Finite deformations of a hyperelastic, compressible and fibre reinforced tube

Finite torsion and axial stretch of a long, hyperelastic, compressible and circular tube is studied for the design of a prototype of small diameter vascular prosthesis. The analysis is carried out in the context of the finite elasticity theory by using a class of Ogden strain energy function augmented with unidirectional reinforcing that is characterized by a single additional constitutive parameter for strength of reinforcement. The highly non-linear differential equations with variable coefficients governing the problem are solved numerically using a Runge–Kutta method. For different prestresses supported by the tube, the effects of the combined deformation on the stress distributions are presented.     

圆中空夹层钢管混凝土柱扭转实验研究

以名义含钢率、外钢管强度和空心率为主要变化参数,设计了6根圆中空夹层钢管混凝土和1根双层空钢管试件,对其进行了扭转试验研究。试验结果表明:在加载过程中,钢管和混凝土变形协调,共同工作;试件表现出很好的塑性性能;试件名义含钢率和外钢管强度越大,试件抗扭承载力也越大;空心率越大,试件抗扭承载力也越大;圆中空夹层钢管混凝土比双层空钢管抗扭承载力有明显的提高。同时用有限元方法对试件扭矩-转角全过程曲线进行计算,计算结果与试验结果吻合良好。     

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介绍了求解复杂截面闭口薄壁杆件扭转问题的网络理论解法,以普朗特应力函 数解法为基础,通过与电路问题比拟,借鉴了电路理论中的网络理论解法. 本文方法对解决复 杂截面闭口薄壁杆件扭转的工程问题有一定的应用价值. 在教学上,可以起到拓宽学生思路 的作用.     

Stress–Strain Analysis of Smooth and Ribbed Shells under Local Loads

Static problems for smooth and discretely reinforced cylindrical shells under local loads and complex boundary conditions are solved. The stress–strain states of the casing and ribs are determined by the technical theory of shells and the Kirchhoff–Clebsch theory of rods, respectively. The reinforcing elements are arranged eccentrically. They are of equal or different stiffness, which is also variable along the length. The problems are solved using the finite-difference method. Theoretical results obtained from a refined mesh are compared with experimental data     

Nonstationary motion of a viscous fluid in a long tube

A number of problems are solved for the nonstationary motion of a viscous compressible fluid in a tube with elastic walls. It is assumed that the tube is semi-infinite, its axis horizontal, and that at one of its ends the flow rate of the fluid can change. The solution of each of the problems is reduced to the finding a generalized solution to a nonlinear system of partial differential equations for two functions — the mean values of the velocity and pressure in the tube section — with certain constant or null initial conditions and with a boundary condition specifying the time dependence of some function of the velocity and the pressure at the end of the tube. It is noted that the same problems can be solved by successive approximation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 35–43, November–December, 1980.     

Semi-inverse solution for Saint-Venant's problem in the theory of porous elastic materials

The purpose of this research is to study the Saint-Venant's problem for right cylinders with general cross-section made of inhomogeneous anisotropic elastic materials with voids. We reformulate the quasi-static equilibrium equations with the axial variable playing the role of a parameter. Two classes of semi-inverse solutions to Saint-Venant's problem are described in terms of five generalized plane strain problems. These classes are used in order to obtain a semi-inverse solution for the relaxed Saint-Venant's problem. An application of this results in the study of extension, bending, torsion and flexure of right circular cylinders in the case of isotropic materials is presented.     

A calculation method for blood flow velocity distribution in smallep elocd vessels

The calculative method presented in this paper is based on an improvement of boundary conditions for a micro-continuum fluid model with blood flow assuming that the blood cell velocity at blood vessel wall is unequal to zero. As for steady state flood flow equation (flow in vitre—a rigid circular tube) presented by Eringen, the magnitude of the blood cell gyroscopic velocity at blood vessel wall and the slope of the blood cell gyroscopic velocity distribution curve at the axis of the blood vessel are assumed. From the above mentioned assumptions the calculating method of velocity distribution curve in blood vessel is derived. The curve calculated by this method is compared with the test curve measured by Bugliarello and Hayden. The results obtained by Turk, Sylvester and Ariman as well as with this method are compared with each other, too.     

