Optimizing Building Structures under Buckling Constraints

Difficulties in structural optimization under constraints on linear or nonlinear buckling load factors are first discussed. The constraints are non-differentiable if the buckling load factors are multiple at the optimal solution. For the case where nonlinear buckling load factors are considered, reduction of maximum load factor due to initial imperfection should be appropriately incorporated, and the possible mode interaction should be investigated. Example of optimum designs are presented for a spherical truss under linear and nonlinear buckling constraints. For linear buckling constraints, optimal solutions with multiple buckling load factors are found by using the formulation of senmi-definite programming。It is shown that the distribution of cross-sectional areas of the optimum design under nonlinear buckling constraints is almost proportional to that under linear constraints. Therefore, it is practically acceptable to find optimai solution under linear buckling constraints and scale it to up to have specified nonlinear buckling load factor, It is demonstrated that imperfection sensitivity does not increase after optimization, and optimization under buckling constraints is not dangerous or meaningless