Continuum Limit of a Double-Chain Model for Multiload Shape Optimization

We compute explicitly the Γ-limit of an energy functional modeling a connected mass-spring double-chain 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 one-dimensional 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