Method of homogeneous solutions in a mixed problem for an elastic halfstrip

Institute of Hydromechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 26, No. 2, pp. 98–108, February, 1990.     

Inhomogeneous to homogeneous dynamical states through symmetry breaking dynamics

Nonlinear Dynamics - We explore the dynamical transitions facilitated by the symmetry breaking dynamical states in a directly coupled limit-cycle oscillators, when the oscillators are interacting...     

Inhomogeneous inverse problem in finite elasticity

For a class of materials for which the principal strain directions always coincide with the principal stress directions one can determine the stress field in an inhomogeneously deformed body from given boundary conditions and a known strain field without knowing the constitutive equations. Each point of the inhomogeneously deformed body contains information such as that derived from an individual homogeneous identification test. The practically important two-dimensional case leads to a problem of solving a linear hyperbolic system where two differential equations describe the principal stress components. The problem can be reduced to that of integration along characteristics.Under a certain globality condition the existence, uniqueness, and correctness of the solution are guaranteed in the whole test piece. It is shown that the globality condition is closely related to whether or not the test piece is isotropic and elastic. The influence of experimental error on the correctness of problem formulation is discussed.

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Abstrakte Für die Klasse der Materialen, für welche die Grundspannungsrichtungen und die Grundverformungsrichtungen gleich sind, kann man das Spannungsfeld in einem inhomogen deformierten Körper für gegebene Randbedingungen und einem bekannten Verformungsfeld ohne Kenntnis der detailierten Form der Dehnungs-Spannungsgleichung bestimmen. Jeder Punkt des inhomogen deformierten Körpers liefert dieselbe Information wie ein individueller homogener Test. Der praktisch wichtige zweidimensionale Fall führt zu einem Problem der Lösung eines linear hyperbolischen Systems von zwei Differentialgleichungen für die Grundspannungskomponenten. Das Problem kann auf die Integration entlang der Charakteristik des Systems reduziert werden.Unter einer Bedingung der Globalität das die Existent, Eindeutigkeit und Richtigkeit der Lösung in der ganzen Testprobe gewährleistet sind. Es wird gezeigt, dass diese Globalitätsbedingung damit zusammenhängt eng, ob die Testprobe isotrop und elastisch ist. Der Einfluss der experimentellen Fehler auf die Richtigkeit der Formulation des Problems wird auch analysiert.

     

Inhomogeneous initial-boundary value problem for Ginzburg-Landau equations

Some integral identities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative and the square norm of partial derivatives were obtained. Then the existence of global weak solution of inhomogeneous initial-boundary value problem of Ginzburg-Landau equations was proved by the method of approximation technique and a priori estimates and making limit.     

ANALYTICAL SOLUTIONS FOR ELASTOSTATIC PROBLEMS OF PARTICLE-AND FIBER-REINFORCED COMPOSITES WITH INHOMOGENEOUS INTERPHASES

IntroductionRecently ,theinterphaseincompositeshasattractedtheattentionofmanyresearchers[1- 7].Someinterphasesareproducedbydesignandothersbychemicalreactionsinfabricatingcomposites.Fromtheviewpointofmechanicsofcompositematerials,oneofthefundamentalproblemsofcompositeswithinterphasesistopredicttheeffectivemoduli.Therearemanymethodsforpredictingeffectivemoduliofcomposites,suchasgeneralizedself_consistentmethod(GSCM) ,compositesphereandcompositecylindermodels (CCAandCSA)andIDDestimate ,etc …     

Hybrid elastostatic and thermostatic analysis from measured data

An effective hybrid method is demonstrated for stress analysis and heat transfer. Measured information is represented and differentiated analytically, while the number of unknown coefficients and amount of experimental input data needed are reduced through field equations. The approach is accurate, full-field, employs arbitrarily shaped elements, does not require a smoothing parameter and is well suited for computer-vision techniques. The concept is presently illustrated by moiré strain analysis, although it can be extended to other disciplines.     

Three-dimensional elastostatic solutions for transversely isotropic functionally graded material plates containing elastic inclusion

Based on the generalized England-Spencer plate theory, the equilibrium of a transversely isotropic functionally graded plate containing an elastic inclusion is studied. The general solutions of the governing equations are expressed by four analytic functions α(ζ), β(ζ), φ(ζ), and ψ(ζ) when no transverse forces are acting on the surfaces of the plate. Axisymmetric problems of a functionally graded circular plate and an infinite func-tionally graded plate containing a circular hole subject to loads applied on the cylindrical boundaries of the plate are firstly investigated. On this basis, the three-dimensional (3D) elasticity solutions are then obtained for a functionally graded infinite plate containing an elastic circular inclusion. When the material is degenerated into the homogeneous one, the present elasticity solutions are exactly the same as the ones obtained based on the plane stress elasticity, thus validating the present analysis in a certain sense.     

