Ex
**Example. Optimal design of a beam**.
**Example. Optimal design of a composite. **
The best structure to resist a one dimensional loading is laminate. It remain the optimal structure for any close to one-dimensional loading.

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AN Example: Optimal design of a structure is placed below, in the Epiloque

Suppose that the the optimal composite is the mixture of a material and the void.
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The best structure against a uniaxial loading is again the laminate:
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The project is extremely unstable to any other loading: it is collapsing as the deck of cards if any loading different from the uniaxial is applied. |

Suppose that admissible loadings are the following:
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The structure stable to the following six loadings
is found from the conditions that the stiffness against five of the loadings (## 1, 3, 4, 5, 6) is equal. These conditions require the symmetry of structure and they lead to the following design. Note that the extremum is non-smooth function of the structural parameters.
Similarly, **optimal design of a wheel ** requires the axial symmetry of the design in spite of the non-symmetry of the loading.