Influence of Discretely Introduced Cutouts on the Buckling of Shallow Shells with Double Curvature

Abstract

The paper analyzes the influence of cutouts on the buckling of shallow shells with double curvature. Based on the Timoshenko-Reissner hypothesis, a mathematical model is presented that considers transverse shifts, material orthotropy, geometric nonlinearity and structural weakening by cutouts. Cutouts are specified discretely by single columnar functions. The computational algorithm is based on the Ritz method and the Newton method. The implementation of the algorithm is carried out in the Maple 2022 software package. To study the buckling, the Lyapunov criterion is adopted. Calculations of the buckling of flat shells of double curvature with square cuts, graphs of the dependence of deflections on loads and deflection fields are given. Accounting for the structural cutouts leads to a decrease in the critical load. At the same time, for the considered problems, it is found that the decrease in the critical load does not exceed 25 % for the cutout volume not exceeding 10 % of the shell volume.

Keywords

• shells
• cutouts
• buckling
• critical load
• ritz method
• newton method