Abstract
Within the framework of the piecewise homogenous body model, with the use of the three-dimensional geometrically nonlinear exact equations of the theory of elasticity, the method developed for the determination of the stress distribution in the composites with unidirectional locally curved covered fibers is used for investigation of the shear stresses acting along the fibers. All the investigations are carried out for an infinite elastic body containing a single locally curved covered fiber, for the case where there exists the bond covering cylinder with constant thickness between fiber and matrix material are considered. It is assumed that the considered material is loaded at infinity by uniformly distributed normal forces in the fiber lying direction. Under formulation and mathematical solution of the boundary value problem, the boundary form perturbation method is used. The numerical results related to stress distribution in considered body and the influence of geometrical nonlinearity to this distribution are presented and interpreted.
Highlights
It is well known that in the structure of the unidirectional fibrous composites in many cases fibers have an initial curving caused by design factors or caused by action of various factors during technological processes [1,2,3,4,5]
Within the framework of the piecewise homogeneous body model, with the use of the three dimensional geometrically nonlinear exact equations of the theory of elasticity, the method developed for the determination of the stress distribution in the composites with unidirectional locally curved covered fibers is used for investigation of the shear stresses acting along the fibers
In the framework of the piecewise homogeneous body model with the use of the threedimensional geometrically nonlinear exact equations of the theory of elasticity, the method developed for the determination of the stress distribution in the unidirectional fibrous composites with locally curved fibers has been used to investigate shear stresses acting along the fibers for the case where there exists the bond covering cylinder with constant thickness between fiber and matrix materials are considered
Summary
It is well known that in the structure of the unidirectional fibrous composites in many cases fibers have an initial curving caused by design factors or caused by action of various factors during technological processes [1,2,3,4,5]. The theoretical investigations of the self-balanced stresses arising as a result of fiber curving have a great significance in the viewpoint of the theoretical and application sense [1,2,3,4,5] For this purpose, within the framework of a piecewise homogenous body model, by using the exact three-dimensional equations of elasticity theory, Akbarov and Guz [6] presented a method for investigation of the stress state in unidirectional composites. The method used by Akbarov and Guz [6] and Kosker and Akbarov [8] is developed in [9] for geometric nonlinear statement, and numerical results for one and two neighboring periodically curved fibers are presented. According to the well-known mechanical considerations and to the results obtained in [9], taking the geometrical nonlinearity into account influences significantly the values
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