Second-Order Displacement Functions for Three-Dimensional Discontinuous Deformation Analysis (3-D DDA)

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 stiffness and force matrices in second-order due to elastic stress, initial stress, point load, body force, inertia force and fixed 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 first-order 3-d dda are far from the theoretical solutions.