Szukana fraza: [Abstract = "The thickness distribution of the arch is optimized for differentiable costs under linear and non\-linear 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 \(Aubert, 1996\)."]