Effective characteristics of layered composites with allowance for structural changes

In moment linear theory of viscoelasticity for layered composites whose components undergo structural changes in the deformation process, we explicitly determine the effective characteristics. The corresponding boundary value problem is solved by the averaging method.     

Effective properties of a nonuniform beam under torsion

Effective characteristics are considered in the pure torsion problem for a nonuniform beam. The Saint-Venant semi-inverse method is used. A torsion stress function is introduced; this function can be found by solving a cross-sectional boundary value problem for a partial differential equation with variable coefficients. Two special boundary value problems are formulated for such an equation; after solving these problems, some effective characteristics are calculated in the case of torsion. It is shown that these effective characteristics satisfy the conditions of symmetry and positive definiteness. The case of an infinite in-plane layer of nonuniform thickness is discussed.     

Hydrodynamic stability of boundary layers with mass transfer

The stability of boundary layers involving mass transfer described by a two-parameter family of Fockner-Scane (F-S) solutions is analyzed. An effective method of solving the boundary problem is proposed for the F-S equation. A determinant method is proposed for solving the stability equation. The critical values of the stability characteristics are found over a wide range of gradient and mass-transfer parameters.     

Uniform motion of a plane punch on the boundary of an elastic half-plane

The dynamic contact problem of a plane punch motion on the boundary of an elastic half-plane is considered. The punch velocity is constant and does not exceed the Rayleigh wave velocity. The moving punch deforms the elastic half-plane penetrating into it so that the punch base remains parallel to itself at all times. The contact problem is reduced to solving a two-dimensional integral equation for the contact stresses whose two-dimensional kernel depends on the difference of arguments in each variable. A special approximation to the kernel is used to obtain effective solutions of the integral equation. All basic characteristics of the problem including the force of the punch elastic action on the elastic half-plane and the moment stabilizing the punch in the horizontal position in the process of penetration are obtained. A similar problem was considered in [1] and earlier in the “mode of steady-state motions” in [2, 3] and in other publications.     

A model of bubbles rising in a fluidized bed

A model for a single fully developed bubble moving in an unbounded fluidized bed is presented. The model allows bubble growth or shrinkage during the rise inside the bed, as well as dependence of the rise velocity upon specified bed parameters. Limiting cases of nearly spherical bubbles and of sufficiently large bubbles whose form resembles that of a spherical segment are considered in more detail. The form of bubbles rising in either fluidized beds or one-phase liquids, and its dependence on the effective “surface tension” acting on the bubble boundary are discussed.     

Forced axisymmetric vibrations of a thick circular rigidly fixed piezoceramic plate

A new closed-form solution of the axisymmetric nonstationary problem of elasticity is constructed for a circular thick piezoceramic plate whose outer cylindrical surface is rigidly fixed. The use of mixed boundary conditions for a curvilinear plane allows one to obtain sufficiently simple computational relations. The closed-form solution is constructed by the method of expansion in the vector eigenfunctions in the form of a structure algorithm of finite transformations. The obtained solutions are used to determine the natural vibration frequency, the stress-strain state of the considered element, and all characteristics of the induced electric field.     

Effective Flux Boundary Conditions for Upscaling Porous Media Equations

We introduce a new algorithm for setting pressure boundary conditions in subgrid simulations of porous media flow. The algorithm approximates the flux in the boundary cell as the flux through a homogeneous inclusion in a homogeneous background, where the permeability of the inclusion is given by the cell permeability and the permeability of the background is given by the ambient effective permeability. With this approximation, the flux in the boundary cell scales with the cell permeability when that permeability is small, and saturates at a constant value when that permeability is large. The flux conditions provide Neumann boundary conditions for the subgrid pressure. We call these boundary conditions effective flux boundary conditions (EFBCs). We give solutions for the flux through ellipsoidal inclusions in two and three dimensions, assuming symmetric tensor permeabilities whose principal axes align with the axes of the ellipse. We then discuss the considerations involved in applying these equations to scale up problems in geological porous media. The key complications are heterogeneity, fluctuations at all length scales, and boundary conditions at finite scales.     

Spin-down of the von Karman flow

The decay of the fluid flow due to a rotating disk is analysed when the disk is stopped suddenly. The interaction of the induced Rayleigh flow and the initial von Karman flow results in the establishment of a boundary layer whose characteristics are studied in detail. Solutions representing the initial and final stages of the spin-down are supplemented by the numerical solution of the governing equations.     

