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1.
V. A. Postnov 《Mechanics of Solids》2010,45(1):51-56
We present a method for solving nonlinear inverse problems, which also include identification problems for elastic systems.
The problems whose initial data contain an error are usually solved by regularization methods [1–5]. In the present paper,
we give preference to Tikhonov’s regularization method, which has been widely used in the recent years in practice to increase
the stability of computational algorithms for solving problems in various areas of mechanics [6–9]. 相似文献
2.
The Hamilton–Ostrogradsky principle is used to substantiate the statement of initial–boundary-value problems of electroelasticity.
The free vibrations of a piezoceramic layer are used as an example to illustrate some features of solving nonstationary problems
of electroelasticity
Translated from Prikladnaya Mekhanika, Vol. 44, No. 12, pp. 62–69, December 2008. 相似文献
3.
In this study, four different versions of the variable metric method (VMM) are investigated in solving standard one-dimensional inverse heat conduction problems in order to evaluate their efficiency and accuracy. These versions include Davidon–Fletcher–Powell (DFP), Broydon–Fletcher–Goldfarb–Shanno (BFGS), Symmetric Rank-one (SR1), and Biggs formula of the VMM. These investigations are carried out using temperature data obtained from numerical simulations. 相似文献
4.
The heat- and mass-transfer processes of a spherically blunted cone and a supersonic air flow are identified by the methods
of solving direct and inverse problems with allowance for the heat flow along the contour and the injection of a gas-cooler.
The ranges of applicability of the standard one-dimensional approaches and the method of a thin wall for recovering heat fluxes
directed toward the body in flow are shown in the entire time period considered.
State University of Tomsk, Tomsk 634050. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp.
123–132, September–October, 1999. 相似文献
5.
A method of studying the natural vibrations of highly inhomogeneous shells of revolution is developed. The method is based
on a nonclassical theory of shells that allows for transverse shear and reduction. By separating variables, the two-dimensional
problem is reduced to a sequence of one-dimensional eigenvalue problems. The inverse iteration method is used to reduce these
problems to a sequence of inhomogeneous boundary-value problems solved by the orthogonal sweep method. The capabilities of
the method are illustrated by solving certain representative problems and comparing their solutions with those obtained using
the three-dimensional theory of elasticity, the classical theory of shells, and the refined Timoshenko model
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 38–47, September 2007. 相似文献
6.
I. I. Ryzhkov 《Journal of Applied Mechanics and Technical Physics》2006,47(1):79-90
The group properties of the thermal-diffusion equations for a binary mixture in plane flow are studied. Optimal systems of
first-and second-order subalgebras are constructed for the admissible Lie operator algebra, which is infinite-dimensional.
Examples of the exact invariant solutions are given, which are found by solving ordinary differential equations. Exact solutions
are found that describe thermal diffusion in an inclined layer with a free boundary and in a vertical layer in the presence
of longitudinal temperature and concentration gradients. The effect of the thermal-diffusion parameter on the flow regime
is studied.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 95–108, January–February, 2006. 相似文献
7.
N. F. Vorob'ev 《Journal of Applied Mechanics and Technical Physics》1998,39(3):399-403
The inverse problem of wing aerodynamics—the determination of the lifting surface shape from a specified load—is solved within
the framework of linear theory. Volterra's solution of the wave equation is used. Solutions are found in the class of bounded
functions if certain conditions imposed on the governing parameters of the problem are satisfied. Solutions of inverse problems
of supersonic flow are presented for an infinite-span wing, a triangular wing with completely subsonic edges, and a rectangular
wing.
Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated
from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 86–91, May–June, 1998. 相似文献
8.
The stress-strain state of an incompressible cylindrical elastic body with antiplane strain under the action of potential
forces and surface loading constant along the body is considered in a nonlinear formulation in actual variables. The stresses
are expressed via the pressure and independent strains, the pressure is expressed via the force and elastic potentials, and
nonlinear boundary-value problems are posed for strains (and displacements). Various methods for solving these problems are
developed. For the nonlinear equations obtained, some analytical solutions containing free parameters are given, which can
be used as a basis for solving particular problems.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 93–101, November–December, 2006. 相似文献
9.
Picard and Newton iterations are widely used to solve numerically the nonlinear Richards’ equation (RE) governing water flow
in unsaturated porous media. When solving RE in two space dimensions, direct methods applied to the linearized problem in
the Newton/Picard iterations are inefficient. The numerical solving of RE in 2D with a nonlinear multigrid (MG) method that
avoids Picard/Newton iterations is the focus of this work. The numerical approach is based on an implicit, second-order accurate
time discretization combined with a second-order accurate finite difference spatial discretization. The test problems simulate
infiltration of water in 2D unsaturated soils with hydraulic properties described by Broadbridge–White and van Genuchten–Mualem
models. The numerical results show that nonlinear MG deserves to be taken into consideration for numerical solving of RE. 相似文献
10.
