OPTIMAL CROSS-SECTION AND CONFIGURATION-DESIGN OF ELASTIC-PLASTIC STRUCTURES SUBJECT TO DYNAMIC CYCLIC LOADING

This paper shows an optimal design problem with continuum variational formulation, applied to nonlinear elastic-plastic structures subject t o dynamic loading. The total Lagrangian procedure is used to describe the response of the structure. The direct differentiation method is us ed to obtain the sensitivities of the structural response that are nee ded to solve the optimization problem. Since unloading and reloading o f the structure are allowed, the structural response is path-dependent and an additional step is needed to integrate the constitutive equati ons. It can be shown, consequently, that design sensitivity analysis i s also path-dependent. A finite element method with implicit lime inte gration is used to discretize the state and sensitivity equations. A m athematical programming approach is used for the optimization process. Numerical applications are performed on a 3-D truss structure, where cross-sectional areas and nodal point coordinates are treated as desig n variables. Optimal designs have been obtained and compared by using two different strategies: a two-level strategy where the levels are de fined according to the type of design variables, cross sectional areas or node coordinates, and optimizing simultaneously with respect to bo th types of design variables. Comparisons have also been made between optimal designs obtained by considering or not considering the inertia l term oi the structural equilibrium.