Mathematical Model of Optimal Stamp Topology Based on the Stability Criterion
I. K. Andrianov
Abstract
The scientific study presents a mathematical model for minimizing the stamp volume based on the stability criterion. The optimization area was replaced by a specified distribution of rod elements with a variable height moment of inertia, which determines the rigidity of the die structure. Volume minimization was based on creating a stress state close to the limit according to the stability criterion. At the stage of mathematical solution of the problem, an energy approach was used, considering the potential energy of compression and bending of the rod when stability is lost. As a result, an integral equation is obtained for numerical calculation of the configuration of optimal volume rod elements. The application of this model has been tested when creating the topology of the stamping matrix with the calculation of the stress-strain state within elastic deformations. The practical use of the resulting model can be successfully implemented in the additive production of stamping tools under conditions of force.