Higher order asymptotic solution of mode I crack growth in elastic-perfectly plastic media

A higher order asymptotic solution of near-tip field is studied for plane-atrain Mode-I quasi-static steady crack growth in the incompressible (v=1/2) elastic perfectly-plastic media. The results show that the near-tip stress and strain are fully continuous, and the strain possesses In (A/r) singularity at the crack tip. The expressions of the stress, strain and velocity in each region are also given. The project supported by National Natural Science Foundation of China     

ASYMPTOTIC NON-STABILITY AND BLOW-UP AT BOUNDARY FOR SOLUTIONS OF A FILTRATION EQUATION

For a class of nonlinear filtration equation with nonlinear second-third boundary value condition, it is shown that a priori boundary of the solution can be estimated and controlled by initial data and integral on the boundary of the region. The priori estimate of the solutions was established by iterative method. By using this estimate the solutions may blow-up on the boundary of the region and thus it may have asymptotic non-stability.     

Residual stress field and reduction of stress intensity factors in cold-worked holes

Closed-form and semi-analytical solutions are obtained for the residual stress distributions in a plate caused by pressure acting on a central circular hole, representing the cold-work process. The material is elastic–perfectly plastic. Both Tresca and von Mises yield criteria are used and the corresponding residual stress distributions are compared. The relation between the dimension of the plastic zone and the value of internal pressure is presented. The relation between the magnitude of the residual stresses and the remote uniform tensile stress required to open symmetrical radial cracks is also presented. The reduction of the stress intensity factors of cracked open and riveted holes as a function of the internal pressure applied (or mandrel radial displacement) is investigated using numerical models for both an elastic–perfectly plastic material and for an Al 2024-T3 Alclad aluminum alloy.     

滑动界面的球形夹杂问题

滑动界面对多相介质力学性能的影响日益受到重视．但已有的解析结果往往假定界面是自由滑动的．即假设界面上的剪应力为零，这与大多数实际情况并不相符．本文假定界面上剪应力不为零并满足线弹簧型界面条件，在这一前提下，首次获得了球形夹杂本征应变问题的解析解．     

SELF-ADAPTIVE STRATEGY FOR ONE-DIMENSIONAL FINITE ELEMENT METHOD BASED ON ELEMENT ENERGY PROJECTION METHOD

Based on the newly-developed element energy projection (EEP) method for computation of super-convergent results in one-dimensional finite element method (FEM), the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient. This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea, implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach.     

Two-dimensional thermoelastic analysis of a functionally graded cylindrical panel due to nonuniform heat supply

This paper is concerned with the theoretical treatment of the steady-state thermoelastic problem of a functionally graded cylindrical panel due to nonuniform heat supply in the circumferential direction. The thermal and thermoelastic constants of the cylindrical panel are expressed as power functions of the radial coordinate. We obtain the exact solution for the two-dimensional temperature change in a steady state, and thermal stresses of a simple supported cylindrical panel under the state of plane strain. Some numerical results are shown in figures and tables. Furthermore, the influence of the nonhomogeneity of the material, the radius ratio and the span angle upon the temperature change, displacements and stresses is investigated.     

横观各向同性三维热弹性力学通解及其势理论法

通过引入两个位移函数，对用位移表达的运动平衡方程作了简化．利用算子理论，严格地导出了横观各向同性非耦合热弹性动力学问题的通解．对于静力学问题，通解的形式可进一步简化成用4个准调和函数来表示．具体考察了横观各向同性体内平面裂纹上下表面有对称分布温度作用的问题，推广了势理论方法，导出了一个积分方程和一个微分-积分方程．针对币状裂纹表面受均布温度作用情形，给出了具体的解。     

Localized solutions to the nonlinear wave equation for flexural motions of an elastic beam traveling in an air-filled tube

Steady-progressive-wave solutions are sought to the nonlinear wave equation derived previously [J. Fluids Struct. 16 (2002) 597] for flexural motions of an elastic beam traveling in an air-filled tube along its center axis at a subsonic speed. Fluid-structure interactions are taken into account through aerodynamic loading on the lateral surface of the beam subjected to small but finite deflection but end effects and viscous effects are neglected. Linear dispersion characteristics are first examined by exploiting the small ratio of the induced mass to the mass of the beam per unit length. Centered around the traveling speed of the beam, there exists such a narrow range of propagation velocity that the linear steady propagation is prohibited. In this range, it is revealed that some interesting nonlinear solutions exist. The periodic wavetrain is found to exist as the exact solution. Asymptotic analysis is then made by applying the method of multiple scales and the stationary nonlinear Schrödinger equation is derived for a complex amplitude. A monochromatic solution to this equation corresponds to the exact periodic solution. Imposing undisturbed boundary conditions at infinity, it is revealed that the localized solution exists as a result of balance between the linear instability and the nonlinearity. This solution is checked by solving the nonlinear equation numerically. It is further revealed that the amplitude-modulated wavetrain exists not only in the range of the velocity mentioned above but also outside of it.     

The Opposing Effect of Viscous Dissipation Allows for a Parallel Free Convection Boundary-Layer Flow Along a Cold Vertical Flat Plate

External free convection boundary-layer flows are usually treated by neglecting the effect of viscous dissipation. This assumption always results in a non-parallel flow, besides a strong parallel component also a weak transversal component of the (steady) velocity field occurs. The present paper shows, however, that the weak opposing effect of the buoyancy forces due to heat release by viscous dissipation, can give rise along a cold vertical plate adjacent to a fluid saturated porous medium to a strictly parallel steady free convection flow. This boundary-layer flow is described by an algebraically decaying exact analytical solution of the basic balance equations.     

Interaction between Low and High-Frequency Modes in a Nonlinear System: Gas-Filled Cylinder Covered by a Movable Piston

A simple mechanical system containing a low-frequency vibration mode andset of high-frequency acoustic modes is considered. The frequencyresponse is calculated. Nonlinear behaviour and interaction betweenmodes is described by system of functional equations. Two types ofnonlinearities are taken into account. The first one is caused by thefinite displacement of a movable boundary, and the second one is thevolume nonlinearity of gas. New mathematical models based on nonlinearequations are suggested. Some examples of nonlinear phenomena arediscussed on the base of derived solutions.