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
A6strucZ-Rectilinear reiaforcing structures are used more often for research of tensely deformed state of flat constructions from fibrous composites. It has been shown in a number of works [I-31, that use o f complex curvilinear structures of reinforcing can results in effective designs taking into account the charge of armature rigidity ana durability. In the given work the general approach on a presence of flat designs reinforcing structures which provide required reinforcing fibres effective work is considered. Resolving systems flat problem are constructed for possible combinations of three fibres families of reinforcing. These families can be not extensible and equal streachable families of fibres. Use of algorithms of invariant solutions of partial differential equations construction has allowed to construct and investigate some model solutions. Let reinforcing is executed by fibres of constant crosssection section. Structural model 141 is used for the statement of a composite. Flat problems of elasticity for the environments reinforced w i t h three families of fibres are considered.The model contains the algebraic and differential equations of reinforcement intensity wk(x, y ) , components of deformations tensor Eii(x,y), deformations in fibres of the first, second and third families E k ( x , y ) , pressure in fibres of the first, second and third families sk (x, y ) , averaging pressure sii (x, y ) where x,y -the Cartesian coordinates, g k ( x , y ) -corners of reinforcing, indexes i, j = 1,2, k = 1,2,3.Under condition of a temperatures field constancy T the initial system is:Notations are used:where Lz -are factors of linear expansion of k -family material of fibres (k = 1,2,3). Symbols mean partial differentiation on coordinates x, y accordingly. The right part in (2) takes into account both a case of equally deformed hmilies offires ( E t = const, E: = const + EL) and a case of not extensible (Ek = 0, E: =E;) fibres families, and their possible combinations (one of families of fibres are equally deformable fibres, others -not extensible fibres). The average pressure sB (x, y ) looks like: 3 k=l sij = USE + s k WRZ bl& .a = 1 -q -wz -w3. (4) 1J Ln (4) pressure in binding are determined under formulas: SF. 3 -EU Eii, ( j = 3 -i , i-l,Z) Here EU ,U,,!,, -are accordingly Jung module, Poisson factor and factor of temperature expansion of a binding material, E; -modules Jung k-family of fibres. Pressure should satis@ to the equations of balance: (l+u) ~l j , l C Q ,~ =+bf,(i=1,2). (5) Right sides in (5) 3 k=l bj = ((1 -U)P, + w~Q)F;: are components of the mass distributed loading on directions of rectangular Cartesian system of coordinates; rc,rk -mass density of materials binding and fibres of families; I$ -components of the specific distributed loading working on a mss unit. Boundary conditions on a contour are added to system (1) -(5). The equation of a contour G is set in the parametrical form: x = fi (s), y = f2 (s), S-any parameter. Here is G = Cp U G, . On a contour Gp static conditions with normal ...
In this article we discuss methods of computing the guaranteed values of the states of a technical system in order to estimate the safety of a technical system The danger of a system functioning is a threat, possibility, probability of damage, system catastrophe, that is, potential damage to a technical system in certain conditions and situations. An analysis of the boundaries of the safety areas of technical systems helps to obtain quantitative estimates of the possibility of dangerous situations. The presence of such estimates may allow a more reasonable search and development of a set of measures to eliminate or mitigate the consequences of such situations. The article discusses the new results of computing the guaranteed boundaries of solution sets and the results of their application for assessing the boundaries of security areas and studying practical stability. Methods are used based on the approximation of the shift operator along the trajectory, and taking into account the influence of constantly acting perturbations on the solutions.
The reliability of a technical system is the ability to perform the required functions, being within the specified boundaries of all parameters and conditions of application of the technical system.The concept of safety of a technical system is based on damage. Damage is the amount of deterioration in the quality of the system.The amount of damage determines two properties: the hazard of the system is a characteristic of the ability to suffer or cause damage;safety of system is a characteristic that prevents damage from occurring or reducing its magnitude to an acceptable value.The article deals with the analysis of safe and dangerous states of a technical system based on the study of the properties of their mathematical models, especially the survival of their trajectories.The relationship between the security areas and the practical stability of the technical system as the limitation of all its trajectories is determined.
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