# Material Optimization for Nonlinearly Elastic Planar Beams

We consider the problem of an optimal distribution of soft and hard material for nonlinearly elastic planar beams. We prove that under gravitational force the optimal distribution involves no microstructure and is ordered, and we provide numerical simulations confirming and extending this observation.

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Sensitivity analysis (SA) is a procedure for studying how sensitive are the output results of large-scale mathematical models to some uncertainties of the input data. The models are described as a system of partial differential equations. Often such systems contain a large number of input parameters. Read More

**Affiliations:**

^{1}DALEMBERT,

^{2}JAD,

^{3}DALEMBERT,

^{4}DALEMBERT

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**Authors:**Mohamed Essadki

^{1}, Jonathan Jung

^{2}, Adam Larat

^{3}, Milan Pelletier

^{4}, Vincent Perrier

^{5}

**Affiliations:**

^{1}IFPEN, FR3487, EM2C,

^{2}LMAP,

^{3}FR3487, EM2C,

^{4}EM2C,

^{5}LMAP

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