Lg. Sousa et al., OPTIMAL CROSS-SECTION AND CONFIGURATION-DESIGN OF ELASTIC-PLASTIC STRUCTURES SUBJECT TO DYNAMIC CYCLIC LOADING, Structural optimization, 13(2-3), 1997, pp. 112-118
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.