%0 Journal Article %T Second-Order Displacement Functions for Three-Dimensional Discontinuous Deformation Analysis (3-D DDA) S.A. %J Scientia Iranica %I Sharif University of Technology %Z 1026-3098 %A Jafari, A. %A Beyabanaki, S. A. R. %A Yeung, M. R. %D 2009 %\ 06/01/2009 %V 16 %N 3 %P - %! Second-Order Displacement Functions for Three-Dimensional Discontinuous Deformation Analysis (3-D DDA) S.A. %K Numerical method %K Three-Dimensional Discontinuous Deformation Analysis (3-D DDA) %K Second-order displacement functions %K Rock mechanics %R %X Abstract. The development of second-order displacement functions for a Three-Dimensional Discontinuous Deformation Analysis (3-D DDA) is made by incorporating the complete second order terms. Formulations of sti ness and force matrices in second-order due to elastic stress, initial stress, point load, body force, inertia force and xed point are derived. Two illustrative examples of 3-D beams subjected to various loads are used to validate the new formulations and code. By contrast, the results calculated for the same model by use of the original rst-order 3-D DDA are far from the theoretical solutions. %U https://scientiairanica.sharif.edu/article_3105_34a797fb82508aaa2e904d8b298a4443.pdf