Sensitivity analysis of coincident critical loads with respect to minor imperfection

A new formulation is presented for sensitivity analysis of a coincident critical load factor. Only symmetric elastic structures subjected to symmetric loads are considered, and sensitivity coefficients are found for a symmetric design modification which corresponds to a minor imperfection. It is shown that the formulation for sensitivity analysis of multiple linear buckling load factor can be successfully combined with that of nonlinear buckling to develop a formulation for coincident nonlinear buckling load factor. The proposed formulation is verified by analytical examples of simple spring–bar systems.