Nonlinear two-dimensional static problems for thin shells with reinforced curvilinear holes

Results on stress concentration in thin shells with curvilinear holes subject to plastic deformation and finite deflections are reviewed. The holes (circular, elliptical) are reinforced with thin-walled elements (rings, rods) of different stiffness. A numerical method of solving doubly nonlinear problems of statics for shells of complex geometry is outlined. The stress distribution near curvilinear holes in spherical, cylindrical, and conical shells under statical loading is studied. The numerical results are analyzed     

Asymptotic analysis of perforated plates and membranes. Part 1: Static problems for small holes

Static problems for the elastic plates and rods periodically perforated by small holes of different shapes are solved using the asymptotic approach based on the combination of the asymptotic technique and the multi-scale homogenization method. Using the asymptotic homogenization method the original boundary-value problem is reduced to the combination of two types of problems. First one is a recurrent system of unit cell problems with the conditions of periodic continuation. And the second problem is a homogenized boundary-value problem for the entire domain, characterized by the constant effective coefficients obtained from the solution of the unit cell problems. The combination of the perturbation method and the technique of successive approximations is applied for the solution of the unit cell problems. Taking into the account small size of holes the method of perturbation of the shape of the boundary and the Schwarz alternating method are used. The problems of torsion of a rod with perforated cross-section; deflection of the perforated membrane loaded by a normal load; and bending of perforated plates with circular and square holes are considered consecutively. The error of the applied asymptotic techniques is estimated and the high accuracy of the obtained solutions is demonstrated.     

On the Torsion of a Class of Nonlinear Fiber Composite Cylinders

This paper presents an analysis of the torsion of a solid or annular circular cylinder consisting of nonlinear material in the form of an elastic matrix with embedded unidirectional elastic fibers parallel to the cylinder axis. The specific class of composite considered is one for which nonlinear fiber-matrix interface slip is captured by uniform cohesive zones of vanishing thickness. Previous work on the effective antiplane shear response of this material leads to a stress–strain relation depending on the interface slip together with an integral equation governing its evolution. Here, we obtain an approximate single mode solution to the integral equation and utilize it to solve the torsion problem. Equations governing the radial distributions of shear stress and interface slip are obtained and formulae for torque–twist rate are presented. The existence of singular surfaces, i.e., surfaces across which the slip and the shear stress experience jump discontinuities are analyzed in detail. Specific results are presented for an interface force law that allows for interface failure in shear.     

Numerical Solution of Static Problems for Multitiered Structures

A linear stress—strain analysis is made of a structure consisting of two discretely reinforced cylindrical shells and an intermediate conical shell with large openings, which is simulated by a three-dimensional framework. This three-tier system is under longitudinal and local flexural loads. The calculations are made by the finite-difference method using modified equations of the mixed method for shells and by the deformation method for the framework. Two forms of the structure differing by specified parameters are studied     

Torsion of chiral Cosserat elastic rods

This paper is concerned with the torsion of isotropic chiral Cosserat elastic cylinders. First, the generalized plane strain problem is defined and an existence result is presented. Then, the three-dimensional problem is reduced to the study of some generalized plane strain problems. In general, the torsion of the cylinder is accompanied by bending and extension. The method is applied to study the torsion of a circular cylinder.     

The Complex-Moduli Solution of an Axisymmetric Dynamic Problem of Coupled Thermoviscoplasticity Under Harmonic Loading

An approximate formulation is given to the axisymmetric dynamic thermoviscoplastic problem with coupled mechanical and thermal fields. The formulation employs an approximate cyclic thermoviscoplastic model based on the concept of complex moduli. The distribution of the field quantities and the temperature— and amplitude—frequency resonant characteristics of a circular disk under forced flexural vibrations are studied. The capabilities of the approximate model in solving this class of problems are also studied     

混凝土结构扭转理论研究的进展

本文回顾了国内外混凝土结构扭转理论的历史发展,尤其是最近十几年来的进展。文中就有代表性的斜弯理论和空间桁架理论进行了述评。并按照结构构件受纯扭、弯扭及弯剪扭联合作用等加载方式,对于素混凝土、钢筋混凝土和预应力混凝土结构扭转的计算方法进行了归纳。最后对我国开展混凝土结构扭转理论的研究提出了建议。      

