A NUMERICAL METHOD FOR OPTIMIZING THE KINEMATIC SCHEME OF DOUBLE CURVATURE PANELS SHAPING
The article develops and investigates a numerical method for solving optimal control problems in the mechanics of a deformable rigid body using CAE systems. This method is used to determine the optimal kinematic scheme for deformation of the workpiece in the technological processes of shaping, as a result of which the part acquires the necessary residual curvature and minimal damage. As devices for forming products from sheets and panels, numerically controlled equipment is considered, in particular, a reconfigurable core punch and tightening equipment. Technological processes for the manufacture of parts in this case are carried out in the creep and plasticity modes, respectively. The value of material damage in creep and plasticity is considered as an optimization criterion. The calculation of the optimal deformation path of the workpiece is performed by modeling and analyzing the nonlinear deformation of a panel with contact constraints by the finite element method. A discrete optimal control problem is formulated, which is solved by the dynamic programming method. Non-monotonic deformation trajectories, taking into account partial unloading, should be included in the space of solutions of optimal control problems by the developed methods.