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Method of solving problems in the mechanics of fiber composites with curved structures. (English. Russian original) Zbl 0568.73080

Sov. Appl. Mech. 20, 777-785 (1984); translation from Prikl. Mekh., Kiev 1984, No. 9, 3-12 (1984).
The composite considered is an infinite elastic body with a single planar curved fiber inside, also linear elastic. The equality of stress vector and displacement at interface is considered. In particular the middle line of the fiber is represented as \(x_ 1=0\), \(x_ 2=A \sin (2\pi /\ell)x_ 3.\) Further A/\(\ell\) is considered as a small parameter. The set of partial differential equations (balance of momentum, kinematic relations and boundary conditions at interface) of the problem are further developed with respect to the small parameter. Successive approximations are given. The conclusion is that the curvature significantly affects the stress-strain state.
Reviewer: N.Cristescu

MSC:

74E30 Composite and mixture properties
74E10 Anisotropy in solid mechanics
74E05 Inhomogeneity in solid mechanics
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