The purpose of this study is to implement a new analytical method which is a combination of the homotopy analysis method (HAM)
and the Padé approximant for solving magnetohydrodynamic boundary-layer flow. The solution is compared with the numerical
solution. Comparisons between the HAM–Padé and the numerical solution reveal that the new technique is a promising tool for
solving MHD boundary-layer equations. The effects of the various parameters on the velocity and temperature profiles are presented
graphically form. Favorable comparisons with previously published works (Crane, J. Appl. Math. Phys. 21:645–647, 1970, and Vajravelu and Hadjinicolaou, Int. J. Eng. Sci. 35:1237–1244, 1997) are obtained. It is predicted that HAM–Padé can have wide application in engineering problems (especially for boundary-layer
and natural convection problems). 相似文献
11.
M. V. Gavrilkina V. V. Glagolev A. A. Markin 《Journal of Applied Mechanics and Technical Physics》2007,48(4):571-576
This paper considers a model for the opening-mode fracture separation process based on the introduction of an interaction
layer. This layer is defined as the region of localization of the fracture process. The stress-strain state of the layer material
is uniform in the cross section of the layer. A study is made of the deformation of a double-cantilever beam weakened by a
notch whose width is equal to the thickness of the interaction layer. The problem is solved in a linearly geometrical approximation.
The thickness of the interaction layer is estimated, and a method for solving the formulated problem is proposed.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 121–127, July–August, 2007. 相似文献
12.
The need of accurate and efficient numerical schemes to solve Richards’ equation is well recognized. This study is carried
out to examine the numerical performances of the nonlinear multigrid method for numerical solving of the two-dimensional Richards’
equation modeling water flow in variably saturated porous media. The numerical approach is based on an implicit, second-order
accurate time discretization combined with a vertex centered finite volume method for spatial discretization. The test problems
simulate infiltration of water in 2D saturated–unsaturated soils with hydraulic properties described by van Genuchten–Mualem
models. The numerical results obtained are compared with those provided by the modified Picard–preconditioned conjugated gradient
(Krylov subspace) approach. 相似文献
13.
A. O. Vatulyan N. O. Soluyanov 《Journal of Applied Mechanics and Technical Physics》2008,49(6):1015-1020
The direct and inverse problems of the steady-state transverse vibrations of a cylindrical rod with a defect in the form of
a cavity of small relative size are considered. An approach to determining the location and volume of the cavity of arbitrary
shape is proposed. Results of computational experiments are analyzed.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 152–158, November–December, 2008 相似文献
14.
Special features of interrelated problems of ecology and climate are analyzed. The technique proposed for solving this class
of problems is demonstrated by an example of evaluating the atmospheric quality and monitoring and predicting the ecological
consequences of man’s impact. An approach based on variational principles in combination with methods of splitting and decomposition
is developed. The structure of algorithms implementing Eulerian and Lagrangian formulations of the problems is described.
Examples of simulation scenarios for particular cases are given.
Institute of Computational Mathematics and Mathematical Geophysics, Siberian Division, Russian Academy of Sciences, Novosibirsk
630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 161–170, September–October, 2000. 相似文献
15.
Two space marching methods for solving the one-dimensional nonlinear inverse heat conduction problems are presented. The
temperature-dependent thermal properties and the boundary condition on the accessible part of the boundary of the body are
known. Additional temperature measurements in time are taken with a sensor located in an arbitrary position within the solid,
and the objective is to determine the surface temperature and heat flux on the remaining part of the unspecified boundary.
The methods have the advantage that time derivatives are not replaced by finite differences and the good accuracy of the method
results from an appropriate approximation of the first time derivative using smoothing polynomials. The extension of the first
method presented in this study to higher dimensions inverse heat conduction problems is straightforward.
Received on 3 May 1999 相似文献
16.
In Part I Moyne and Murad [Transport in Porous Media 62, (2006), 333–380] a two-scale model of coupled electro-chemo-mechanical phenomena in swelling porous media was derived by
a formal asymptotic homogenization analysis. The microscopic portrait of the model consists of a two-phase system composed
of an electrolyte solution and colloidal clay particles. The movement of the liquid at the microscale is ruled by the modified
Stokes problem; the advection, diffusion and electro-migration of monovalent ions Na+ and Cl− are governed by the Nernst–Planck equations and the local electric potential distribution is dictated by the Poisson problem.
