A method for optimizing a twelve-cornered strengthening member comprises: modeling a vehicle assembly including a strengthening member having a twelve-cornered cross section; parameterizing a geometry of the strengthening member with a plurality of control parameters; defining a design of experiment using the plurality of control parameters; modeling a vehicle using the vehicle assembly; simulating a frontal impact event with the vehicle; generating a response surface based on the frontal impact event; and determining a set of optimized control parameters for the strengthening member based on the response surface.