Transformation of a Pressure Pulse in a Fluid-Filled Cylindrical Elastic Shell

The influence of a tubular elastic insert of finite length in a fluid-filled elastic shell on the propagation of a pressure pulse generated at a certain distance from the insert is investigated. The Laplace integral transform is used to solve the corresponding mathematical problem. Analytical solutions are first obtained in each separate domain of the hydroelastic system, subject to the coupling boundary conditions, and then the Laplace transforms are inverted numerically. The influence of the geometrical parameters of the insert and the shell on the pressure distribution in the fluid, the radial displacement, the bending moments, and the shearing forces are analyzed in detail both quantitatively and qualitatively. It is shown that the transmission of the pressure pulse in the junctions of the insert with the shell is accompanied by highly localized stress concentration there, which is several orders of magnitude greater than in the homogeneous shell.     

Propagation of Transient Hydroelastic Waves in a Semiinfinite, Piecewise-Constant Cylindrical Shell Containing a Fluid

A solution is formulated for a new problem of wave propagation in a semiinfinite cylindrical shell with a junction connecting two shells of different radii. The material of the shell is assumed to be viscoelastic, and the fluid is assumed to be viscous. The motion of the shell is described by Kirchhoff–Love theory, and the motions of the fluid are described by equations averaged over the cross section. The problem is solved by means of the time Laplace transform and subsequent numerical inversion. The numerical results for the pressure and radial displacement of the shell are analyzed for various values of the parameters.     

Multiobjective Optimization of a Composite Cylindrical Shell with an Elastic Core with Account of Reliability

Multiobjective optimization of the structure and geometry of a laminated anisotropic composite shell with an elastic core under thermal action is considered. The thermoelastic properties of the laminated composite are determined from the known properties of the monolayer and the given values of the variable structural and geometric parameters. The properties to be optimized - the critical load and thermal stresses - depend on two variable parameters, the stochastic properties of the composite, and the temperature. In the space of the properties being optimized, the domain of allowable solutions and the property scatter ellipses for the optimum compromise project are found. The reliability of the project is determined with regard for the correlation between the critical and thermal stresses.     

圆柱壳在径向冲击载荷作用下的弹性脉冲屈曲

当圆柱壳承受径向脉冲载荷时，如果其径厚比大于一特定值，圆柱壳将产生弹性动力屈曲．本文根据有关实验结果，假定变形模态，采用Ｌａｇｒａｎｇｅ方法分析了有限长薄圆柱壳（ａ／ｈ＝４８０）在余弦冲击载荷作用下的弹性脉冲动力屈曲．导出了动力屈曲方程组，借助数值方法求解方程，并与有关计算结果进行了比较．     

Coupled Frequencies of a Fluid in Circular Cylindrical Tank with an Elastic Inclusion in its Roof

A closed upright rigid circular cylindrical tank is filled with a compressible and inviscid fluid as a part of the tank roof is an elastic plate. It is supposed that the tank roof and the elastic plate are eccentrically and the plate is clamped. The problem about the determination of the free coupling vibrations of the received hydroelastic system is considered. Using the Bubnov‐Galerkin method, the frequency equation is obtained. Some numerical examples are made and the results show the influence of the sizes of the radius of the elastic plate as well as of the other parameters of the hydroelastic system on its coupled frequencies.     

Cylindrical Tank Filled With a Liquid in a Three-Dimensional Temperature Field

In the cylindrical coordinate system, we construct an exact solution of the threedimensional thermoelasticity problem for a tank filled with a liquid. After determining the temperature field from the heat conduction equation, we solve the equations of the asymmetrical problem of the theory of elasticity. In doing so, the system of resolving equations is reduced to four separate equations with respect to the displacements of the construction. Several exact solutions of boundary-value problems are found. The results are presented in the form of rather simple formulas.     

