Abstract
We consider a problem about non-uniformly scaled buckling modes of isolated fiber (without accounting of interaction with the surrounding epoxy) or bundle of fibers, which are structural elements of fiber reinforced plastics under the transverse tension (compression) and shear stresses in prebuckling state. Such initial state is formed in fibers and bundles of fibers at tension-compression tests of flat specimens from cross ply composites with unidirectional fibers. For problem statement we use equations recently constructed by reduction of consistent version of geometrically nonlinear equations of theory of elasticity to one dimensional equations of rectilinear beams. Equations are based on refined shear S. P. Timoshenko model with accounting of tension-compression stresses in transverse directions. We give theoretical explanation of developed phenomenon as reducing shear modulus of elasticity of fiber reinforced plastic during the increasing of shear strains. We show that under the loading process of specimens under review uninterruptedly structure reconstruction of composite trough implementation and uninterruptedly changing of internal buckling modes at changing wave parameter is feasible.
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Original Russian Text © V.N. Paimushin, N.V. Polyakova, S.A. Kholmogorov, M.S. Shishov, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 9, pp. 89–95.
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Paimushin, V.N., Polyakova, N.V., Kholmogorov, S.A. et al. Non-uniformly scaled buckling modes of reinforcing elements in fiber reinforced plastic. Russ Math. 61, 79–84 (2017). https://doi.org/10.3103/S1066369X17090092
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DOI: https://doi.org/10.3103/S1066369X17090092