The method involves realizing a concave material preform (1) of a plate using shaping tools having specific regulated shape. The preform is deformed using the shaping tools. The deformation step is realized by heating the preform. The deformation step is realized by adapted movements of the shaping tools in a direction causing deformation of folds of the preform. A non-developable piece is strengthened by polymerization in the case of the piece having a thermohardening matrix or by cooling in the case of the piece having a thermoplastic matrix. An independent claim is also included for a tool for realization of non-developable pieces from composite plates.
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