An asymptotic non-linear model for thin-walled rods with strongly curved open cross-section

In this paper, we present a non-linear one-dimensional model for thin-walled rods with open strongly curved cross-section, obtained by asymptotic methods. A dimensional analysis of the non-linear three-dimensional equilibrium equations lets appear dimensionless numbers which reflect the geometry of the structure and the level of applied forces. For a given force level, the order of magnitude of the displacements and the corresponding one-dimensional model are deduced by asymptotic expansions.     

The nonaxisymmetric thermostressed state of laminated isotropic and rectilinearly orthotropic solids of revolution

A technique for determination of the nonaxisymmetric elastoplastic stress-strain state of laminated isotropic and rectilinearly orthotropic solids of revolution under nonisothermal loading is described. The semianalytic method of finite elements is used together with the method of successive approximations. The deformation of isotropic materials is described by the equations of the theory of deformation along trajectories of small curvature, and the deformation of orthotropic materials is described by the equations of the theory of elasticity. The thermostressed state of a three-layered solid of revolution of complex form made from isotropic and cylindrically and rectilinearly orthotropic materials subject to nonaxisymmetric heating is studied. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 4, pp. 88–95, April, 2000.     

Flow of second-order fluid in a curved duct with square cross-section

This paper investigates the inertial and creeping flow of a second-order fluid in a curved duct with a square cross-section. Numerical modeling is employed to analyze fluid flow, and the governing equations are discretized using the finite difference method on a staggered mesh. The marker-and-cell method is employed to allocate the parameters on the staggered mesh, and static pressure is calculated using the artificial compressibility approach. The effect of centrifugal force due to the curvature of the duct and the opposing effects of the first and second normal stress difference on the flow field are investigated. In addition, the order-of-magnitude technique is used to derive the force balance relations for the core region of flow. Based on these relations, the performance mechanism of centrifugal force and normal stress differences on the generation of secondary flows is considered. We also present an analytical relation for the axial velocity profile and flow resistance ratio of creeping flow. For this kind of flow, previous studies have investigated the effect of the first normal stress difference on the transition from one pair to two pairs of vortices while we show that the negative second normal stress difference has the opposite effect on this transition and can stabilize the flow.     

Double-moment of spacial curved bars with closed thin-wall cross-section

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Mixed thermoplasticity problem for open solids of revolution

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 24, No. 6, pp. 3–9, June, 1988.     

Instability investigation of creeping viscoelastic flow in a curved duct with rectangular cross-section

In this paper, instability in the creeping viscoelastic flow inside a curved rectangular duct is investigated numerically for the first time. Using the Criminale–Eriksen–Filbey (CEF) model as the constitutive equation, the governing equations are solved by a second order of finite difference method based on the artificial compressibility algorithm in a staggered mesh. The effects of normal stress differences on the flow stability are investigated. The numerical results obtained indicate that the increase of the negative second normal stress difference of viscoelastic fluid causes stability in the creeping flow in curved ducts, however, the increase of the first normal stress difference intensifies the instability. Furthermore, at the special value of Ψ₂/Ψ₁=?0.5, the interaction of the two normal stress differences results in a stable flow field.     

Stress state of solids of revolution with elastic inclusions

S. P. Timoshenko Institute of Mechanics, Ukrainian Academy of Sciences, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 4, pp. 54–64, April, 1994.     

A constitutive model for plastically anisotropic solids with non-spherical voids

Plastic constitutive relations are derived for a class of anisotropic porous materials consisting of coaxial spheroidal voids, arbitrarily oriented relative to the embedding orthotropic matrix. The derivations are based on nonlinear homogenization, limit analysis and micromechanics. A variational principle is formulated for the yield criterion of the effective medium and specialized to a spheroidal representative volume element containing a confocal spheroidal void and subjected to uniform boundary deformation. To obtain closed form equations for the effective yield locus, approximations are introduced in the limit-analysis based on a restricted set of admissible microscopic velocity fields. Evolution laws are also derived for the microstructure, defined in terms of void volume fraction, aspect ratio and orientation, using material incompressibility and Eshelby-like concentration tensors. The new yield criterion is an extension of the well known isotropic Gurson model. It also extends previous analyses of uncoupled effects of void shape and material anisotropy on the effective plastic behavior of solids containing voids. Preliminary comparisons with finite element calculations of voided cells show that the model captures non-trivial effects of anisotropy heretofore not picked up by void growth models.     

Stability of laminated shells of revolution with plies subject to long-term damage

The problem of bifurcational instability of shells of revolution made of laminated composite materials with plies subject to long-term damage is formulated and solved     

Steady laminar flow of a power-law fluid in a curved pipe of circular cross-section with varying curvature

The steady laminar flow of power-law fluid through pipes of circular cross-section, whose center-line curvature varies locally, is analyzed theoretically. The flows, in three kinds of pipes whose center-lines are specified by

as examples of once, twice, and periodically-curved pipes, respectively, are discussed in comparison with Newtonian flow. The analysis is valid for any other two-dimensionally curved pipes, when the center-line curvature is small.     

Stability of laminated convex shells of revolution with microdamages in laminate components

The problem of bifurcation instability of shells of revolution made of a laminate material with progressively damaged components under loading is formulated and solved __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 7, pp. 98–106, July 2006.     

A new non-linear higher-order shear deformation theory for large-amplitude vibrations of laminated doubly curved shells

A consistent higher-order shear deformation non-linear theory is developed for shells of generic shape, taking geometric imperfections into account. The geometrically non-linear strain-displacement relationships are derived retaining full non-linear terms in the in-plane displacements; they are presented in curvilinear coordinates in a formulation ready to be implemented. Then, large-amplitude forced vibrations of a simply supported, laminated circular cylindrical shell are studied (i) by using the developed theory, and (ii) keeping only non-linear terms of the von Kármán type. Results show that inaccurate results are obtained by keeping only non-linear terms of the von Kármán type for vibration amplitudes of about two times the shell thickness for the studied case.     

Steady laminar flow of viscoelastic fluid in a curved pipe of circular cross-section with varying curvature

The steady laminar flow of viscoelastic fluid through pipes of circular cross-section, whose center-line curvature varies locally, is analyzed theoretically. The flows in three kinds of pipes whose center-lines are specified by

as the examples of once, twice, and periodically curved pipes, respectively, are discussed in comparison with purely viscous flow. The analysis is valid for any other two-dimensionally curved pipes, when the center-line curvature is small. In addition, the reason why the secondary flow of a viscoelastic fluid in a curved pipe of circular cross-section is stronger than that of a purely viscous fluid is explained. In the present paper, the White—Metzner model is employed as the constitutive equation.     

A method to study the nonaxisymmetric plastic deformation of solids of revolution with allowance for the stress mode

The paper proposes a method to allow for the stress mode in analyzing the thermoelastoplastic stress-strain state of compound bodies of revolution under asymmetric loading and heating. Use is made of a semianalytic finite-element method and the method of successive approximations. Some numerical results are presented Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 26–35, September 2008.