Nonlinear stability analysis of thin doubly curved orthotropic shallow shells by the differential quadrature method

The geometric nonlinear buckling problem of a thin doubly curved shallow shell with all edges hinged is complicated and difficult to obtain an exact analytical solution. Thus, differential equations are solved incrementally by using the differential quadrature method in this paper. Detailed formulations are worked out. Convergence study is performed. Several examples with various material properties, curvatures and dimensions are investigated. Comparisons are made with existing semi-analytical data or finite element data. It is shown that the critical loads are lower than the data obtained by either so-called Adjacent Equilibrium Method or Partitioned Solution Method. The possible reasons to cause the difference are discussed.