Optimal Design Luhorator), C'olleqe of Engrneerinq, The Unn,er\itc of lowu, l o w Cili. I A 52242-1527, U S A SUMMARY A design optimization process for non-linear structures with history-dependent materials modelled using the endochronic constitutive theory is described. This constitutive model does not use the concept of a yield surface and describes plastic, viscoplastic and viscoelastic behaviour with one set of equations. Therefore, development of the yield surface is not traced in numerical calculations, simplifying the implementation of response and sensitivity analyses. The total Lagrangian formulation incorporating both geometric and material non-linear effects is used. Shape, non-shape and material design parameters are treated simultaneously using the control volume concept, and static and dynamic problems are treated. A simple structure is optimized for several cases of static and impact loading conditions to demonstrate the procedure. Plastic and viscoplastic material behaviour as well as shape and non-shape design parameters are treated in the example problems.