Dynamics of strings made of phase-transforming materials

This paper presents a theory to describe the dynamical behavior of a string made of a phase-transforming material like a shape-memory alloy. The study of phase boundaries, the driving force acting on them and the kinetic relation governing their propagation is of central concern. The paper proposes a qualitative experimental test of the notion of a kinetic relation, as well as a simple experimental method for measuring it quantitatively. It presents a numerical method for studying general initial and boundary value problems in strings, and concludes by exploring the use of phase transforming strings to generate motion at very small scales.     

Large deflection of curved elastic beams made of Ludwick type material

The large deflection of an axially extensible curved beam with a rectangular cross-section is investigated. The elastic beam is assumed to satisfy the Euler-Bernoulli postulation and be made of the Ludwick type material. Through reasonably simplified integration, the strain and curvature of the axis of the beam are presented in implicit formulations. The governing equations involving both geometric and material nonlinearities of the curved beam are derived and solved by the shooting method. When the initial curvature of the beam is zero, the curved beam is degenerated into a straight beam,and the predicted results obtained by the present model are consistent with those in the open literature. Numerical examples are further given for curved cantilever and simply supported beams, and the couplings between elongation and bending are found for the curved beams.     

On the theory of elastic shells made from a material with voids

In this paper we present a theory for porous elastic shells using the model of Cosserat surfaces. We employ the Nunziato–Cowin theory of elastic materials with voids and introduce two scalar fields to describe the porosity of the shell: one field characterizes the volume fraction variations along the middle surface, while the other accounts for the changes in volume fraction along the shell thickness. Starting from the basic principles, we first deduce the equations of the nonlinear theory of Cosserat shells with voids. Then, in the context of the linear theory, we prove the uniqueness of solution for the boundary initial value problem. In the case of an isotropic and homogeneous material, we determine the constitutive coefficients for Cosserat shells, by comparison with the results derived from the three-dimensional theory of elastic media with voids. To this aim, we solve two elastostatic problems concerning rectangular plates with voids: the pure bending problem and the extensional deformation under hydrostatic pressure.     

Buckling of a column made of functionally graded material

Buckling of a column made of functionally graded material is investigated. The functional grading is performed in the longitudinal direction. The following problem is addressed: determine the variation of the elastic modulus with the axial coordinate such that the buckling load exceeds the preselected value. In this study, only polynomial variation of the buckling mode is considered and only the case of cantilever column is treated.     

On linearization of the stiffness characteristics of flexible beams made of physically nonlinear materials

The geometry of flexible beams that are made of a physically nonlinear material and have a nearly linear load-deflection characteristic is identified for a wide range of monotonic and harmonic loads. The geometrically nonlinear beam equations are used. The physically nonlinear behavior of the material is described using a unified viscoplastic theory. A beam thickness criterion is formulated to provide nearly linear stiffness characteristic of the beam in the case of significant deflections and physically nonlinear deformations of the beam’s outer layers __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 85–92, February 2006.     

Torsional waves in a cylinder made from a composite material

International Applied Mechanics -     

Stability of plates made of a damageable physically nonlinear material

The bifurcation instability problem for rectangular plates made of physically nonlinear materials progressively damaged with increasing load is formulated and solved __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 79–88, September 2006.     

Axisymmetric strain of a thick-walled pipe made of a highly elastic material

We reduce the plane strain problem to a nonlinear elasticity problem for inhomogeneous bodies by choosing a new form of the elastic potential, whose parameters are determined from the data known in the literature. By using the geometric linearization method, we reduce that problem to a sequence of linear elasticity problems for inhomogeneous bodies. We obtain an analytic solution of the corresponding linear elasticity problem in the case of an arbitrary continuously differentiable dependence of the shear modulus on the radial coordinate. We determine the pipe stress-strain state and parameters in the case of finite and large strains for given sets of initial data and estimate the accuracy of the solution thus obtained.     

Rippling and a phase-transforming mesoscopic model for multiwalled carbon nanotubes

We propose to model thick multiwalled carbon nanotubes as beams with non-convex curvature energy. Such models develop stressed phase mixtures composed of smoothly bent sections and rippled sections. This model is motivated by experimental observations and large-scale atomistic-based simulations. The model is analyzed, validated against large-scale simulations, and exercised in examples of interest. It is shown that modelling MWCNTs as linear elastic beams can result in poor approximations that overestimate the elastic restoring force considerably, particularly for thick tubes. In contrast, the proposed model produces very accurate predictions both of the restoring force and of the phase pattern. The size effect in the bending response of MWCNTs is also discussed.     

Stability of cylindrical shells made of a damageable physically nonlinear material

The bifurcation-instability problem for cylindrical shells made of physically nonlinear materials progressively damaged with increasing load is formulated and solved __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 10, pp. 56–66, October 2006.     

Two-dimensional model of a plate made of an anisotropic inhomogeneous material

We present an asymptotic derivation of the two-dimensional equations of equilibrium of a thin elastic inhomogeneous plate manufactured of an anisotropic material of general form with 21 moduli of elasticity. We also consider simplified models obtained under special assumptions on the moduli. We use test examples to illustrate the error estimate of the proposed model and discuss its scope. The model is compared with the classical Kirchhoff–Love and Timoshenko–Reissner models.     

Transient delivery movement of a fluid in pipes made of a viscoelastic material

The propagation of perturbation waves in an infinite viscoelastic pipeline is examined in [1], where the initial equations describing the movement of a fluid in pipelines made of viscoelastic materials are given. The subject of this paper is the transient movement of a fluid in viscoelastic pipes of finite length, a topic which has been already partially investigated in [2, 3] for a Maxwell model of a standard linear body. Solutions are given below for the problem of the movement of a fluid in pipes of constant diameter and in a pipeline made up of pipes of different diameters, and actual models of the pipe materials are examined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 178–182, March–April, 1976.