Nonlinear boundary value problems related to the stress distribution of infinite body containing a covered fiber

The curvature of the fibers in the structure of the unidirectional fibrous composite materials isdue to design requirements or to technological processes. Usully the curvature caused bydesign features is modeled as a periodical, whereas the curvature caused by the technologicalprocess is modeled as a local one. In the study the case is considered where a single locallycurved fiber with an infinite length is contained by an infinte body with low concentration offibers and stress distrubition in that is investigated. Taking the low concentration of fibers intoaccount the interaction between them is neglected. The investigations are carried out withinthe framework of the piecewise homogeneous body model with the use of the three-dimensional geometrical nonlinear exact equations of the theory of elasticity. Morever it isassumed that the body is loaded at infinity by uniformally distrubuted normal forces which actalong the fibers and the crosssection of the fibers, normal to its axial line, is a circle ofconstant radius along the entire fiber length.For the solution of concidered boundary value problem an aproximate analitical method isdeveloped by using the boundary form perturbation method.In addition to these, the problem related to the case where there exists the bond hollowcovering cylinder between above mentioned fiber and matrix materials are also concideredand stresses on interfaces are studied.The numerous numerical results related to the stress distrubition in concidered body and theinfluence of geometrical nonlinearity to this distrubition are obtained and interpreted.Moreover, the influence of the geometrical and mechanical problem parameters to thesedistrubutions are also analyzed.Keywords: Fibrous composite, stress distrubition, geometrical nonlinearity, local curving,covering material.JURY:1. Prof. Dr. Surkay D. AKBAROV (Supervisor) Date : 13.10.20062. Prof. Dr. Yasemin KAHRAMANER Page : 1083. Prof. Dr. Abdullah YILDIZ4. Prof. Dr. Adnan MAZMANOĞLU5. Doç. Dr. Kamil ORUÇOĞLU