Disc-based DDA And The Application Of Meshless Method And DDA Coupled Model

The original DDA theory is more accurate in calculating the kinematic velocity and displacement of the bulk,but for the contact or boundary contact between the blocks,the use of a penalty function method will result in an inaccurate selection criterion for the parameter selection and the calculation result varies from person to person.The calculation of the total energy between blocks during the movement of a simulated block system is inaccurate,and the error is greater in the case of friction.In this paper,the accurate block displacement formula is used to correct the false expansion of the block area caused by the rotation of the block body in the original DDA.The contact between the disc and the convex angle and the concave angle is corrected by the angular bisection line method,and the MATLAB program is written to verify it.The effect of different disc radius on the calculation accuracy of cantilever beam with free end is studied.The results of DDA calculation are processed by point interpolation method and moving least square method,and the related formulas are derived.Using the meshless displacement model to improve the DDA method,the system general equation and the submatrix are derived,and the influence of the loading rate on the calculation results is studied.A program was written to plot the stress cloud of the cantilever beam with the free end loading.The detailed conclusions are as follows:(1)This paper introduces the treatment of rigid disc and side contact,and deduces the contact sub-matrix by the penalty function method,and the friction sub-matrix is deduced by different directions of the needle motion.In view of the problem that multiple contact springs are found in the contact between the disc and the convex angle and the concave angle in the original DDA,a new contact judgment of the disc with the convex angle and the concave angle is proposed,and the angle bisector method is applied to the contact judgment.Verify the accuracy and effectiveness of the angle bisector method.By analyzing the error between the calculation value of the system energy and the theoretical value when the disc is in contact with the convex angle and the co ncave angle,the practicability of the angular bisection line method is verified.(2)For the cantilever beam model with discrete rigid disk,the influence of disk size on the accuracy of the calculation results is analyzed under the same constraint.When the disc radius is reduced from 0.1m to 0.015 m,the number of disc increases from 360 to 16000,and the accuracy of stress calculation is greatly improved.However,the increase of disk number makes the dimension of the balance equation increase greatly and the computation time increases sharply.(3)DDA interpolation results are processed by point interpolation and moving least squares.The results show that the interpolation results depend on the size of the disc.Too large or too small will affect the interpolation results.The size of the disc i s too large and the interpolation points are too small.It is impossible to get a higher precision interpolation solution.The disk size is too small,and the interpolation points will lose their characteristics and are too smooth,and the error will also be increased.The example shows that when the disc radius is 0.03~0.02 m,the interpolation effect is the best in the discrete model of cantilever used in this paper.(4)Using the meshless displacement mode to improve the DDA method,we derive the global equilibrium equation and all sub matrices.The influence of loading rate on the calculation results is studied,and the stress nephogram of cantilever beam is drawn.