Modeling limit states for curvilinearly reinforced rotated disks

Abstract

This paper describes a new approach to development of planar for aircraft design reinforced by curvilinear fibers sets. The structural model of composite is used, based on the planar non-homogeneous thermoelasticity theory for curvilinear coordinates. The resolving system of differential equations is obtained. The boundary conditions are defined for curvilinear coordinates. The resolving system of differential equations with radial and circular movement variables is obtained for an axisymmetric problem. This system is a second-order differential equations system, highest derivatives of which are not isolated. An effective numerical method which takes into account the factors of the resolving system for a reinforced material is designed. Different mixed configurations of two sets of curvilinear trajectories are considered for the direct problem when a planar construction is under the conditions of axisymmetric strain. We use an example of the logarithmic spiral trajectories set and the "wheel spokes" trajectories set. Effective reinforcement structures and reasonable reinforcement structures are studied. The reinforcement power subject to additional conditions of fibers cross-sections constancy is considered. It corresponds to industrial conditions. Our original contribution is a new integral characteristic of the effeciency of armature arrangement. It is called "efficient armature arrangement". We studied its properties for different initial stages of an industrial workflow and for different curvilinear trajectories of reinforcement by two curilinear. We solved the axisym fibers sets. metric problem of rotating hydra and gas turbines disk extremal deformations through curvilinear trajectories reinforcing technique. We demonstrated that