No abstract

No abstract

Three-dimensional discontinuous deformation analysis (3-D DDA) with high-order displacement functions has been derived for the requirement of highly accurate stress and strain calculations. The high-order displacement function allows nonlinear distributions of stresses and strains within a discrete block, which significantly enhances 3-D DDA as an analysis technique. Formulations of stiffness and force matrices in second-and third-order 3-D DDA due to elastic stress, initial stress, body force, point load, fixed point, inertial force, normal and shear contact forces and friction force are presented. The VC++ codes for the second-and third-order cases have been developed, and they have been applied to examples of 3-D beams, bending under various loading conditions applied at the end and to an example of discontinuous problem. Results of modeling, are well in agreement with theoretical solutions. In contrast, the results calculated for the same model, using original first-order 3-D DDA are far from the theoretical solutions.blocks [13,14]. The NMM, still retaining most of the DDA's attractive features, can be considered a generalized finite element and DDA method. Additionally, Chen et al. developed the high-order version of the manifold method [15] and Cheng et al. [16] showed that the use of more advanced Wilson non-conforming element in NMM can be useful in obtaining more accurate results for simple covers. Cheng and Zhang [17] presented three-dimensional NMM based on tetrahedron and hexahedron elements.An alternative approach is to include more polynomial terms in the displacement function. Unlike the sub-blocking method, it is possible to obtain good results using high-order displacement functions without discretizing the blocks. In the sub-blocking method, constraints between subblocks may not be satisfied accurately, which may lead to some errors in results, but this source of error is avoided in higher-order methods. The number of unknowns of analysis for one block using third-order displacement function is equal to the unknowns of analysis for a block divided into five sub-blocks. Using the sub-blocking method, to obtain good results comparable those from using a third-order displacement function, it is usually necessary to divide a block to many sub-blocks; however, the accuracy is problem dependent. Chern et al. [18] and Koo et al. [19] implemented a second-order displacement function in 2-D DDA. Ma et al. [20] and Koo and Chern [21] implemented a third-order displacement function in 2-D DDA method. Hsuing [22] developed a more general formulation for 2-D DDA. These studies showed that complicated stress and strain fields can be modeled using high-order displacement functions. MacLaughlin and Doolin [23] provided a review of more than 100 published and unpublished validation studies on the DDA approach. Previous DDA studies focused on solving problems in two dimensions, but in many engineering problems, three-dimensional effects have to be considered. Up to now, relatively little work on DDA development ...

This paper presents a new point-to-face contact algorithm for contacts between two polyhedrons with planar boundaries. A new discrete numerical method called three-dimensional discontinuous deformation analysis (3-D DDA) is used and formulations of normal contact submatrices based on the proposed algorithm are derived. The presented algorithm is a simple and efficient method and it can be easily coded into a computer program. This approach does not need to use an iterative algorithm in each time step to obtain the contact plane, unlike the 'Common-Plane' method applied in the existing 3-D DDA. In the present 3-D DDA method, block contact constraints are enforced using the penalty method. This approach is quite simple, but may lead to inaccuracies that may be large for small values of the penalty number. The penalty method also creates block contact overlap, which violates the physical constraints of the problem. These limitations are overcome by using the augmented Lagrangian method that is used for normal contacts in this research. This point-to-face contact model has been programmed and some illustrative examples are provided to demonstrate the new contact rule between two blocks. A comparison between results obtained by using the augmented Lagrangian method and the penalty method is presented as well.

No abstract