Saint-Venant's problem for inhomogeneous bodies

In this paper is given a method to solve Saint-Venant's problem in the case of the inhomogeneous and isotropic elastic solids.     

Bounds for eigenvalues in some vibration and stability problems

In finite element displacement methods for vibration and stability problems, upper bounds to eigenvalues are ensured only if consistent and conforming elements arte used, whereas the use of other elements may yield an upper or a lower bound. Here a systematic perturbation of the mass (or geometric stiffness) matrix is used to generate two classes of eigenvalue sequences whose respective members tend to a common limit from opposite sides.     

Certain exact solutions to steady-state problems in the theory of heat conduction applied to inhomogeneous bodies

A method is shown of constructing exact analytical solutions to steady-state problems in the theory of heat conduction where the thermal conductivity is a special kind of function of the space coordinates.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 23, No. 3, pp. 554–556, September, 1972.     

Simulation of vibration of inhomogeneous,loaded plates

Summary The Timoshenko-Mindlin type wave equation is derived for a plate which is inhomogeneous in material and geometric properties. A numerical analogue to this wave equation for a plate is presented and results of propagation studies of Gaussian and sinusoidal wavepackets along a plate reinforced by ribs of up to five times the thickness of the plate are discussed. Results are presented for an infinite plate supported by two ribs. The plate equation includes consideration of shear and rotary inertia, external loading and plastic-visco-elastic loss. A spectral analysis of the inhomogeneous plate equation is presented.     

Stressed state of cylindrical bodies with multilayer inhomogeneous coatings

We deduce engineering formulas for the evaluation of stresses in a cylinder with inhomogeneous multi-layer coatings by using the approach based on the application of generalized boundary conditions and the approach based on the reduction of the corresponding boundary-value problem of elasticity to the solution of integral equations. We also compare and analyze the ranges of applicability of each approach.     

Thermodynamic influences on shock waves in inhomogeneous elastic bodies

Summary In this paper, the differential equation governing the behavior of shock waves propagating in inhomogeneous thermoelastic bodies is derived. The implications of this equation on the local behavior of the amplitudes are examined. It is shown that the behavior depends on the relative magnitudes of a number , called the critical jump in strain gradient, and the jump in strain gradient across the shocks.

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Thermodynamische Einflüsse auf Stoßwellen in inhomogenen elastischen Körpern

Zusammenfassung In dieser Arbeit wird die das Verhalten von in inhomogenen thermoelastischen Körpern sich ausbreitenden Stoßwellen charakterisierende Differentialgleichung abgeleitet. Die Folgerungen auf das lokale Verhalten der Amplituden wird untersucht. Es wird gezeigt, daß das Verhalten von der relativen Größe einer Zahl , genannt kritischer Sprung des Verzerrungsgradienten, und dem Sprung im Verzerrungsgradienten über den Stoß abhängt.

     

Vibrations of inhomogeneous anisotropic viscoelastic bodies described with fractional derivative models

The dynamic response of plane inhomogeneous anisotropic bodies made of linear viscoelastic materials is investigated. The mechanical behavior of the viscoelastic material is described by differential constitutive equations with fractional order derivatives. The governing equations, which are derived by considering the dynamic equilibrium of the plane body element, are two coupled linear fractional evolution partial differential equations in terms of the displacements, whose order is in general greater than two with respect to time derivatives. A method is presented to establish the additional required initial conditions beside the described initial displacements and velocities. Using the Analog Equation Method (AEM) in conjunction with the Domain Boundary Element Method (D/BEM) the governing equations are transformed into a system of multi-term ordinary fractional differential equations (FDEs), which are solved using the numerical method for multi-term FDEs developed recently by Katsikadelis. Numerical examples are presented, which not only demonstrate the efficiency of the solution procedure and validate its accuracy, but also permit a better understanding of the dynamic response of plane bodies described by different viscoelastic models.     

Some heat conduction problems in an inhomogeneous body

Solutions are obtained for the heat conduction equation in the case when the thermal conductivity is a homogeneous function of the coordinates.     

Generalized regular regime of inhomogeneous exothermic bodies with fragmentary heat transfer conditions

The case of convective heat transfer of film-coated fragments of a body surface with media of different constant temperature is discussed. In the stage of a generalized regular regime the difference between the final and actual temperatures decreases in an inhomogeneous exothermic body in accordance with an exponential law.Riga Technical University, Riga, Latvia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 4, pp. 687–692, July–August, 1995.     

The method of fundamental solutions for inhomogeneous elliptic problems

We investigate the use of the Method of Fundamental Solutions (MFS) for solving inhomogeneous harmonic and biharmonic problems. These are transformed to homogeneous problems by subtracting a particular solution of the governing equation. This particular solution is taken to be a Newton potential and the resulting homogeneous problem is solved using the MFS. The numerical calculations indicate that accurate results can be obtained with relatively few degrees of freedom. Two methods for the special case where the inhomogeneous term is harmonic are also examined.     

Fundamental thermo-elasticity equations for thermally induced flexural vibration problems for inhomogeneous plates and thermo-elastic dynamical responses to a sinusoidally varying surface temperature

Equations of motion governing thermally induced vibration of plates with inhomogeneous material properties through the thickness direction are presented. Equations of motion for thermally induced flexural vibration for inhomogeneous rectangular plates in which the material properties are given in the form of a power of the thickness coordinate are derived from the above-mentioned fundamental equations. An exact solution of the one-dimensional temperature change is presented for an inhomogeneous plate in which one surface is exposed to a sinusoidally varying temperature, and the other is kept at zero temperature change. The associated quasi-static and dynamic solutions pertinent to deflection and thermal stresses in the inhomogeneous rectangular plate are derived under the condition of simply supported edges. Numerical calculations are performed, and the effects of material inhomogeneity such as Young’s modulus, coefficient of linear thermal expansion, and mass density, angular frequency in cyclic heating, and aspect ratio on the thermo-elastic response of the rectangular plate are shown in graphical form. Comparing the dynamic solutions with quasi-static ones, the effect of inertia on the thermo-elastic response of the inhomogeneous rectangular plate is evaluated.     

A finite element analysis of some boundary value problems for a new type of constitutive relation for elastic bodies

Recently, there has been interest in the study of a new class of constitutive relation, wherein thelinearized strain tensor is assumed to be a function of the stresses. In this communication, some boundaryvalue problems are solved using the finite element method and the solid material being described by such aconstitutive relation, where the stresses can be arbitrarily ‘large’, but strains remain small. Three problems areanalyzed, namely the traction of a plate with hyperbolic boundaries, a plate with a point load, and the tractionof a plate with an elliptic hole. The results for the stresses and strains are compared with the predictions thatare obtained by using the constitutive equation of the classical linearized theory of elasticity.     

Energy-dynamic modification of the inhomogeneous surface of loose bodies under the effect of seismics

Energy and dynamic models which explain the effect of rejection of a foreign structure from a loose medium are suggested. The corresponding evaluations show that forces which can expel the body to the surface appear in a fast seismic field. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 5, pp. 961–963, September–October, 2000.     

Influence of inhomogeneous electric and magnetic fields on internal mass transfer in capillary-porous bodies

Equations are derived for mass transfer in inhomogeneous electric and magnetic fields. Experimental results are given in support of the theoretical conclusions.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 7, pp. 93–100, July, 1978.