Representation of the solution of refined bending theory for isotropic plates

A solution of the bending problem for isotropic plates in a refined statement based on the system of six-order differential equations is proposed. A procedure for determining the general solutions of the corresponding biharmonic and metaharmonic equations is suggested. A method for satisfying the boundary conditions is given. The results of numerical studies of the stress state of an infinite plate with an elliptic cavity are given.     

Establishing foundations of the mechanics of nanocomposites (Review)

A general idea of the mechanics of nanocomposites that allows formulating a system of approaches and methods of analysis in this area is given. The place of mechanics in materials research and the structural levels that divide mechanics into macromechanics, mesomechanics, micromechanics, and nanomechanics are discussed. A brief historical sketch of the nanomaterial technology is presented. Examples of different nanotechnologies and nanomaterials are given. Typical nanomaterials and their properties are described. Matrices and reinforcements of nanocomposite materials as well as their properties are considered separately. A classification of nanocomposites is proposed. Special attention is given to modeling in the structural mechanics of nanocomposites, the principles of continualization and homogenization, edge and near-surface effects, validity limits of the continuum approach, and two-sided estimates. A discussion is given of two basic models within the framework of the basic approach as a set of concepts, models, and problem statements and of the development of methods adequately describing mechanical phenomena in nanocomposites. The presented material is mainly taken from the book A. N. Guz, J. J. Rushchitsky, and I. A. Guz, Introduction to the Mechanics of Nanocomposites [in Russian], S. P. Timoshenko Inst. Mech., Kyiv (2010)     

Solution of the variational problem of shaping a nozzle to achieve a uniform supersonic flow

A solution is given to the problem of constructing a supersonic flat unsymmetrical nozzle achieving a given uniform flow at the outlet with a minimal length of one of the contours and a given length (or ordinate of the end point) of the other contour.     

On the representation of the solutions of the equilibrium equations of a piezoelectric transversally-isotropic spherical shell

A method is proposed for constructing equilibrium equations for thickness-polarized transversally isotropic piezoceramic shells. The method is based on Fourier expanding the required functions in Legendre polynomials. The appropriate system of differential equations is formed for the expansion coefficients as functions of two independent variables. The equilibrium equations are given in particular for transversally isotropic spherical shells. A method is given for constructing the general solution in the first approximation. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 7, pp. 59–68, July, 1999.     

A lower bound for the invariants of the configuration tensor for some well-known differential models

A method is given to determine lower bounds for the invariants of a configuration tensor in 3D flows. For some well-known differential models these lower bounds are given. Except for the Giesekus and the FENE-P model, the lower bounds are the values in equilibrium.     

Simulation of the stress-strain state and evaluation of the blade loading capacity in the case of impermeability testing of engine housings

A numerical methodology for determining the stress-strain state and the blade loading capacity is proposed to study the blade failure on the basis of stress redistribution in a given blade cross section due to an additional thermal loading and on the basis of the failure enforcement action on this cross section at a given frequency of rotation. The stress-strain state of the blade is numerically studied when the blade cross section is weakened. The proposed methodology is used to test the impermeability of a gas turbine engine housing using an acceleration stand.     

Not fully established flow around bodies under the conditions of the law of localness

A solution is given to the problem of determining the aerodynamic characteristics of bodies under not fully established conditions of flight, where the law of localness can be used (the modified Newton theory, free molecular flow of the gas, flow of a rarefied gas under intermediate conditions, etc.) It is shown that it is relatively easy to calculate the coefficients of the rotational derivatives of the first order. Numerical examples of the calculation are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 168–173, May–June, 1977.In conclusion, the author thanks A. I. Bunimovich for his interest in the work and M. A. Vorotyntsev for his useful observations.     

Minimization of the Wing Airfoil Drag Coefficient Using the Optimal Control Method

The problem of designing a wing airfoil starting from the surface velocity (or pressure) distribution, given in multi-parameter form, is considered. In the diffuser region, the velocity decrease law is determined from the conditions of minimum drag and separationless flow for a given Reynolds number. The case of boundary layer suction for the purpose of improving the aerodynamic characteristics of the airfoil is studied. A solution is obtained using optimal control theory.     