摩擦表面边界膜温度特性的神经网络模型

采用非线性变换单元组成的多层前馈神经网络建立了丝杆螺母磨擦副表面边界膜温度特性的磨损自补偿教学模型,该模型可用于准确地预测边界膜对摩擦学特性的影响。采用Ｌ－Ｍ规则进行神经网络学习训练使网络收敛快且误差小,所得网络输出结果与实验结果有较好的吻合性。该神经网络可为工程设计人员进行摩擦学设计提供有效的计算工具。     

Influence of polymer additives in a flow on the hydrodynamic characteristics of two-dimensional profiles

The problem of separationless flow of homogeneous dilute polymer solutions over two-dimensional profiles is considered. The complete flow is divided by the outer edge of the boundary layer and the wake into two regions: a region of irrotational flow and a region of viscous flow — the boundary layer and wake. The characteristics of the two regions are matched at their boundary. The problem is solved by successive approximation with allowance for the mutual influence of the two regions on each other. The influence of the irrotational region on the viscous region is taken into account through the distribution of the pressure on the boundary of the wake and the boundary layer. The influence of the viscous part of the flow is taken into account by the introduction of an associated vortex whose intensity is equal to the integral of the vorticity in the complete viscous region, and also by the introduction of additional velocities on the boundary of the wake and the boundary layer. These deform the streamlines in the irrotational part of the flow and ensure that they match the flow pattern in the real fluid. The results of the calculations of the hydrodynamic characteristics of a Zhukovskii profile are compared with experimental data. The influence of the introduction into the flow of polymer additives on the distributed and total characteristics of the flow at a number of Reynolds numbers is analyzed for the example of the modified profile NACA66.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 35–41, October–December, 1981.     

Determination of column-buckling criteria using vibratory data

A mathematical model is presented which describes a nondestructive testing procedure for determining buckling criteria for structures. The procedure requires identification of the structure's support boundary conditions using vibration data. Column-buckling experiments are presented which validate the model. The results illustrate the feasibility of using such models to predict the buckling load for structures whose support boundary conditions are not known in advance of service.     

Calculation of the initial segment and the stabilized flow segment in two-dimensional separation-free diffusers

The aerodynamic characteristics of a series of plane diffusere with straight walls are calculated for a broad range of divergence angles, Reynolds numbers, and the parameter which characterizes the initial flow nonuniformity.The fluid is assumed to be incompressible. The calculations are made for the case in which the boundary layer is fully turbulent, i. e., there is no laminar flow segment near the entrance section.The calculation of separation-free flow in diffuser channels is based on the use of boundary layer theory [1]. It has now become possible to carry out large-scale calculations for diffusers whose geometric and aerodynamic parameters vary over rather wide limits. This is the result both of the use of computers and of the fact that the modern approximate methods for calculating the turbulent boundary layer have been reduced to comparatively simple interpolation formulas [2].Usually, in the calculation of diffusers we examine only the initial flow segment, within the limits of which the boundary layers which form on the walls do not come together, i. e., there is a potential core. The laws governing diffuser flow in the absence of the potential core have been studied relatively little; the only known solutions are those of [3], which are valid at a very great distance from the entrance section.In this study we examine three characteristic flow zones: the initial segment, extending from the entrance section to the section at which the boundary layers come together; the stabilized-flow zone with closed boundary layers comprised of two characteristic segments-the transitional segment extending from the plane where the boundary layers join to the beginning of the radial flow segment; and, finally, the radial (self-similar) flow segment, characterized by constancy of all the dimensionless boundary layer characteristics along the flow. It is obvious that this division into characteristic zones is arbitrary: a consequence of the adopted flow idealization is a break in the curves expressing the aerodynamic characteristics as a function of the axial coordinate at the junction of the initial segment and the stabilized-flow segment. It is well known that a similar phenomenon occurs in the calculation of free turbulent jets based on arbitrary division of the jet into two segments-initial and primary segments [4].The computer calculation of the initial segments was performed by A. N. Smol'yaninova, and the stabilized-flow segments were calculated by I. N. Podol'nyi.     

On the asymptotic boundary conditions of an anisotropic beam via virtual work principle

In this research, an efficient and effective method is proposed to derive the boundary conditions of an anisotropic beam in the asymptotic sense. We first set up the constrained virtual work by introducing the Lagrange multiplier on the displacement prescribed boundary. The macroscopic beam and microscopic cross-section equations with the boundary conditions are simultaneously obtained by taking the asymptotic expansion on the displacement vector. In this way, the three-dimensional characteristics of the beam are asymptotically smeared into the macroscopic beam equations and the beam boundary conditions. The boundary conditions obtained are then compared to those from the decay analysis method. The beam bending slope boundary condition obtained in the frame work of variational principle is different from the well-known average condition. This new boundary condition is more accurate than the average one for a sandwich beam. This is further demonstrated and discussed via the examples of a cantilever beam loaded at the end.     

