online read us now
Paper details
Number 2  June 1996
Volume 6  1996
Thickness optimization of a geometrically nonlinear arch at a limit point
Pierre Aubert
Abstract
An optimization method for geometrically nonlinear mechanical structures based on a sensitivity gradient is proposed. This gradient is computed by using an adjoint state equation and the structure is analysed by means of a total Lagrangian formulation. This classical method is wellunderstood for regular cases, but standard equations (see e.g. Rousselet et al., 1995) have to be modified
for the limitpoint case. The case of sensitivity of a bifurcation point is under development (see (Mróz and Haftka, 1994) for more details). An arclength algorithm embedded in the optimization algorithm is built. These modifications introduce numerical problems which occur at limit points (Doedel et al., 1991). All systems are very stiff and the quadratic convergence of the NewtonRaphson
algorithm is lost, so higherorder derivatives with respect to state variables have to be computed (Wriggers and Simo, 1990). The thickness distribution of the arch is optimized for differentiable costs under linear and nonlinear constraints. Numerical results of optimal design of arches undergoing small and large displacements are given and compared with analytic solutions. Related topics of
shape optimization can be found in (Aubert and Rousselet, 1996), and theoretical results with details in (Aubert, 1996).
Keywords
