Cross-section optimisation for curved and twisted3D beams via a mixed forwardand backward optimisation algorithm
by
Pierre Aubert
INSA Lyon

We would like to find an optimal cross-section for a complex structure build with 3D curved beams. The hard part is due to the L or H shape of the cross-section. This open sections enhance the beam's model. This model introduce strong nonlinearity between the parameters of the cross-section and the parameters needed in the finite element computation. In order to compute the shape gradient we have to deal with 2 FEM softwares, the first one computes some parameters relative to the cross-section and feed them to the second software. Due to the nonlinearities, a finite difference procedure has failed to give enough accurate results. As the number of parameters in play are small, we use a forward differentiation method for the first software and an adjoint method for the second. Both forward and backward mode are implemented in C++ via overloading and a cleaver use of expressions templates in order to enhance both computational times and simplicity of use.

http://pcmath03.insa-lyon.fr/~paubert/research/ad2000.ps

Date received: February 21, 2000