بررسی تحلیل دینامیکی و تصحیح قیود تماس نقطه به وجه با استفاده از روش لاگرانژ

Abstract

In this paper, first the validity of 3-D DDA is examined by comparing its solution for dynamic block displacement with analytical solution. Displacement of a single block on an inclined plane subjected to a dynamic loading is studied for analytical solution with respect to the frictional resistance offered by the inclined slope. 3-D DDA predicts accurately the analytical displacements. The modification of point-to-face contact constraints is also studied too. In the original 3-D DDA method, block contact constraints are enforced using the penalty method. This approach is quite simple, but may lead to inaccuracies which 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 two limitations are overcome by using the Augmented Lagrangian Method which has been programmed in VC++ and its implementation into the 3-D DDA is presented by an illustrative example. This method has been found to model block contact quite well.