Journal of Applied Mechanics and Technical Physics最新文献

The feasibility of joining of the 6061 aluminum alloy to double-layer oxygen-free copper (TU1) by laser welding technology is reported. The weld formation and microstructure of the Cu–Cu–Al welding joint for various technological parameters are analyzed. The assessment of experimental results is based on macro- and microstructure observations of the weld using the Axio Observer D1M and Gemini SEM 300 scanning electron microscopes. The width and depth of the molten pool and the mechanical properties of the Cu–Cu–Al welding joint are tested by the Eagle-MD semiautomatic image measuring instrument and the YH-9002 computerized tension and compression machine. Among the nine tested samples, the most favorable weld parameters values are obtained with a laser power at 1600 W and a welding speed of 90 mm/s. The aluminum side area has a richer metallographic structure than the copper side area after welding.

Nonlinear vibrations, buckling, and aeroelasticity of a thin nonlinear orthotropic composite plate have been analyzed. The types of symmetric and antisymmetric sheet layering, the number of layers, the fiber angle ranging from 0 to 90°, the effect of constant and variable thermal loads, the temperature dependence of the specific heat coefficient and the elastic modulus of the material, along with the local geometric defects have been investigated. Using Galerkin’s weighted residual theory, partial differential equations have been transformed into nonlinear ordinary differential equations, which are solved by the Runge–Kutta method.

Abstract

The stress-strain elastic field in a square array of N non-overlapping circular inclusions is described by approximate analytical formulas. In particular, soft inclusions are studied by an asymptotic analysis. The case with N = 1 yields a regular square array of disks of radius r embedded in an elastic matrix. The computations of Natanzon and Filshtinsky are based on an infinite system of linear algebraic equations solved by the truncation method. The infinite system determines the Taylor series coefficients of the Kolosov–Muskhelishvili complex potentials. A method of functional equations is used to write the series coefficients in symbolic form up to terms of the order of O(r^2s) at a fixed value of s. Approximate analytical formulas for local elastic fields are derived.

The main types of strain of an adhesive cross-reinforced with composite fibers is analyzed using a solution to the cell problem of the elasticity theory. It is shown that all previously predicted possible types of local strain of a fiber composite adhesive are revealed in numerical solutions to the cell problem of the homogenization theory. The local stress-strain state of the adhesive significantly depends on the cross-sectional shape of the fibers. The stress-strain state in the case of square fibers can be calculated either using explicit formulas, and the stress-strain state in the case of fibers of other shapes can be estimated only using a computer.

The process of buckling of the von Mises truss in the case of material instability, i.e., with allowance for material non-ellipticity, is considered. Force-displacement diagrams are constructed. Results that allow one to study buckling of thin-walled structures (arches or shells) made of materials for which the loss of ellipticity of equilibrium equations is possible are obtained.

The classical time-harmonic plane strain problem for a fluid-loaded cylindrical elastic shell is revisited. The results of the low-frequency asymptotic analysis, including explicit formulae for eigenfrequencies, are presented. A refined version of the semi-membrane shell theory is formulated. It is shown that the shell inertia does not affect significantly the lowest eigenfrequencies. It is also demonstrated that the ring stress component has a parabolic linear variation.

Various crossovers of the effective permeability of certain analytically treatable models of the Darcy flow in porous media are studied. They account for the critical behavior as well for the regimes with low concentrations of obstacles. Transverse permeability of spatially periodic arrays of impenetrable cylinders is found in an analytical form and accounts for various asymptotic regimes. Longitudinal permeability for a square array of cylinders is found as well. Transverse flows past hexagonal and square arrays of cylinders are also considered based on expansions for small concentrations and lubrication approximation for high concentrations of cylinders. Threedimensional periodic arrays of spherical obstacles are considered as well. Formulas for the drag force exerted by various lattices of obstacles are derived from low-concentration expansions. The Stokes flow through two-dimensional and three-dimensional channels enclosed by two wavy walls is studied by means of expansions for small waviness amplitudes. Compact formulas for permeability are derived in the form of factor approximants for arbitrary values of waviness. Various power laws are accounted for in the regime of large waviness parameters, as well as the existing expansions at small amplitudes.

Abstract

It has been found that heat release in a homogenized composite model is described by the Joule–Lenz law for the averaged current strength and voltage. It has been shown that the local electric field strength and the local electric current in a real composite are usually significantly different from those in the homogenized model despite the fact that the electric field potentials in the homogenized model and the real composite are close.

Abstract

This paper presents a method of transforming from the three-dimensional piezoelastic problem for a composite material to the one-dimensional problem for a piezoelastic beam. This is done using the asymptotic homogenization technique based on the separation of fast and slow variables in the solution. A special feature of the problem is the presence of two small parameters, one of which characterizes the microstructure of the composite material, and the other defines the cross-sectional size. Homogenized relations describing the piezoelastic beam and fast correctors were obtained. Their joint use makes it possible to correctly describe the total stress-strain state of the original three-dimensional body. The proposed method is suitable for solving the three-dimensional problem of deformation of an extended body with an arbitrary periodic structure as well as for solving new problems (e.g., the torsion problem) that have no analogues in the theory of piezoelastic plates.

Abstract

A small-size elastic isotropic beam-strip loaded by variable body and surface forces is considered. On the front surfaces, surface shear stresses and inertia are taken into account within the framework of the Gurtin–Murdoch surface elasticity theory. Asymptotically correct equations describing the long-wavelength bending deformation of micro- and nano-beams taking into account shears and surface effects are derived by asymptotic integration of the two-dimensional elasticity equations over the strip thickness. The influence of surface stresses and inertia on the lower spectrum of natural vibrations of metal micro- and nano-beams is studied. It is shown that surface inertia has the same effect on the frequency spectrum of natural flexural vibrations as surface stresses.