By choosing the density of particle as the design variables, a new implementation method of topology optimization is presented based on the Element-free Galerkin (EFG) method in this paper, in which the optimal objective is to minimize structural compliance. The advantage of using nodal density is that the displacement and density in the influence domain have the same approximation scheme, and the smoothness of the density field can be improved. Nodal density method presented can prevent the checkerboard from the mathematical model proposed. The topology optimal model based on EFG method under multiple loading cases and stress constraints is proposed, and the sensitivity analysis of optimal design is derived in detail. By using solid isotropic material with penalization (SIMP) method and optimality criteria (OC) method, an algorithm of topology optimization based on the EFG method is presented. The shortcoming of using nodal density can be overcome by introducing the penalty function method. Three topology optimal examples are solved successfully and test the model and algorithm proposed. The results obtained show that the checkerboard phenomenon arisen in topology optimization is not found, and the method proposed is not only effective in suppressing checkerboards but also has better convergence.

DEM simulations of particle mixing process in the intensive mixer were conducted to study the influence of blade configuration and impeller speed on the particle dynamics and mixing performance. Two tagged particles at different locations were used to discuss the influence of blade configuration on the particle trajectory and residence time in the intensive mixing region. The average magnitude velocity in the intensive mixing region, time-averaged velocity fluctuation, coordination number, impeller torque and relative standard deviation (RSD) were adopted to quantify the mixing performance during the mixing process. It was found that the blade configuration plays a vital role in the mixing process as it affects the residence time, particle velocity and mixing performance. The magnitude velocity of particles agitated by the thread blades is lower than that agitated by the arc and straight blades. The residence time for the thread blade mixer is longer than that for the arc and straight blade mixers. The mixing performance of particles in the thread blade mixer is better than that in the arc and straight blade mixers. Results obtained show that a proper impeller speed is very important for the mixing of particles, and the optimal impeller speed for granular mixing in the intensive mixer is 150 rpm.