# Study on Stress Field Near the Notch and Crack Tip Solved by Element-Free Method

• 許 信翔

Student thesis: Doctoral Thesis

### Abstract

Generally speaking the stress in crack and notch tip will produce infinitely great phenomenon For the two-dimensional crack and notch problems stress near the crack and notch tip can solved exactly by the theoretical analysis but for the three-dimensional crack and notch ones for example a plate with a notch there is no rational solutions at present In this thesis the element-free method will be used to solve the mechanics problem of crack and notch and the main reason is that the element-free method can add stress and strain functions in the strength matrix easily The element-free method has a wild application on crack problem but there are no relevant documents using this method on the notch mechanics problem at present First the basic theory of the element-free method will be further extended to solve the numerical problems associated with this method in this thesis Second the theoretical formula will be used to derive the stress and displacement fields on in-plan notch problems with anisotropic materials and then this theory results will be applied to the element-free method Finally a singularity notch element is set up in this thesis and this method can obtain more accurate analysis result with the node that is relatively dredged Furthermore this thesis proposes the theoretical solution for the three-dimensional problem containing a semi-infinite crack with primary and shadow solutions where the primary solution is the traditional plane-strain solution and the shadow ones can be obtained from the 3D equilibrium equation of the theory of elasticity A least-squares method incorporating the finite element results was used to determine these factors in this theoretical solution The results of this research show that if enough primary and shadow solutions are included numerical simulations indicate that the proposed method can obtain an accurate displacement field for 3D crack problems The major advantage of this method is that a 3D whole displacement field with the analytic singular effect near the crack tip can be obtained without any limitation with regard to the material properties boundary conditions and applied loads Finally the element-free method is applied to the three-dimensional fracture mechanics preliminarily and the result was compared with the normal finite element method result using a fine mesh The major advantage is that the crack stress singularity which is ignored in the finite element method can be obtained in the proposed method
Date of Award 2015 Feb 2 English Shen-Haw Ju (Supervisor)

'