Breaking strains of planar thermoelastic constructions reinforced by curvilinear structures

This paper describes a new methodological approach to development of planar aeronautical constructions reinforced by curvilinear fibers sets. The structural model of composite in terms of the planar non-homogeneous thermoelasticity problem in the case of curvilinear coordinates is used to simulate the problem. The resolving system of differential equations is obtained. The direct problem and the inverse problem of a material reinforcement are stated on the basis of this system. The boundary conditions are defined for curvilinear coordinates. The resolving system of differential equations with radial and circular movement’s variables is obtained for an axisymmetric problem. This system is a second-order differential equations system, highest derivatives of which are not isolated. The 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 conditions of axisymmetric strain. The following examples are described: the logarithmic spiral trajectories set and the set of trajectories isogonal to it (to logarithmic spiral), the Archimedean spiral trajectories set and the “wheel spokes” trajectories set, the logarithmic spiral trajectories set and the “wheel spokes” trajectories set. Effective reinforcement structures and reasonable reinforcement structures are studied. The reinforcement power is considered with subject to additional conditions of fibers cross-sections constancy. It corresponds to the industrial process conditions. The reinforcement effectiveness integral characteristic is defined. It is called an “armature spending”. Its properties are studied for different initial states of an industrial process and for different curvilinear trajectories of reinforcement by two curvilinear fibers sets. The inverse problem for a plate which is symmetric with respect to its median surface is stated. A plate consists of a binding material layer and an armature layer. Layers are thin. A plate has a plain stress condition. The temperature is constant across a plate cross-section. A binding material layer is isotropic and equal cracking resistant.