Variational inequality‐based particle discontinuous deformation analysis

Abstract

Summary Orienting the circular and rigid particle medium, the variational inequality‐based discontinuous deformation analysis (DDA) is established. In the proposed DDA, the global stiffness matrix, the penalty parameters, and the open‐close iteration are successfully avoided. The contact constraint is transferred into the problem of variational or quasi‐variational inequalities. And explicit variational expression on the contact force is firstly established. To speed up the rate of solving contact force, on the basis of the two‐stage prediction‐correction method, we design a compatibility iteration algorithm (PPC‐CI). The C++ code is developed in multicore environment through the open multi‐processing (OpenMP) in order to take advantage of the parallelizable features of the new DDA. Numerical tests suggest that the presented DDA is effective and promising.

A new family of high‐order triangular weight functions for mass lumping in vibration analysis

“…Taking any two adjacent 6-node triangular elements, for example, as shown in Figure 10, element E 1 is denoted by the global indices as [1][2][3][4][5][6], while E 2 is denoted as [2,3,5,[7][8][9]. Edge 253 (anticlockwise) is the common edge shared by these two elements.…”

“…The local node indices of the 6-node element is denoted as [ 1 , 2 , 3 , 4 , 5 , 6 ], see the left side of Figure 11, in which the edge [2,3,5] (anticlockwise) of E 1 is labeled locally as [ 2 , 5 , 3 ]. On the other hand, there are three possible cases for the edge [2, 3, 5] (anticlockwise) of E 2 , as shown on the right side of Figure 11.…”

“…On the other hand, there are three possible cases for the edge [2, 3, 5] (anticlockwise) of E 2 , as shown on the right side of Figure 11. In case I, the edge [2,3,5] corresponds to local node [ 3 , 6 , 1 ]; in Case II and III, the corresponding local node numbering becomes [ 2 , 5 , 3 ] and [ 1 , 4 , 2 ], respectively. The weights of w 36 i evaluated at each local node are listed in Table 1, from which we can conclude:…”

“…A convenient and effective construction of the LMM is still greatly needed in many engineering practices. It is interesting to note that the CMM is exactly the LMM in the discontinuous deformation analysis [1][2][3] for rigid bodies.…”

A cover‐based contact detection approach for irregular convex polygons in discontinuous deformation analysis

“…It is necessary to measure their distance and establish the geometrical relationship in all contact scenarios for successful contact interaction simulation. Both explicit and implicit schemes have been applied to solve contact problem, [38][39][40][41][42][43][44][45][46] where contact constraints and associated physical states should be obtained and updated by the contact detection and solution process in all analysis steps. For the explicit schemes, the contact force with its acting position for specific instant is needed in computation of the acceleration term.…”