Abstract
The problem of designing the elastic properties of a laminate is considered. It is shown that a unique formulation for all the design problems with respect to elastic symmetries can be found using polar invariants of the stiffness tensors. In this way, the design of laminates having some general elastic properties is reduced to a classical optimisation problem: the search for the absolute minimum, whose value is 0, of a positive semi-definite form in the space of the polar invariants. A minimum characterisation of some important elastic properties is also given. Some numerical examples and a discussion of the results are also included in the paper.
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Vannucci, P. Designing the elastic properties of laminates as an optimisation problem: a unified approach based on polar tensor invariants. Struct Multidisc Optim 31, 378–387 (2006). https://doi.org/10.1007/s00158-005-0566-5
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DOI: https://doi.org/10.1007/s00158-005-0566-5