Determination of the size of the representative volume element for random composites: statistical and numerical approach

The representative volume element (RVE) plays a central role in the mechanics and physics of random heterogeneous materials with a view to predicting their effective properties. A quantitative definition of its size is proposed in this work. A RVE size can be associated with a given precision of the estimation of the wanted overall property and the number of realizations of a given volume V of microstructure that one is able to consider. It is shown to depend on the investigated morphological or physical property, the contrast in the properties of the constituents, and their volume fractions. The methodology is applied to a specific random microstructure, namely a two-phase three-dimensional Voronoı̈ mosaic. Finite element simulations of volumes of different sizes are performed in the case of linear elasticity and thermal conductivity. The volumes are subjected to homogeneous strain, stress or periodic boundary conditions. The effective properties can be determined for large volumes and a small number of realizations. Conversely, smaller volumes can be used providing that a sufficient number of realizations are considered. A bias in the estimation of the effective properties is observed for too small volumes for all types of boundary conditions. The variance of computed apparent properties for each volume size is used to define the precision of the estimation. The key-notion of integral range is introduced to relate this error estimation and the definition of the RVE size. For given wanted precision and number of realizations, one is able to provide a minimal volume size for the computation of effective properties. The results can also be used to predict the minimal number of realizations that must be considered for a given volume size in order to estimate the effective property for a given precision. The RVE sizes found for elastic and thermal properties, but also for a geometrical property like volume fraction, are compared.     

On a generalized taylor theorem: A rational proof of the validity of the homotopy analysis method

IntroductionIn 1 7thcenturyIsaacNewton[1]gavesuchabinomialexpressionforfractionalandnegativeexponents(1 +t) α,i.e.,(1 +t) α =1 + +∞k=1α(α-1 ) (α-2 )… (α -k+ 1 )k !tk　　 (α≠ 0 ,1 ,2 ,… ) ,(1 )whoseconvergenceradiusisone.Furthermore ,theclassicalTaylorseries (seeRef.[2 ] )limm→+∞ mk=0f(k) (z0 )k !(z-z0 ) k (2 )ofacomplexfunctionf(z)atz=z0 isvalidmostlyinarestrictedconvergenceregion｜z-z0 ｜相似文献   

摩擦学白层的研究现状

综述了摩擦学领域的白层研究现旨出了当层（特别是微动白层）研究中存在的分歧和急论,分析归纳不同摩擦磨损条件下白层的形成条件和基本特征,重点讨论了白层的形成机制,提出了今后研究的方向。     

On the derivation for the gradients of the principal invariants

In this notes, it is shown that the method carried out by Truesdell and Noll [1] for the gradients of the principal invariants is available to be used for arbitrary second-order A. Finally, some trace identities for the derivatives of invariants are given.     

An optimum implicit recurrence formula for the solution of the equation of the vibrating beam

Summary A method is given for generating a high order difference replacement of the equation governing the transverse vibrations of a beam. This difference replacement involves a parameter which can be chosen either to increase the range of stability of the formula or to increase its accuracy.     

On the completeness of Lamb modes

A completeness result for Lamb modes in homogeneous waveguides is proved. The problem is formulated as a linear eigenvalue problem in an appropriate Hilbert space of functions. Orthogonality and biorthogonality relations are given. A detailed spectral analysis which is necessary for the application of a general completeness theorem is presented.     

The determination of the components of the strain tensor in holographic interferometry

The general problem of obtaining the derivatives of the displacements in holographic interferometry is analyzed. Expressions for the most general case are derived and a particular solution is suggested. A data-reduction method is proposed. Application examples are given.     

Method of Optimization of Blade Shapes in Aerodynamic Design of the Fan Cascade

A method is developed for calculating the geometric parameters of the cascade of an axial fan with a given performance. The method is based on minimization of a certain functional and using the solution of an inverse problem of the flow around the cascade within the framework of the hypothesis of cylindrical cross sections. The functional is minimized by an iterative method of linearization. Examples of calculations are given.     

Effect of Non-Stoichiometry and Difference between the Tensile and Compressive Moduli of Elasticity of Perovskite on the Diffusion Creep of a Thick-Walled Perovskite Cylinder

International Applied Mechanics - A physical model for describing the diffusion creep in perovskite-type material given oxygen non-stoichiometry and tensile–compressive asymmetry is...     

Geometrical Representation of the Motion of a Body Through a Medium

The paper presents a complete qualitative analysis of the model plane-parallel motion of a body (plate) through a resisting medium with jet or detached flow. A simplified system is analyzed on the phase plane. A geometrical interpretation is given to the motion of the plate     

柔性结构振动的有限目标控制

根据实际问题的背景 ,分别提出了局部状态保持和有限目标控制两个问题。首先讨论了局部状态保持问题 ,给出了一个局部状态能局部状态保持的充分必要条件 ,并说明了如何选择控制力 ,即找到一个反馈增益矩阵 ,使该局部状态满足局部关态保持的条件 ,然后提出了有限目标控制的思想 ,进行了初步探讨 ,针对一特殊情况给出一个设计方法