充液功能梯度材料圆柱壳振动特性的波动解

利用波动法,研究充满非粘滞不可压缩流体的,功能梯度材料圆柱壳的振动特性.相关的轴向形态用指数函数来近似,在两端简支、一端固支另一端简支和两端固支边界条件下,计及流体的影响,理论研究了壳的振动频率.通过与现有文献研究结果的比较,验证了该方法的有效性和精确性,发现二者吻合得很好.     

Predominantly Unidirectional Flow of a Viscous Fluid

Journal of Applied and Industrial Mathematics - We consider the problem of the flow of a viscous fluid in the presence of solid bodies (namely, the two walls and a permeable plate) under...     

粘弹性柱壳的若干动力学性质

本文讨论了轴向压力和一致分布的径向压力作用下粘弹性柱壳的动力稳定性问题.利用Laplace变换,得到了常载作用下粘弹壳的稳定性条件.综合利用动力学的经典方法,得到了由粘弹性壳所定义的动力系统的各种动力学性质及各种参数对结构稳定性的影响.     

Computing Viscous Flow in an Elastic Tube

We have developed a numerical method for simulating viscous flow through a compliant closed tube, driven by a pair of fluid source and sink. As is natural for tubular flow simulations, the problem is formulated in axisymmetric cylindrical coordinates, with fluid flow described by the Navier-Stokes equations. Because the tubular walls are assumed to be elastic, when stretched or compressed they exert forces on the fluid. Since these forces are singularly supported along the boundaries, the fluid velocity and pressure fields become unsmooth. To accurately compute the solution, we use the velocity decomposition approach, according to which pressure and velocity are decomposed into a singular part and a remainder part. The singular part satisfies the Stokes equations with singular boundary forces. Because the Stokes solution is unsmooth, it is computed to second-order accuracy using the immersed interface method, which incorporates known jump discontinuities in the solution and derivatives into the finite difference stencils. The remainder part, which satisfies the Navier-Stokes equations with a continuous body force, is regular. The equations describing the remainder part are discretized in time using the semi-Lagrangian approach, and then solved using a pressure-free projection method. Numerical results indicate that the computed overall solution is second-order accurate in space, and the velocity is second-order accurate in time.     

Optimal Thickness of a Cylindrical Shell Under a Time-Dependent Force

We discuss thickness optimization problems for cylindrical tubes that are loaded by time-dependent applied force. This is a problem of shape optimization that leads to optimal control in linear elasticity theory. We determine the optimal thickness of a cylindrical tube by minimizing the deformation of the tube under the influence of an external force. The main difficulty is that the state equation is a hyperbolic partial differential equation of the fourth order. The first order necessary conditions for the optimal solution are derived. Based on them, a numerical method is set up and numerical examples are presented.     

冲击扭矩作用下弹性圆柱壳中应力波导致的动力屈曲问题

圆柱壳的屈曲问题曾被许多力学工作者从不同的角度进行过研究．本文以半无限长弹性圆柱壳为研究对象，将冲击扭矩作用下圆柱壳的动力屈曲归结为由于扭转应力波的传播导致的分叉问题，最后将此分叉问题化为一个非线性方程组的求解，并对动力屈曲时横向惯性的影响进行了讨论，最后进行了数值分析，得到了一些有益的结论．     

Determination of the Limit Equilibrium of a Piecewise-Homogeneous Cylindrical Shell with a Longitudinal Crack

Using the method of generalized problems of conjugation, for a piecewise homogeneous cylindrical shell with a longitudinal crack we develop a system of integral equations (some of which are singular) for functions of displacement jumps and their derivatives on the line of the crack and on the surfaces of separation of dissimilar component shells. The particular features of application of the method proposed to the case of a nonthrough crack are analyzed with due regard for plastic zones near its front and, also, for determining the redistribution of residual and temperature stresses, caused by the presence of a crack. The numerical analysis of the problem is performed, and certain relationships between the coefficients of intensity of efforts, moments, opening of the crack, and its size and distance to the surface of separation are established.