Lagrangian approach embed with discrete element method for extreme deformation study in frangible bullet designs fragmentation and penetration on viscoelastic ballistic gel.

Development of a model for analyzing a bullet's impact is important in the military field to design a bullet with desired properties. This study uses a finite element model with a Lagrangian framework and Lagrange-discrete element method (DEM) model by ANSYS Explicit Dynamic to investigate the effect of frangible bullet designs on bullet deformation and penetration in ballistic gel setting. A modeling approach with ballistic gel can analyzed the extreme deformation of bullets much faster compared to the more resource intensive real life ballistic gel test. The study starts with developing a 3D model, then importing it to an ANSYS workbench to solve the problems. Overall, the results of Lagrange-DEM shows deeper penetration and better accuracy to represent the real life ballistic gel test than other simulation method. The fluted bullet design has a shorter penetration depth but a bigger temporary cavity diameter than the flat-nosed one due to its notch and asymmetrical design, which becomes the part that is easily deformed and leads to directional deformation.

Well-conditioned model predictive control.

Model-based predictive control is an advanced control strategy that uses a move suppression factor or constrained optimization methods for achieving satisfactory closed-loop dynamic responses of complex systems. While these approaches are suitable for many processes, they are formulated on the selection of certain parameters that are ambiguous and also computationally demanding which makes them less suited for tight control of fast processes. In this paper, a new dynamic matrix control (DMC) algorithm is proposed that reduces inherent ill-conditioning by allowing the process prediction time step to exceed the control time step. The main feature, that stands in contrast with current DMC approaches, is that the original open-loop data are used to evaluate a "shifting factor" m in the controller matrix where m replaces the move suppression coefficient. The new control algorithm is practically demonstrated on a fast reacting process with better control being realized in comparison with DMC using move suppression. The algorithm also gives improved closed-loop responses for control simulations on a multivariable nonlinear process having variable dead-time, and on other models found in the literature. The shifting factor m is generic and can be effectively applied for any control horizon.