Improvement On Displacement Functions Of The Discontinuous Deformation Analysis Method And The Application To Engineering Mechanics Problems

The Discontinuous Deformation Analysis (DDA) method is suitable for solving engineering problems with many discontinuous interfaces inside the concerned domain, e.g. the stability analysis of fractured rock mass. The history of various discontinuous deformation analysis methods including DDA is stated. The basic theory of DDA is introduced, and the comparisions between DDA and other numerical methods (the finite element methods, the discrete element methods, etc.) are made. Since DDA is still under development, one of concerns is how to improve block displacement functions so that the block stress precision can be improved. Based on the analysis of some related techniques, this dissertation proposes that the meshfree method be unilized to construct the displacement patterns, which can be considered as a technique of coupling DDA with meshfree methods. By the new technique, many new numerical abilities of DDA can be explored such as calculating the precious block stress fields, analyzing the block bending, and imitating the propagation of cracks etc. The detailed works are as follows:In chapter 2, the DDA theory is stated. The relationship between DDA and other numerical methods is discussed, such as the finite element methods and the discrete element method.In chapter 3, firstly the defect of linear displacement function is discussed, as well as some related techniques for improving this. Then the displacement interpolation mode based on the meshfree methods is introduced in DDA. By this new mode some interpolative nodes are needed to be scattered in the blocks. According to the principle of the minimum potential, the system of equations is deduced. Through solving the system, the displacements of the nodes are obtained. In this chapter, the Move Least-Square (MLS) technique is adopted to construct the displacement functions and the features are discussed.Chapter 4 makes an attempt to use an alternative meshfree method to interpolate the displacement, namely the Natural Neighbor Interpolation (NNI). By comparing this with MLS Interpolation, it is founded that the former are more efficient then the latter, but the former may need to adjust the mesh within the blocks.Those who have some expericences in the stability analysis of slopes by DDA know that DDA in gereral gives too conservative results. In chapter 5, the reason that causes DDA to underestimate the safety factors is analyzed. It is found that this is because the origional DDA ignores the effect of cohesion within the contact interfaces. The origional DDA considers that once slide happens on an interface, the C of the interfaces would be taken zero during the subsequent sliding. While the behavior of the interface might be true, it contradicts the classical limit equlibrium methods. For this reason, by keeping the cohesion force along the sliding surface, the safety factor based on the strength reservation is calculated. Compariosns with the classical limit equilibrium methods have shown that the improved DDA aggress with the classical limit equilibrium methods.Chapter 6 is devoted to the propagation of cracks in the blocks. The similar techniques in the meshfree methods are utilized and improved.Finally in chapter 7, the methods proposed in this dissertation are used to solve some engineering problems.From chapter 3 to 7, many typical numerical examples are presented which testify this new DDA method is feasible.