Approximate critical load of cambered double-layered grids by shell analogies

Studies have shown that design of double-layered grids based on classical theories may lead to unsafe design. For square-on-diagonal grids, the load carrying capacity is almost the same as the buckling load. Therefore the buckling load can be used as the critical load in the design. In this study, the non-linear behavior of the grids is considered using shell analogies to determine the critical load. By applying the theorem of study and energy to a dimple, an empirical formula to predict the buckling load of thin spherical shells was derived. Then using finite element modeling, post-buckling load was identified and used to calculate the value of constant C. It is observed that the buckling load is proportional to t ^2.5, which gives a critical load close to what is observed in experiments and a more realistic load as compared to the Classical theory prediction. Loaddeflection curves drawn for the grids and their equivalent continuum shells correlate closely showing that the findings are valid.