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Vol 72, No 3 (2017)
- Year: 2017
- Articles: 5
- URL: https://journals.rcsi.science/0027-1330/issue/view/10011
Article
General properties of relaxation curves in the case of the initial stage of strain with a constant rate in the linear heredity theory
Abstract
Qualitative properties of relaxation curves are analytically studied in the case of linear-time strain at the initial stage. These curves are induced by an integral constitutive relation of viscoelasticity with an arbitrary relaxation function. Among these properties are the intervals of monotonicity and convexity, jumps, breaks, the asymptotics of curves, their dependence on the parameters of the initial stage of strain and on the properties of a relaxation function, the convergence type of a family of relaxation curves when the duration of the initial stage tends to zero, etc.
55-58
Formation fronts of a nonlinear elastic medium from a medium without shear stresses
Abstract
The fronts of phase transition of a medium without shear stresses to a nonlinear incompressible anisotropic elastic medium are considered. The mass flux through unit area of a front is assumed to be known. The variation of the tangential components of the medium’s velocity and the variation of the arising shear stresses are studied. An explicit form of boundary conditions is found using the existence condition of a discontinuity front structure. The Kelvin–Voight viscoelastic model is adopted for this structure.
59-65
An eigenvalue problem for tensors used in mechanics and the number of independent Saint-Venant strain compatibility conditions
Abstract
A number of questions concerning the eigenvalue problem for a tensor \(\mathop A\limits_ \approx\) ∈ ℝ4(Ω) with special symmetries are considered; here Ω is a domain of a four-dimensional (three-dimensional) Riemannian space. It is proved that a nonsingular fourth-rank tensor has no more than six (three) independent components in the case of a four-dimensional (three-dimensional) Riemannian space. It is shown that the number of independent Saint-Venant strain compatibility conditions is less than six.
66-69
Effective characteristics of fiber composites in the linear moment theory of elasticity
Abstract
A special boundary value problem whose solution is used to determine the effective characteristics in the linear moment theory of elasticity is considered. A procedure of finding the effective characteristics is proposed by the example of a fiber composite whose matrix and inclusions are isotropic. The boundary effects of structure functions are also discussed.
70-73
Steady-state seismic vibrations of a buried pipeline in a viscoelastic soil
Abstract
Steady-state coupled longitudinal vibrations of a buried pipeline and a viscoelastic soil during an earthquake are studied. Using specific examples of soils described by the Kelvin–Voigt model and by the viscous liquid model, the main qualitative and quantitative effects of viscosity on the behavior and seismic stability of metallic (steel) and concrete pipelines are clarified.
74-77