The numerical investigation of shape optimization problems is both computationally and theoretically more complex than solving direct analysis problems using the finite element method. The limitations are mainly due to the involvement of both structural analysis and optimization processes. To overcome these numerical challenges, we present an adaptive approach to solve the shape optimization problem associated with the compliance objective. This approach takes into account not only the errors due to the discretization of the constraining PDE, in particular the linear elasticity system, but also the errors due to the discretization of the deformation bilinear form that provides a descent direction. Moreover, the step length in 0.00,0.07,1.00gradient-based optimization is adaptively adjusted by estimating the Lipschitz constant. Finally, in numerical simulations, we present the superiority of the adaptive procedure compared to the fixed mesh refinement, in addition to some cases of failure.
ALTINTAŞ et al. (Fri,) studied this question.