On the constraint and scaling methods to derive the equations of linearly elastic rods

The theory of linearly elastic rods may be obtained from three-dimensional elasticity either by the method of internal constraints or by the scaling method. Both methods have been applied to obtain linear plate and shell equations ([1], [2]–[5]); the relationships between the two methods are discussed in [6]. For rods, a version of the constraint method has been developed in [7], whereas a scaling method has been presented in [12]. In this paper a direct comparison is made between the mechanical basis and analytical results of the constraint and the scaling methods, and it is shown how the scaling method yields the same Kirchhoff hypothesis that forms the starting point of the constraint method.

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Sommario La teoria delle travi elastiche lineari puó essere ottenuta a partire dalla teoria tridimensionale dell'elasticitá tanto con il metodo dei vincoli interni che con il metodo di riscalamento. Entrambi i metodi sono giá stati utilizzati per ottenere le equazioni delle piastre e dei gusci lineari ([1], [2]–[5]); in quel contesto, le relazioni tra i due metodi sono state discusse in [6]. Una versione del metodo dei vincoli appropriata al caso delle travi é stata sviluppata in [7], mentre i metodi di riscalamento per le travi si trovano esposti in [12]. Scopo di questo lavoro é compiere un paragone diretto tra i fondamenti meccanici e le risultanze analitiche, rispettivamente, del metodo dei vincoli e di quello di riscalamento, mostrando come il metodo di riscalamento imponga di accogliere proprio quelle ipotesi all aKirchhoff sulle quali si basa il metodo dei vincoli interni.

     

刚－弹惯性耦合下变形体动力学响应分析

本文以绕定轴转动弹性梁为对象对其在刚－弹惯性耦合下的动力学响应进行数值分析，并与传统的准静态分析方法，线弹性动力学分析方法在理论与数值上进行比较。对所研究的对象用Ｊｏｕｒｄａｉｎ变分原理建立动力学方程，用一致质量有限单元法对弹性梁进行离散；用正则振动模态降低弹性自由度数目。通过数值计算比较说明传统分析方法的局限性。     

The thermostressed state of electrically conductive bodies subjected to an external electromagnetic field

A technique is proposed for mathematical and numerical modeling of thermomechanical processes in electrically conductive bodies subjected to an external electromagnetic field. The initial relations for the determination of the electromagnetic field are the Maxwell equations. The stress and strain states of the body are described using the equations of nonisothermal elastoplasticity. The model takes into account the coupling of the electromagnetic and thermal fields. All physical and mechanical parameters of the material depend on temperature. The process of high-temperature induction treatment of a ferromagnetic cylinder is considered as an example __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 13–25, December 2005.     

Influence of a thin isotropic coating on the edge effect zone in isotropic and transversely isotropic materials

The effect of a thin isotropic coating on the edge effect zone in a representative element of a coated material is examined. Isotropic and transversely isotropic materials are considered. The transversely isotropic material has the elastic properties of unidirectional glass-fiber-reinforced plastic. The decay of the edge effect in the directions perpendicular to the coating plane and to the plane of isotropy is studied. A boundary-value problem of elasticity for piecewise-homogeneouse orthotropic bodies and a quantitative edge effect decay criterion for normal stresses are used as a design model. The problem is solved using the finite-difference method and base schemes. The results of evaluation of the edge effect zone in homogeneous and inhomogeneous materials are presented. It is shown that the presence of a thin isotropic coating blocks the edge effect, that is, decreases the edge effect zone in both isotropic and transversely isotropic materials __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 61–67, December 2007.     

Force Action of a Body with a Permeable Boundary on a Wall in a Fluid

The ideal fluid flow due to fluid penetration through the boundary of an infinitely long solid cylinder in contact with a solid wall is determined. A formula is derived according to which the force exerted by a finite-length part of the cylinder on the wall is directed into the wall and can thus have an arbitrarily large absolute value. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 82–84, January–February, 2006.     

Semianalytic Finite-Element Method in Problems of Nonlinear Continuum Mechanics

A technique for solving problems of nonlinear continuum mechanics associated with contact interaction, plastic distortion, and continuous and discrete fracture of spatial bodies is developed based on the semianalytic finite-element method generalized to noncanonical bodies. Solutions are obtained to new applied problems in various branches of technology. Compared with the traditional FEM, the technique is highly efficient—the amount of computation needed to solve spatial problems reduces by several orders of magnitude     

Numerical modeling of the effect of geometric asymmetry on the damping aerodynamic characteristics of supersonic sectional flight vehicles

A method for calculating the steady inviscid supersonic flow past equivalent bodies is applied to the analysis of the time-dependent aerodynamic characteristics of sectional flight vehicles with an asymmetric rear stabilizer. The stabilizer asymmetry can be caused by either its deflection or a change in its shape due to heat-shield coating removal, boundary layer displacement thickness, developed separation flow zones, local deformations, or other distortions in the baseline form. Amathematical apparatus for modeling asymmetric sectional configurations by means of ruled surfaces with arbitrary contours of the reference cross-sections is developed. The uniform perfect-gas M_∞ = 6 flow past sectional vehicles performing plane oscillations about the zero angle of attack is calculated (the adiabatic exponent γ = 1.4). The calculated results demonstrate the effect of various asymmetries in the body shape on the aerodynamic coefficients.     

Study of the damping characteristics of sectional flight vehicles of different length

The dependence of the damping characteristics of axisymmetric tri-sectional flight vehicles executing plane oscillations about the zero angle of attack on their geometric parameters is investigated on the supersonic range of uniform oncoming air flow Mach numbers. Systematic data are obtained using the least laborious approach, namely, by calculating the steady-state inviscid flow past equivalent bodies determined from the principle of the local similarity of force interaction. Ranges of the vehicle design parameters on which the dependence of the damping moment coefficient in pitch on the length of the conical or cylindrical-conical stabilizer of the vehicle is nonmonotonic are found. Typical viscosity effects on the characteristics under study are estimated using a method based on the assumptions of the linear theory for finite-thickness bodies. It is established that the damping coefficient increases monotonically with decreasing Reynolds number; moreover, even transition to oscillation antidumping regimes is possible when the sign of the damping coefficient changes.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 153–162. Original Russian Text Copyright © 2004 by Antonets and Shmanenkov.     

Systematic closed form modeling of hybrid parameter multiple body systems

Presented in this paper is a systematic approach to modeling non-holonomic hybrid parameter multiple body systems. The continuum bodies are represented with the postulates usually associated to the non-linear theories, the Timoshenko (like) beam theories, the higher order plate and shell theories, and the rational theories (e.g. rods) with intrinsic rotary inertia properties.The methodology is an extension of previous work. It is founded in variational principles, but uses vector algebra to eliminate tedium. The variational nature of the methodology allows rigorous equation formulation providing not only the complete non-linear hybrid differential equations, but also the boundary conditions. The methodology is formulated satisfying general non-holonomic constraints; it produces a minimal realization. The spatial dimensions of the continuua are not restricted and the inter-body connections are completely general.To demonstrate the application of the technique, a two-link elastic pendulum or manipulator is modeled. The algorithmic modeling steps are demonstrated. Numerical simulations are presented.