A computational study in optimum formulations of optimization problems on laminated cylindrical shells for buckling II. Shells under external pressure

Different formulations of optimization problems are considered for multi-layered composite cylindrical shells under external pressure in terms of buckling. The problem is posed as follows: along with the global extremum of the buckling load, one must find local extrema which are sufficiently close to the global one (or practically indistinguishable from it) but more convenient in practice for the design and production of realistic shells. The comparison is made between uni-dimensional, two-dimensional and multi-dimensional formulations of optimization problems for the shells including various number of the layers. It is shown that three layers in the shell are sufficient to achieve the maximum buckling load in most practically important cases. Optimum structures can be obtained as a result of the uni-dimensional optimization (parametric analysis) of [90°/ϕ/90°] or [0°/ϕ/0°] structures. Revealed rules are studied in different intervals of shell dimensions and material characteristics.