A novel semi-inverse solution method for elastoplastic torsion of heat treated rods

Torsion rods are a primary component of many power transmission and other mechanical systems. The behavior of these rods under elastoplastic torsion is of major concern for designers. Different methods have so far been proposed which deal with the elastoplastic torsion of rods, most of which assume constant yield stress. This assumption produces rough and inaccurate results when the rods are heat treated, since in the process of heat treatment the form of yield stress distribution across the rod cross section changes. We propose a new method for calculating elastoplastic torsion of rods of simply connected cross section which is based on heat treatment observations. In our method the full plastic stress function is obtained by using the semi-inverse method. Elastoplastic stress function is obtained by generalizing the idea of the membrane analogy and using a piecewise continuous stress function. Since the proposed form of yield stress distribution can not be handled by the current Finite Element packages, we produce a computer package with a 3D graphical interface capable of calculating and displaying the 3D elastoplastic stress function, shear stress contours, and torque-angle of rotation per unit length. We show that our method produces excellent agreement for several known cross sections in comparison to methods which assume constant yield stress.     

On the torsion of chiral bars in gradient elasticity

This paper contains a study of the problem of torsion of chiral bars with arbitrary cross-sections in the context of the linear theory of gradient elasticity. The solution is expressed in terms of solutions of four auxiliary plane problems characterized by loads which depend only on the constitutive coefficients. It is shown that, in general, the torsion produces extension (or contraction) and bending effects. The results are used to investigate the torsion of a homogeneous circular bar. In contrast with the case of achiral circular cylinders, the torsion and extension cannot be treated independently of each other.     

Heat transfer and pressure drop characteristics of turbulent flow in a circular tube fitted with regularly spaced twisted-tape elements

The results of an experimentalnvestigation of turbulent flow heat transfer and pressure drop characteristics in a circular tube fitted with regularly spaced twisted-tape elements connected by thin circular rods are reported. The characteristics are governed by Reynolds number, Prandtl number, twist ratio, space ratio, and rod-to-tube diameter ratio. Correlations for friction factor and Nusselt number are also reported. It is shown that on the basis of both constant pumping power and constant heat duty, regularly spaced twisted-tape elements do not perform better than full-length twisted tapes.     

Impact of axial compression and torque on strain localization and fracture under complex cyclic loading of Plexiglas rods

Experimental studies of deformation and fracture of rods made of Plexiglas (PMMA) under complex loading (quasi-static and cyclic torsion under axial compression) are performed. The existence of a range of critical values of axial stress, within which the rod is fractured by the torque, is established. The localization of “frozen” highly elastic strains in constrained cyclic torsion is revealed, and the conditions of its occurrence are determined. The effect of axial stress on strain localization and fracture and the influence of cyclic torsion on the loss of stability of a rod under axial compression are shown.     

Saint-Venant problem for solids with helical anisotropy

We discuss the solution of Saint-Venant’s problem for solids with helical anisotropy. Here the governing relations of the theory of elasticity in terms of displacements were presented using the helical coordinate system. We proposed an approach to construct elementary Saint-Venant solutions using integration of ordinary differential equations with variable coefficients in the case of a circular cylinder with helical anisotropy. Elementary solutions correspond to problems of extension, of torsion, of pure bending and of bending of shear force. The solution of the problem is obtained using small parameter method for small values of twist angle and numerically for arbitrary values. Numeric results correspond to problems of extension–torsion. Dependencies of the stiffness matrix (in dimensionless form) on angle between the tangent to the helical coil and the axis of the cylinder corresponding to stiffness on stretching and torsion are illustrated graphically for different values of material and geometrical parameters.     

One-dimensional deformations of nonlinearly elastic micropolar bodies

We find families of finite deformations of a Cosserat elastic continuum on which the system of equilibrium equations is reduced to a system of ordinary differential equations. These families can be used to describe the expansion, tension, and torsion of a hollow circular cylinder, cylindrical bending of a rectangular slab, straightening of a circular arch, reversing of a cylindrical tube, formation of screw and wedge dislocations in a hollow cylinder, and other types of deformations. In the case of a physically nonlinear material model, the above-listed families of deformations can be used to construct exact solutions of several problems of strong bending of micropolar bodies.