Multi-scale nonlinear modelling of sandwich structures using the Arlequin method

The paper presents a combination of the Arlequin Method (AM) and the Asymptotic Numerical Method (ANM) for studying nonlinear problems related to the mechanical behavior of sandwich composite structures. The Arlequin Method is a multi-scale method in which different models are crossed and glued to each other. The ANM is an alternative method which falls into the category of numerical perturbation techniques. By introducing the power series expansions into the equilibrium equation, the nonlinear problem is transformed into a sequence of linear problems and solved by the standard finite element method. Compared to other classical solvers (Newton–Raphson Method, Modified Newton–Raphson Method), ANM offers a considerable interest in the computation time and reliability. To validate this method, the AM is combined with the ANM to simulate the local damage of 2D–2D and 2D–2D-coupled sandwich beams. The simulation results are compared to a reference solution calculated from a 2D beam without any coupling. In case of the 2D–2D-coupled sandwich beam, the simulation shows a good agreement with the reference solution for both the local damage and the deformation at the loaded point. However, in case of 2D–1D-coupled sandwich beam, the simulation deviate from the reference solution due to the constant thickness of the 1D zig-zag element used to model the 1D zone of the sandwich beam.     

Solution of a mixed boundary-value problem by the Bubnov-Galerkin method

A method is proposed of constructing a sequence of coordinate functions with the aid of R-functions [1–3], for the solution of a mixed boundary-value problem. The approximate solution to the given problem is qualitatively the same as that obtained by the relaxation method [6].Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 23, No. 4, pp. 732–736, October, 1972.     

Analysis of Thin Isotropic Rectangular and Circular Plates with Multiquadrics

A computational method based on radial basis functions has been applied to the linear solution of thin plates. This meshless numerical method gives high flexibility in the analysis of irregular geometries, due to its insensivity to spatial dimension. The multiquadrics approach is used in this paper. The numerical solution is compared with Kirchhoff theory for plates.__________Translated from Problemy Prochnosti, No. 2, pp. 72 – 84, March – April, 2005.     

Heat transfer in the case of a semiinfinite body heated by thin parallel plates

An exact solution is obtained to the steady-state heat conduction problem with mixed boundary conditions. The solution is carried out by the author's own method shown in earlier publications [4–6].Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 2, pp. 331–338.     

In-vitro apatite formation on phosphorylated bamboo

Natural self-reinforced composite, bamboo, was surface modified by phosphorylation with urea–H3PO4 and NaOH–H3PO4 methods; then precalcification was performed by immersing samples in saturated Ca(OH)2 solution. After that, calcium phosphate can be formed on the surface of bamboo samples in calcification media: simulated body fluid (1.5 SBF) and accelerated calcification solution (ACS). Experimental results reveal that pre-calcification is an inevitable step for the formation of calcium phosphate. The calcium phosphate formed in 1.5 SBF was identified by thin-film X-ray diffraction as apatite which was not well crystallized. Compared with the urea–H3PO4 method, the NaOH–H3PO4 method has the advantages of quicker and continuous apatite formation and stronger adhesive between apatite and bamboo.     

Low-temperature liquid-phase epitaxy growth from Ga–As–Bi solution

Measurements of Ga–As–Bi liquidus composition at 600 °C for Ga–Bi–GaAs range are reported. High quality GaAs layers and Al_0.28Ga_0.72As/GaAs single quantum well (SQW) structures with different well thicknesses are grown from a mixed Ga + Bi solvent by low-temperature liquid-phase epitaxy method. They are characterized by the Hall effect and photoluminescence (PL) measurements. Significant changes in the layer electrical properties are observed with varying the Bi content in the solution. The layers grown from a mixed solution with 20–30% Bi content are n-type with carrier concentration of 10¹⁴ cm^− 3 and mobility of 40 000 cm²/Vs at 77 K, while p-type high resistivity layers are obtained from a solution with more than 70% Bi content. PL spectra of the SQW structures grown from Ga + 25% Bi solution at 2 K show that the roughness at the interface is less than two monolayers.     

Evaluation of small hydrogen sulfide concentrations in calibrating commercial gas analyzers for hydrogen sulfide

Conclusions Small concentrations (10^–5–10^–2 by volume) of hydrogen sulfide in gas mixtures can be analyzed by means of the photocolorimetric method based on the formation of molybdenum blue by the interaction of hydrogen sulfide with ammonium molybdate in an acidic medium.The optimum conditions for reducing molybdate by hydrogen chloride are provided by a content of 50 mg/ml of ammonium molybdate in the absorbing solution, a sulfuric solution with an acidity of 0.6 N, and a coloration ripening time of 15–20 min.     

Laminar Heat Transfer in a Rotating Disk under Conditions of Forced Air Impingement Cooling: Approximate Analytical Solution

The laminar heat transfer of a rotating disk under conditions of forced impingement cooling with a uniform velocity profile at infinity is investigated. The integral method is used to obtain an approximate analytical solution whose constants are found by adjustment to the exact numerical solution of the problem for different values of the Prandtl number Pr = 0.1–1 and the exponent in the power radial distribution of the disk temperature n* = –2–4. Boundaries of different modes of heat transfer are determined. The results of simulation are in good agreement with experiments in the stagnation region for impinging jets flowing coaxially against the disk.     

Axially symmetric stefan problem with a boundary condition of the third kind

The solution of an axially symmetric single-phase Stefan problem with a boundary condition of the third kind is reduced to the solution of a nonlinear integrodifferential equation, the latter solution being obtained with the aid of the method of successive approximations.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 23, No. 6, pp. 1113–1117, December, 1972.     

