Application of wavelets and conformal reflections to finding optimal scheme of fiber placement at 3d printing constructions from composition materials

Abstract

The article is devoted to finding the optimal schemes of fiber placement at the production of constructions, reinforced with continuous fibers by 3D printing method. As the optimization of the objective function one of the criteria for the destruction of the composite was chosen. For the process acceleration of multiple solution of the system of partial differential equations describing the stress-strain state of the structure, a computational algorithm based on wavelets built through subdivision schemes is proposed. To set the local coordinate system, it is proposed to use analytical functions, which will be constructed using the well-known Dini and Cisotti formulas, just by specifying the direction of laying the fiber at the product boundary. The article also presents a lifting scheme (lifting scheme) allowing to construct biorthogonal wavelet systems with specified properties using some initial biorthogonal wavelet systems with filters.