Pre-stressed and reinforced hollow cylindrical mixture of non-linearly elastic solid and ideal fluid subjected to combined deformations: A study within the context of the theory of interacting continua

The theoretical result dealing with the saturation boundary condition, first investigated by [On boundary conditions for a certain class of problems in mixture theory, Int. J. Eng. Sci. 24 (1986) 1453-1463], has been recently extended by [On the saturation boundary condition within the context of the theory of interacting continua containing a certain distribution of fibers, Int. J. Eng. Sci. 41 (2003) 2273-2280] to the case of fibers-reinforced solid-ideal fluid mixture. Taking advantage of this new result, the problem of a hollow cylindrical mixture subjected to combined deformations, previously treated by Gandhi et al. [Some non-linear diffusion problems within the context of interacting continua, Int. J. Eng. Sci. 25 (1987) 1441-1457], is revisited in this contribution and improved by introducing the presence of fibers and residual stress (or pre-stress) characterized by the opening angle of the sector-like cross-section.     

Existence and continuous dependence results in the theory of interacting continua

This paper is concerned with the linear theory for binary mixtures of elastic bodies. In the first part of the paper we study boundary-value problems of the equilibrium theory. Existence and uniqueness theorems are established. The second part of the paper is devoted to the dynamic theory. We use the semigroups theory of linear operators to obtain existence and continuous dependence results.     

Modeling and numerical simulation of blood flow using the theory of interacting continua

In this paper we use a modified form of the mixture theory developed by Massoudi and Rajagopal to study the blood flow in a simple geometry, namely flow between two plates. The blood is assumed to behave as a two-component mixture comprised of plasma and red blood cells (RBCs). The plasma is assumed to behave as a viscous fluid whereas the RBCs are given a granular-like structure where the viscosity also depends on the shear-rate.     

Radiation from point source within a hollow elastic cylinder in an acoustic medium

Conclusions An accurate solution has been obtained for the sound emission by a point source in a complex fluid-elastic system. Analytical representation of the wave characteristics is converted to the form of contour integrals, permitting effective numerical estimates of the influence of the geometric and physical parameters of the waveguide structure. A computational algorithm has been proposed, and its effectiveness has been estimated. The existence of two types of surface waves that are not subject to radiative damping has been established. Translated from Prikladnaya Mekhanika, Vol. 33, No. 5, pp. 20–29, May, 1997.     

Solving the problem of expansion and extension of a hollow cylinder with the use of the gradient plasticity theory

An exact solution of the problem of expansion and extension of a hollow cylinder, which generalizes the known solutions based on the classical and gradient theories of plasticity under plane strain conditions, is obtained. The numerical solution reduces to calculating several ordinary integrals. The effect of the characteristic size of the material on the solution behavior near the cylinder orifice is studied.     

压电空心圆柱中波的传播

应用三维压电弹性体轴对称模型对压电空心圆柱中波的传播进行了研究. 发现在 圆柱中是否具有压电性质会对波的传播带来显著的差异. 当波长趋向于零时，在压电圆柱中 拟P波的波速渐进趋向于横观各向同性弹性体的准P波波速，而非压电圆柱中拟P波的波速 渐进趋向于一维杆模型中的P波波速；在压电圆柱中拟SV波存在驻波现象. 圆柱中的SH波 同电场无关，所以在压电圆柱和非压电圆柱中SH波具有相同的频散曲线. 应用积分变 换方法将圆柱的控制方程同其侧边界条件相结合，得到了一组动力学方程. 针对具体的侧边 界条件，得到相对应的波导条件和频散方程. 在此基础上通过数值计算模拟了圆柱受到端部 应力脉冲激励后的瞬态响应. 同时讨论了空心圆柱的半径比对轴向波传播的影响.     

On the flow of a fluid–particle mixture between two rotating cylinders, using the theory of interacting continua

Mixture theory is used to develop a model for a flowing mixture of solid particulates and a fluid. Equations describing the flow of a two-component mixture consisting of a Newtonian fluid and a granular solid are derived. These relatively general equations are then reduced to a system of coupled ordinary differential equations describing Couette flow between concentric rotating cylinders. The resulting boundary value problem is solved numerically and representative results are presented.     

Determination of the thermal stress wave propagation in orthotropic hollow cylinder based on classical theory of thermoelasticity

The thermoelasticity problem in a thick-walled orthotropic hollow cylinder is solved analytically using finite Hankel transform and Laplace transform. Time-dependent thermal and mechanical boundary conditions are applied on the inner and the outer surfaces of the cylinder. For solving the energy equation, the temperature itself is considered as boundary condition to be applied on both the inner and the outer surfaces of the orthotropic cylinder. Two different cases are assumed for solving the equation of motion: traction–traction problem (tractions are prescribed on both the inner and the outer surfaces) and traction–displacement (traction is prescribed on the inner surface and displacement is prescribed on the outer surface of the hollow orthotropic cylinder). Due to considering uncoupled theory, after obtaining temperature distribution, the dynamical structural problem is solved and closed-form relations are derived for radial displacement, radial and hoop stress. As a case study, exponentially decaying temperature with respect to time is prescribed on the inner surface of the cylinder and the temperature of the outer surface is considered to be zero. Owing to solving dynamical problem, the stress wave propagation and its reflections were observed after plotting the results in both cases.     

Elastodynamic solution of a non-homogeneous orthotropic hollow cylinder

A theoretical method for analyzing the axisymmetric plane strain elastodynamic problem of a non-homogeneous orthotropic hollow cylinder is developed. Firstly, a new dependent variable is introduced to rewrite the governing equation, the boundary conditions and the initial conditions. Secondly, a special function is introduced to transform the inhomogeneous boundary conditions to homogeneous ones. By virtue of the orthogonal expansion technique, the equation with respect to the time variable is derived, of which the solution can be obtained. The displacement solution is finally obtained, which can be degenerated in a rather straightforward way into the solution for a homogeneous orthotropic hollow cylinder and isotropic solid cylinder as well as that for a non-homogeneous isotropic hollow cylinder. Using the present method, integral transform can be avoided and it can be used for hollow cylinders with arbitrary thickness and subjected to arbitrary dynamic loads. Numerical results are presented for a non-homogeneous orthotropic hollow cylinder subjected to dynamic internal pressure. The project supported by the National Natural Science Foundation of China (10172075 and 10002016)     

Torsion of hollow cylinder with variable shear moduli

Kiev Institute of Civil Aviation Engineers, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 29, No. 11, pp. 41–46, November, 1993.     

A theory of composites modeled as interpenetrating solid continua

The differential equations and boundary conditions describing the behavior of a finitely deformable, heat-conducting composite material are derived by means of a systematic application of the laws of continuum mechanics to a well-defined macroscopic model consisting of interpenetrating solid continua. Each continuum represents one identifiable constituent of the N-constituent composite. The influence of viscous dissipation is included in the general treatment. Although the motion of the combined composite continuum may be arbitrarily large, the relative displacement of the individual constituents is required to be infinitesimal in order that the composite not rupture. The linear version of the equations in the absence of heat conduction and viscosity is exhibited in detail for the case of the two-constituent composite. The linear equations are written for both the isotropic and transversely isotropic material symmetries. Plane wave solutions in the isotropic case reveal the existence of high-frequency (optical type) branches as well as the ordinary low-frequency (acoustic type) branches, and all waves are dispersive. For the linear isotropic equations both static and dynamic potential representations are obtained, each of which is shown to be complete. The solutions for both the concentrated ordinary body force and relative body force are obtained from the static potential representation.