent.Combine the displacement trend extrapolation and the couple stress theory finite element method to research the style Ⅰand style compound crack fracture problem. The result shows that:without the effect of couple stress, the result given by displacement trend extrapolation is close to the classic result. In the situation of consider the effect of couple stress, stress intensity factors given by finite element method is less than the classic result. When the space of style Ⅰparallel cracks is bigger, the stress intensity factors is smaller. In the point which is closed to another crack, the result of compound collineation cracks is bigger than sole cracks, when the space of compound collineation cracks is smaller, the stress intensity factors is bigger. In the point which is far from another crack, the result is smaller than sole cracks. If the characteristic length is close to the characteristic size,the scale effect is clearly.At last, the form function of the singular element has been derived, the singular element has been applied to the research of fracture mechanics problem. The result shows that when the grids have the same element size, the result given by sharp element is more closed to classic result than result given by normal element.