The microscopic governing equations in the fluid domain are coupled with the elasticity problem for the clay particles through
boundary conditions on the solid–fluid interface. The up-scaling procedure led to a macroscopic model based on Onsager’s reciprocity
relations coupled with a modified form of Terzaghi’s effective stress principle including an additional swelling stress component.
A notable consequence of the two-scale framework are the new closure problems derived for the macroscopic electro-chemo-mechanical
parameters. Such local representation bridge the gap between the macroscopic Thermodynamics of Irreversible Processes and
microscopic Electro-Hydrodynamics by establishing a direct correlation between the magnitude of the effective properties and
the electrical double layer potential, whose local distribution is governed by a microscale Poisson–Boltzmann equation. The
purpose of this paper is to validate computationally the two-scale model and to introduce new concepts inherent to the problem
considering a particular form of microstructure wherein the clay fabric is composed of parallel particles of face-to-face
contact. By discretizing the local Poisson–Boltzmann equation and solving numerically the closure problems, the constitutive
behavior of the diffusion coefficients of cations and anions, chemico-osmotic and electro-osmotic conductivities in Darcy’s
law, Onsager’s parameters, swelling pressure, electro-chemical compressibility, surface tension, primary/secondary electroviscous
effects and the reflection coefficient are computed for a range particle distances and sat concentrations. 相似文献
17.
Yu. M. Volchkov 《Journal of Applied Mechanics and Technical Physics》2000,41(5):945-949
Numerical techniques are proposed for determining the integral characteristics of penetration of a rod into an target. An
algorithm for solving two-dimensional elastoplastic problems is employed. To construct the solution, a one-dimensional finite-element
column is used (a two-dimensional domain is replaced by a one-dimensional domain).
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 205–210, September–October, 2000. 相似文献
18.
In this study, we use the method of homogenization to develop a filtration law in porous media that includes the effects of
inertia at finite Reynolds numbers. The result is much different than the empirically observed quadratic Forchheimer equation.
First, the correction to Darcy’s law is initially cubic (not quadratic) for isotropic media. This is consistent with several
other authors (Mei and Auriault, J Fluid Mech 222:647–663, 1991; Wodié and Levy, CR Acad Sci Paris t.312:157–161, 1991; Couland
et al. J Fluid Mech 190:393–407, 1988; Rojas and Koplik, Phys Rev 58:4776–4782, 1988) who have solved the Navier–Stokes equations
analytically and numerically. Second, the resulting filtration model is an infinite series polynomial in velocity, instead
of a single corrective term to Darcy’s law. Although the model is only valid up to the local Reynolds number, at the most,
of order 1, the findings are important from a fundamental perspective because it shows that the often-used quadratic Forchheimer
equation is not a universal law for laminar flow, but rather an empirical one that is useful in a limited range of velocities.
Moreover, as stated by Mei and Auriault (J Fluid Mech 222:647–663, 1991) and Barree and Conway (SPE Annual technical conference
and exhibition, 2004), even if the quadratic model were valid at moderate Reynolds numbers in the laminar flow regime, then
the permeability extrapolated on a Forchheimer plot would not be the intrinsic Darcy permeability. A major contribution of
this study is that the coefficients of the polynomial law can be derived a priori, by solving sequential Stokes problems.
In each case, the solution to the Stokes problem is used to calculate a coefficient in the polynomial, and the velocity field
is an input of the forcing function, F, to subsequent problems. While numerical solutions must be utilized to compute each coefficient in the polynomial, these
problems are much simpler and robust than solving the full Navier–Stokes equations. 相似文献
19.
The stress state of an elastic isotropic layer with a finite through crack is considered. At the boundary planes of the layer,
the normal component of the displacement vector and the tangential stress are zero. The crack surface is subject to normal
forces that vary arbitrarily. On the basis of three-dimensional elasticity theory, a method of solving the problem is proposed.
Numerical results characterizing the behavior of the normal-stress intensity coefficient are obtained.
Translated from Prikladnaya Mekhanika, Vol. 33, No. 1, pp. 43–51, January, 1997. 相似文献
20.
L. A. Tolokonnikov 《Journal of Applied Mechanics and Technical Physics》1999,40(5):936-941
The problem of reflection and refraction of a planar acoustic wave by an inhomogeneous elastic layer whose material possesses
general-type anisotropy is considered. The equations of motion of the elastic layer are reduced to a system of ordinary differential
equations. The boundary-value problem for this system is solved by two methods: by reduction to problems with initial conditions
and by the method of power series. Analytical expressions that describe acoustic fields outside the layer are obtained. Calculation
results of the transmission factor for transversely isotropic layers inhomogeneous in thickness are presented.
Tula State University, Tula 300600. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 179–184,
September–October, 1999. 相似文献