Optimal shakedown design of bar systems: Strength, stiffness and stability constraints

Using the concept of a variable repeated load and shakedown theory, a unified technique is proposed for formulating mathematical models for the optimization of frame- and truss-like structures under different loads. Strength, stiffness and stability (for trusses only) constraints are included in non-linear mathematical models of structure volume minimization and load optimization problems. Even though the load is prescribed within certain limits, the mathematical models allow the variational bounds of the displacement (the stiffness of the structure depends on them) to be evaluated in the deformed state. Numerical example concerning calculation of frame structure is presented. The results are valid for small displacements.