The Nelder-Meade method for solving the problem of optimizing the geometric shape of the barrel of an automatic cannon to improve oscillatory characteristics

The paper presents the formulation of the problem of optimizing the shape of the barrel on the basis of mathematical modeling of the firing process from an automatic 30-mm cannon. The work considers both the standard annular section of the trunk and with stiffeners of two types. The oscillation amplitude was chosen as the objective function of the minimization algorithm. The maximum mass of the trunk and the minimum allowable thickness of the trunk, determined in accordance with the theory of the greatest deformations, were chosen as restrictions. For a standard barrel with an annular cross-section, the external diameters of the barrel were controllable, for barrels with stiffeners past the diameters, the distances to the stiffeners and their size were taken into account. The problem of internal ballistics in the thermodynamic formulation was solved to determine the gas-noise parameters inside the barrel. Muzzle vibrations were determined on the basis of solving the problem of the stress-strain state of the barrel in a one-dimensional formulation, taking into account technological irregularities and the interaction of the projectile with the barrel. The search for the optimal shape of the trunk was carried out by the Nelder-Meade method, restrictions were taken into account using the penalty function method. The results of optimizing the shape of the trunk are presented in graphical and tabular form. The scattering of shells for the barrels of the considered cross-sectional shapes is determined. As a result of optimization, it was possible to increase the accuracy of shooting by more than 2 times.