Shakedown analysis of spatial frames with parameterized load domain

This work addresses shakedown analysis of geometrically linear spatial frames with linearized yield criteria and parameterized general variable load domain. If the boundary of the load domain is curved, the respective optimization problem has an infinite number of constraints. Using parameterization, a computational bi-level decomposition methodology is developed, which is capable of treating problems of this kind. Two alternative bi-level procedures are presented: the centered minmax technique and the parameterized Maier’s technique. The lower level, shared by both procedures, comprises a series of local constrained optimization problems for the check points across the frame. These low-order problems, solved either algorithmically or analytically, provide data for the upper level, where a linear programming problem of limit analysis type is solved in each procedure for the whole frame. Two examples with ellipsoidal load domain are presented. Several aspects are discussed.