桁架板等效刚度分析

桁架材料的连续介质等效模型的研究已有相当基础,而工程中桁架材料往往以类板结构形式出现,其变形表现出明显的弯曲特征。将类板桁架材料采用弯曲板模型模拟,研究合理的方法确定等效板模型的刚度具有重要意义。本文在基于Kirchhoff假定的小挠度薄板弹性理论框架下,研究了类板桁架材料的等效弯曲薄板模型,提出了确定薄板模型等效刚度的基于Dirichlet位移边界条件的代表体元法,给出了确定各刚度系数所对应的代表体元的边界位移形式。具体计算了几种典型形式桁架板的等效刚度,并采用有限元离散模型和实验技术分析了桁架板在一定的边界约束和荷载作用下的响应,并与等效板模型的分析结果进行了对比。结果表明,在响应分析中,具有等效刚度的薄板模型可准确模拟类板桁架材料;连续介质板等效刚度计算的积分法不能给出准确的桁架板等效刚度,而基于Dirichlet位移边界条件的代表体元法获得的等效板的刚度具有很高的精度。     

Exterior statistics based boundary conditions for representative volume elements of elastic composites

Statistically equivalent representative volume elements or SERVEs are representations of the microstructure that are used for micromechanical simulations to generate homogenized material constitutive responses and properties (Swaminathan et al., 2006a, Ghosh, 2011). Typically, a SERVE is generated from the parent microstructure as a statistically equivalent region, whose size is determined from the requirements of convergence of macroscopic properties. Standard boundary conditions, such as affine transformation-based displacement boundary conditions (ATDBCs), uniform traction boundary conditions (UTBCs) or periodic boundary conditions (PBCs) are conventionally applied on the SERVE boundary for micromechanical simulations. However, when the microstructure is characterized by arbitrary, nonuniform distributions of heterogeneities, these simple boundary conditions do not represent the effect of regions exterior to the SERVE. Improper boundary conditions can result in significantly larger than optimal SERVE domains, needed for converged properties. In an attempt to overcome the limitations of the conventional boundary conditions on the SERVE, this paper explores the effect of boundary conditions that incorporate the statistics of the exterior region on the SERVE of elastic composites. Using Green's function based interaction kernels, coupled with statistical functions of the microstructural characteristics like one-point and two-point correlation functions, a novel exterior statistics-based boundary condition or ESBC is derived for the SERVE. The advantages of the ESBC are established by comparing with results of simulations using conventional boundary conditions. Results of the SERVE simulations subjected to ESBCs are also compared with those from other popular methods like statistical volume element (SVE) and weighted statistical volume element (WSVE). The proposed ESBCs offer significant advantages over other methods in the SERVE-based analysis of heterogeneous materials.     

Characteristics of a trailing flap flow with small separation

Detailed measurements of pressure and velocity characteristics are reported for the flow on and downstream of a trailing flap, whose 16 degree angle of incidence resulted in boundary layer separation, a small region of recirculating flow, and a curved downstream wake. Emphasis is placed on the region of recirculating flow and on the downstream wake. The characteristics were quantified by the use of pressure, hot-wire, and flying hot-wire probes. The flow characteristics are compared to those of a similar flow but with a larger region of recirculation reported by Thompson and Whitelaw (1985). The relative importance of the terms in the transport equations for mean momentum and turbulence energy are quantified and the implications of the results for viscous-inviscid interaction methods and turbulence modelling are discussed.     

辛体系下平面热黏弹性圣维南问题的解析解

借助积分变换,将辛体系引入平面热黏弹性问题,建立了基本问题的对偶方程,并将全 部圣维南问题归结为满足共轭辛正交关系的零本征值本征解问题. 同时,利用变量代换和本 征解展开等技术给出了一套求解边界条件问题的具体方法. 算例讨论了几种典型边界条件问 题,描述了热黏弹性材料的蠕变和松弛特征,体现了这种辛方法的有效性.     

Laminar boundary layer stability on membrane type deformable surfaces

In connection with the successful experiments of Kramer [l, 2] on models sheathed by flexible coverings, attempts have been made to explain theoretically the effect of boundary deformation on the position of the point of stability loss in the boundary layer. Korotkin [3] examined the stability of a plane laminar boundary layer on an elastic surface under the assumption of a linear connection between the pressure perturbation and the normal deformation of the surface. Benjamin [4] and Landahl [5] investigated the stability of the laminar boundary layer on a membrane type surface under the assumption that the physical characteristics of the surface depend on the perturbing flow wavelength. In the following we examine stability of Blasius flow on a membrane type surface whose physical characteristics are constant along the length.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, vol. 10, no. 6, pp. 52–56, November–December, 1969.     

Effective constitutive relations for inelastic composites

The first special boundary value problem in the mechanics of deformable solids is considered to derive the effective constitutive relations for a heterogeneous inelastic body. The problem is reduced to a number of auxiliary boundary value problems for functions dependent on the shape of the body and on the form of constitutive relations. In the case of a layer of nonuniform thickness, the problem of finding the effective constitutive relations is reduced to an operator equation whose solution is sought by an iterative method of successive approximations. An approximate analytical formula is proposed to find the effective constitutive relations for a laminated composite on the basis of known inelastic constitutive relations for its components. This approximate formula takes into account the character of structural anisotropy in a laminated composite and, in the elastic case, yields the exact values of the effective elastic modulus.