Tension of a nonthin transversely isotropic plate with a noncircular cylindrical cavity

The three-dimensional stress state of a transversely isotropic plate with a nearly circular cylindrical cavity is examined. The cavity surface is subject to normal and tangential stresses and the plate is subject at infinity to tensile and shear forces. The problem is solved by expanding unknown functions into Fourier-Legendre series in the thickness coordinate and using the boundary-shape perturbation method. The equations and recurrence formulas needed to solve the problem in an arbitrary approximation are presented __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 101–113, November 2006.     

Analysis of a transversely isotropic rod containing a single cylindrical inclusion with axisymmetric eigenstrains

This paper studies a transversely isotropic rod containing a single cylindrical inclusion with axisymmetric eigenstrains. The analytical elastic solution is obtained for the displacements, stresses and elastic strain energy of the rod. The effects of microstructural parameters and its evolution on the elastic stress and strain fields as well as the strain energy of the rod are quantitatively demonstrated through examples.     

Computation of flexible finite-size cylindrical panels of noncircular cross section

Institute of Mechanics, Academy of Sciences of the Ukraine, Kiev. Polytechnical Institute, L'vov. Translated from Prikladnaya Mekhanika, Vol. 28, No. 12, pp. 71–75, December, 1992.     

Concavities on the zonal slowness section of a transversely isotropic elastic material

The section of the slowness surface of a transversely isotropic elastic material in a zonal plane consists of an ellipse and a quartic curve with two nested branches, the inner of which is convex. Concavities can therefore occur only on the outer branch S and five possibilities arise: (I) S is convex; (II) S has two axial concavities (centred on the points of intersection of S with the axis of transverse isotropy); (III) S has two basal concavities (centred on the points of intersection of S with the basal plane); (IV) S has two axial and two basal concavities; (V) S has four oblique concavities, neither axial nor basal. The first and last of these are commonly realized in actual materials, the others only rarely. A unified treatment of stationary points and concavities on S is given in the course of which some previous results are simplified and their relationship clarified.     

Heat propagation in a nonuniform rod of variable cross section

An integral formula is used to average a coupled problem of thermoelasticity for a nonuniform rod of variable cross section. Effective characteristics are found. It is shown that, in addition to the expected effective coefficients, there appear five independent coefficients characterizing the temperature change rate effect on the stresses in the rod, on the longitudinal heat flux, and on the entropy distribution along the length of the rod. A feature of these new coefficients is that they become equal to zero in the case of a uniform rod. The homogenization of the thermoelasticity equations for nonuniform rods allows one to propose a new theory of heat conduction in rods. This new theory differs from the classical one by the fact that some new terms are added to the Duhamel–Neumann law, to the Fourier heat conduction law, and to the entropy expression. These new terms are proportional to the temperature change rate with time. It is also shown that, in the new theory of heat conduction, the propagation velocity of harmonic heat perturbations is dependent on the oscillation frequency and is finite when the frequency tends to infinity.     

On the rotating rod with variable cross section

Summary Stability of a heavy rotating rod with a variable cross section is studied by energy method. Bifurcation points for the system of equilibrium equations are analyzed. It is shown that for the case when the rotation speed exceeds the critical one, the trivial solution ceases to be the minimizer of the potential energy, so that rod loses stability, according to the energy criteria. Also, a new estimate of the maximal rod deflection in the post-critical state is obtained. Accepted for publication 11 November 1996     

Dynamic deformation of a thermoviscoelastic rod of triangular cross section in a coupled formulation

For the coupled model of a thermoviscoelastic rod of equilateral triangular cross section, two exact solutions are obtained for the cases where a normal displacement and a shear stress or a tangential displacement and a normal stress are specified on the lateral surface of the rod. A dimensionless parameter R₀ is introduced to judge the appropriateness of taking into account the coupling in the formulation of the problem. Formulas are given for the velocities and lengths of the temperature, shear, and longitudinal waves, which can be used in experiments to determine the physical properties of thermoviscoelastic materials. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 128–143, July–August, 2007.     

《Elaticity of Transversely Isotropic Materials》一书评介

浙江大学土木系丁皓江教授和陈伟球教授及澳大利亚悉尼大学航空、机械与机电工程学院章亮炽教授的专著“Elasticity of Transversely Isotropic Ma- terials”(ISBN：1-4020-4033-4),2006年由Springer公司出版,该书是加拿大著名力学家G．M．L．Gladwell     

Thermoelastic deformation of a transversely isotropic parabolic cylinder

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 25, No. 7, pp. 3–9, July, 1989.     

Representations for transversely hemitropic and transversely isotropic stress-strain relations

The sets of polynomial stress-strain relations for elastic points which are transversely hemitropic and transversely isotropic are presented as projections of free algebraic modules having 20 and 10 generators, respectively. Complete sets of relations for the projections are presented which allow the sets of interest to be identified as free submodules having 12 and 6 generators, respectively. The results are established using the Cartan decomposition of the representation of the adjoint action of the two-dimensional rotation and orthogonal groups on the space of three-by-three symmetric matrices. The results are compared to known representations for nonlinear transversely isotropic stress-strain relations and for linear, transversely hemitropic and transversely isotropic ones.Work supported in part by National Science Foundation Grant INT-9106519.     

Representations for transversely hemitropic and transversely isotropic stress-strain relations

The sets of polynomial stress-strain relations for elastic points which are transversely hemitropic and transversely isotropic are presented as projections of free algebraic modules having 20 and 10 generators, respectively. Complete sets of relations for the projections are presented which allow the sets of interest to be identified as free submodules having 12 and 6 generators, respectively. The results are established using the Cartan decomposition of the representation of the adjoint action of the two-dimensional rotation and orthogonal groups on the space of three-by-three symmetric matrices. The results are compared to known representations for nonlinear transversely isotropic stress-strain relations and for linear, transversely hemitropic and transversely isotropic ones.     

Spheroidal inhomogeneity in a transversely isotropic piezoelectric medium

Summary Piezoelectric material containing an inhomogeneity with different electroelastic properties is considered. The coupled electroelastic fields within the inclusion satisfy a system of integral equations solved in a closed form in the case of an ellipsoidal inclusion. The solution is utilized to find the concentration of the electroelastic fields around an inhomogeneity, and to derive the expression for the electric enthalpy of the electroelastic medium with an ellipsoidal inclusion that is relevant for various applications. Explicit closed-form expressions are found for the electroelastic fields within a spheroidal inclusion embedded in the transversely isotropic matrix. Results are specialized for a cylinder, a flat rigid disk and a crack. For a penny-shaped crack, the quantities entering the crack propagation criterion are found explicitly. Received 17 February 2000; accepted for publication 9 May 2000     

Bending of a packet of transversely isotropic circular plates

A mechanical-mathematical model of the bending of transversely isotropic plates is developed on the basis of the model constructed by é. I. Grigolyuk and V. M. Tolkachev. The original model is generalized with allowance for anisotropy. The new model is used to solve the problem of the axisymmetric bending of a packet of circular plates. The existence of regions of adhesion, slip, and separation is taken into account. The problem of determining the contact stresses in the model is reduced to the integration of a system of differential equations. Ivano-Frankovsk Division, Institute of Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 8, pp. 71–77, August, 1999.     

Shear modulus of transversely isotropic materials

A new and simple method is presented to determine the inde-pendent shear modulus of transversely isotropic material.Mathematical formulation,derivation and solution are given,and test apparatus and results are presented.The method wastested on one of such materials-Green River Formation oilshale.Comparisons wich other approximate results and acou-stical methods are made.Confirmation of the test methodwith materials having known shear moduli is also presented.