Geodesic
Continuum Limit of a Double-Chain Model for Multiload Shape Optimization
Journal of convex analysis, Tome 18 (2011) no. 1, pp. 153-172.

Voir la notice de l'article provenant de la source Heldermann Verlag

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. 
@article{JCA_2011_18_1_JCA_2011_18_1_a7,
     author = {P. Atwal},
     title = {Continuum {Limit} of a {Double-Chain} {Model} for {Multiload} {Shape} {Optimization}},
     journal = {Journal of convex analysis},
     pages = {153--172},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2011},
     url = {http://geodesic.mathdoc.fr/item/JCA_2011_18_1_JCA_2011_18_1_a7/}
}
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P. Atwal. Continuum Limit of a Double-Chain Model for Multiload Shape Optimization. Journal of convex analysis, Tome 18 (2011) no. 1, pp. 153-172. http://geodesic.mathdoc.fr/item/JCA_2011_18_1_JCA_2011_18_1_a7/