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Examples of optimal design include:
- Elastic structures of maximal stiffness.
- Conducting structures, able to concentrate current.
- A game between the load and the structure.
- Composite with extremal properties.
Mathematically, we are dealing with variational problems with non-convex Lagrangians. We develop the technique that enables to correctly formulate and solve these variational problems with non-stable solutions. We discuss special methods based on the quasiconvex envelopes. Applying the technique to the mechanical and transport problems, we are able to find optimal structures for the above mentioned problems.
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