One steady-state heat-conduction problem for a polygonal region with mixed boundary conditions

An exact solution is given for one heat-conduction problem involving a polygonal region with mixed boundary conditions. The solution method is based on development of a method presented by the author in previous publications.Translated from Inzhenerno-Fizi-cheskii Zhurnal, Vol. 17, No. 2, pp. 306–312, August, 1969.     

Determination of the stress-strain state of a cooling plane region with account for a polymorphic transformation

A simplified method for finite-element calculation of the stressed state of a plane region undergoing a polymorphic transformation is described. An exact solution is obtained for a circular region and the exact solution is compared with the numerical one. The effect of an austenite-ferrite transformation on the behavior of the stressed state in the circular region is analyzed.Izhevsk Mechanical Works, Izhevsk, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 1, pp. 123–127, January–February, 1995.     

Iteration Algorithms for Solving Boundary-Value Problems of the Theory of Small Elastic-Plastic Strains on the Basis of the Mixed Finite Element Method

A mixed projection-mesh scheme has been formulated for the solution of nonlinear boundary-value problems of the theory of small elastic-plastic strains in displacements, strains, and stresses. Iteration algorithms of the solution of nonlinear equations of the mixed method have been considered. Numerical results of the solution of two model problems are presented. The data obtained on the basis of the classical and mixed finite element methods are compared.__________Translated from Problemy Prochnosti, No. 3, pp. 111 – 127, May – June, 2005.     

Heat and mass transfer in a binary laminar boundary layer with free convection on a vertical porous surface

An approximate analytical solution of heat and mass transfer in a binary laminar boundary layer with free convection on a vertical surface is presented. The numerical solution is compared with an approximate analytical solution obtained by another method.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 21, No. 1, pp. 19–28, July, 1971.     

Solution for the 3D Temperature Problem of the Thermoelasticity Theory in Displacements

A new method of solution for the 3D problem of the thermoelasticity theory in displacements is proposed. The resultant general solution can be used in solving thermoelastic problems both for half-space and an elastic layer. The second boundary-value problem for half-space is detailed and numerical calculation is given.__________Translated from Problemy Prochnosti, No. 3, pp. 86 – 95, May – June, 2005.     

Determining the thermal stresses in a hollow viscoelastic sphere

For a viscoelastic sphere with spherical cavity, solution of the quasistatic problem of the stresses produced by a nonstationary temperature field reduces to solution of an integral-differential equation whose right side depends on an unknown function of the time. A numerical solution method is described.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 17, No. 2, pp. 300–305, August, 1969.     

Method of determining bending stress intensity coefficients for cracked ferroconcrete components

Summary A method is proposed for calculating the stress intensity coefficient in a ferroconcrete element containing a crack in bending with reinforcement by rods. A three-dimensional solution has been obtained. The attachment of the reinforcement to the concrete is incorporated.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, No. 3, pp. 98–104, May–June, 1992.     

Conservative Eulerian method for numerical investigation of the hydrodynamics of liquids with a free surface

An effective numerical method is suggested for investigation of the hydrodynamics of liquids with a free surface. The method is a conservative Eulerian method that is useful for investigation of processes with turbulent behavior of the surface of the liquid that are accompanied by generation of waves, splash, spatter, etc. In the present method, apart from hydrodynamic equations, a transfer equation is used to describe transfer of the liquid phase. A method of numerical solution free from grid diffusion is suggested for this equation. It is proved that the conservative Eulerian method is adequate quantitatively for modeling the motions of a liquid with a slight deformation on its surface and adequate qualitatively for complicated motions.Dneprodzerzhinsk Industrial Institute, Dneprodzerzhinsk, Ukraine. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 67, Nos. 3–4, pp. 228–234, September–October, 1994.     

Solutions of partial differential equations with random Dirichlet boundary conditions by multiquadric collocation method

Problems described by deterministic partial differential equations with random Dirichlet boundary conditions are considered. Formulation of the solution to such a problem by the global collocation method using multiquadrics is presented. The quality of the solution to a stochastic problem depends on both its expected value and its variance. It is proposed that the shape parameter of multiquadrics should be chosen to optimize both the accuracy and the variance of the solution. Test problems described by the Poisson, the Helmholtz, and the diffusion–convection equations with random Dirichlet boundary conditions are solved by the multiquadric collocation method. It is found that there is a trade-off between solution accuracy and solution variance for each problem.     

Regular heat transfer of external walls

A method of isolating the regular solution from the numerical solution is proposed. The accuracy of solution according to explicit and implicit schemes is considered, and the applicability conditions are determined.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 6, pp. 977–981, June, 1982.     

Dynamic analysis of dam–reservoir-foundation interaction in time domain

In this paper, a time domain dynamic analysis of the dam–reservoir-foundation interaction problem is developed by coupling the dual reciprocity boundary element method (DRBEM) for the infinite reservoir and foundation domain and the finite element method for the finite dam domain. An efficient coupling procedure is formulated by using the substructuring method. Sharans boundary condition at the far end of the infinite fluid domain is implemented. To verify the proposed scheme, numerical examples are carried out and compared with available exact solutions and finite–finite element coupling results for the problem of the dam–reservoir interaction. Finally, a complete dam–reservoir-foundation interaction problem is solved and its solution is compared with previously published results.The author is thankful to the anonymous reviewer of this paper for his suggestions and comments, which improved considerably the present paper.