Nonlinear Instability of Dished Shallow Shells Under Uniformly Distributed Load

In this paper, the nonlinear instability of dished shallow shells under a uniformly distributed load is investigated. The dimensionless governing differential equations for the problem are derived and the equations solved by using the Free-Parameter Perturbation Method with the Spline Function Method. By analyzing the instability modes of dished shallow shells, we obtain the variation rules of the maximum deflection area of initial instability of the uniformly loaded dished shallow shell, and discuss the relationship between the initial instability area and the maximum deflection area of initial instability. These results provide some theoretical basis for engineering design and instability prediction and control of shallow shell structures.