
Journal of Convex Analysis 18 (2011), No. 1, 153172 Copyright Heldermann Verlag 2011 Continuum Limit of a DoubleChain Model for Multiload Shape Optimization Pradeep Atwal Institut für Angewandte Mathematik, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany pradeep.atwal@unibonn.de We compute explicitly the Γlimit of an energy functional modeling a connected massspring doublechain in the limit of small separations. The point masses interact with each other through nearest neighbor potentials that have to be convex and fulfill a growth condition (e.g. modeling harmonic springs). This results in a continuous onedimensional variational problem whose minimum approximates those of the discrete problem for large N, which is used to numerically compute the deformation under various loadings. In a second step, we use our model to numerically optimize the macroscopic distribution of material strength in the presence of stochastic loads. [ Fulltextpdf (198 KB)] for subscribers only. 