Model selection in fracture mapping from elastostatic data

In this paper, the inverse problem of imaging internally pressurized cracks from elastostatic measurements is investigated with special attention to the question of model choice. The selection of the most probable model from among a finite set of fracture geometry and loading model is carried out using Bayes factors. The modelling error variance is also estimated during the inversion procedure. This Bayesian model selection method also produces a known limit for the resolution of fracture dimensions, which depends on the configuration of the measurements. Both synthetic and real field examples in hydraulic fracture mapping applications are presented.     

Generalized homogeneous functions and the two-body problem

IntroductionInthispaper,wegeneralizetheclassicconceptofhomogeneousfunctionofdegreeαandwestudytherelationbetweenthehomogeneousfunctionconceptandthemovementofabodythatsatisfiestheKepler’ssecondlaw .Asanapplicationoftheinvolvedtechniquesthatwereused ,wepresentasolutionofthetwo_bodyproblem ,givingawaytoobtainatimeequationforthebodythatrotatesaroundtheother,usingtheconceptofhomogeneousfunction .WeobtainedaserieslikeasthatwaspresentedinRef.[1 ] .1　GeneralizedHomogeneousFunctionsLetUbeanopensub…     

Viscoelastic problem for piecewise homogeneous piezoelectric plates

The electromagnetoviscoelastic problem is solved for piecewise-homogeneous plates. The problem is reduced to solving a sequence of electromagnetoelastic problems with complex potentials. General representations of approximation functions for multiply connected domains and boundary conditions for their determination are given. An analytical solution of the problem for a plate with one inclusion and an approximate solution for a plate with a finite number of inclusions are obtained. The change in the electromagnetoelastic state is investigated numerically as a function of time, the properties of the plate and inclusion materials, and the distance between the inclusions.     

An image treatment of elastostatic transmission from an interface layer

A basic theorem for representing the Airy stress function for two perfectly bonded semi-infinite planes in terms of the corresponding Airy function for the unbounded homogeneous plane is applied in a systematic stepwise fashion to generate the corresponding Airy stress function for a three-phase composite comprising two semi-infinite planes separated by a thick layer. The loading of the three-phase composite is arbitrary, and may be in or near the interface layer. The basic theorem is first illustrated by applying it to an elastic medium which is bounded by two unloaded straight edges which intersect at an angle π/n, where n is a positive integer. This example illustrates a case of a finite system of images, while the plane-layered medium problem leads to an infinite series of images.     

Higher approximations to the homogeneous solutions for toroid

To analyze the strength of the elastic, isotropic toroid with axisymmetrical loads, it is necessary to find the solutions for a nonhomogeneous second-order ordinary-differential equation in complex form. When the parameter = 12(1-v²) a² / (r ₀ h), which occurs in the equation, is large, the asymptotic approach is often used. Up to now, only the first approximations to its homogeneous solutions are found. In this paper the author has obtained higher approximations to the homogeneous solutions, thus, reaching the precision of linear thin shell theory.This work was supported by the National Natural Science Foundation of China.     

Method of homogeneous solutions in problems with mixed boundary conditions

Kramatorsk Industrial Institute. Donetsk University. Translated from Prikladnaya Mekhanika, Vol. 25, No. 9, pp. 57–61, September, 1989.     

Two-dimensional thermoelastic problem of an infinite magneto-microstretch homogeneous isotropic plate

In this work, the magneto-thermoelastic problem of an infinite microstretch homogeneous isotropic plate placed in a transverse magnetic field is studied in the context of different theories of generalized thermoelasticity. The upper surface of the infinite plate is subjected to a zonal time-dependent heat shock. The problem is investigated by applying finite element method. The solution is obtained by solving finite element governing equations of the problem in time domain directly. The results, including temperature, stresses, displacements, microrotation, microstretch, induced magnetic field, and induced electric field, are presented graphically. Comparison is made in the results predicted by different theories of generalized thermoelasticity, to show that the micropolar effect has a slight influence on the results while the microstretch effect has a great influence on the results. Finally, a parameter study provides an idea about the influence of the respective terms of the theories.     

General solutions of coupled thermoelastic problem

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Transition solutions in the Taylor problem

Communicated by K. Kirchgässner     

Existence of solutions of Kraiko's problem

Three initial-boundary-value problems for the equations of gas dynamics are formulated. Successive solution of these problems yields a solution of Kraiko's problem of the isentropic transition of an ideal gas from a homogeneous state of rest to another state of rest with higher or lower density. Solutions are constructed for plane, cylindrical, and spherical layers of an ideal gas. The existence of locally analytic solutions is proved. Ural State Academy of Service, Ekaterinburg 620034. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 48–55, May–June, 2000.