厚圆板轴对称振动的弹性力学解

本文以轴对称三维弹性力学基本方程为基础,导出厚圆板强迫振动的状态方程式。利用Ｍａｃｌａｕｒｉｎ级数和Ｓｙｌｖｅｓｔｅｒ定理,厚圆板的位移和应力可以用中面位移和应力的微分算子表示。通过载荷分解和圆板表面条件,可以得到厚圆板在对称载荷与反对称载荷作用下的振动控制方程。求解了厚圆板在周边固支和简支条件下的对称与反对称的自由振动问题。通过数值计算得到了这两类自由振动的固有频率。本文的方法适用于求解厚圆板在     

Approximate Solution of an Axisymmetric Contact Problem with Allowance for Tangential Displacements on the Contact Surface

A structurally nonlinear contact problem of a punch shaped like a paraboloid of revolution is studied. An equation for the contactpressure density is derived with allowance for the radial tangential displacements of the boundary points of an elastic halfspace. A method for constructing a closedform approximate solution is proposed. The effect of the tangential displacements on the main contact parameters is discussed.     

Three-Dimensional Analytical Solution for an Axisymmetric Biharmonic Problem

In this paper, we propose a method for the solution of the axisymmetric boundary value problem for a finite elastic cylinder with assigned stress and/or displacements acting on the ends and side. The technique utilizes the Love representation, which allows for reduction of the solution of the elastic problem to the search for a biharmonic function on a cylindrical domain. In the solution method suggested here, we write the Love function with a Bessel expansion and analyze in detail the conditions under which it is possible to differentiate the expansion term by term. We show that this is possible only for a restricted class of elastic solutions. In the general case, we introduce two new auxiliary functions of the z-coordinate. In this way, we obtain the general form of the axisymmetric biharmonic function, which is discussed in relation to certain specific boundary conditions applied on the side and ends of the cylinder. We obtain an exact explicit solution of practical interest for a cylinder with free ends and assigned displacements applied to the side.     

The Local Conditional Stability Estimate for an Inverse Contact Problem in the Elasticity

In this paper, we consider an inverse problem in elasticity of determining stress on a contact domain from measurements outside the contact domain. The local conditional stability estimate for determining the stress vector is obtained. This conditional stability can give the convergence rate for Tikhonov's regularized solutions. This revised version was published online in July 2006 with corrections to the Cover Date.     

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     

横观各向同性圆柱体端部问题的三维弹性理论解

从位移的通解出发，用分离变量法得到横观各向同性圆柱体的位移和应力的特征函数展开式，并把位移势函数的解用付里叶积分的形式表示。利用留数运算，该积分解可以转换成类似于特征函数的展开式。通过混合端部边界问题，得到与特征函数解成双正交关系的另一组函数。利用这种双正交关系，可以处理不同的端部边界问题。     

Axisymmetric Dynamic Problem of Coupled Thermoviscoplasticity

An axisymmetric dynamic thermoviscoelastic problem is formulated with allowance for the coupling of mechanical and thermal fields. The behavior of the material is described by the Bodner–Partom model. A technique for numerical solution of the problem is developed. The laws governing the stress–strain state and the temperature field of a circular disk under forced flexural vibrations are studied     

An Elastic-viscoplastic Quasistatic Contact Problem: Existence and Uniqueness of a Weak Solution

In this paper, the contact between an elastic-viscoplastic body and a deformable obstacle is studied. The effect of the damage, due to internal tension or compression and caused by the opening and growth of micro-cracks and micro-cavities, is also considered. The variational formulation leads to a coupled system of evolutionary equations. An existence and uniqueness result is established by using approximate problems, the pseudomonotone operators theory, Schauder fixed-point theorem and a comparison result.     

Steady Sliding Frictional Contact Problems in Linear Elasticity

The existence and uniqueness of an equilibrium solution to frictional contact problems involving a class of moving rigid obstacles is studied. At low friction coefficient values, the steady sliding frictional contact problem is uniquely solvable, thanks to the Lions-Stampacchia theorem on variational inequalities associated with a nonsymmetric coercive bilinear form. It is proved that the coerciveness of the bilinear form can be lost at some positive critical value of the friction coefficient, depending only on the geometry and the elastic properties of the body. An example presented here, shows that infinitely many solutions can be obtained when the friction coefficient is larger than the critical value. This result is paving the road towards a theory of jamming in terms of bifurcation in variational inequality. The particular case where the elastic body is an isotropic half-space is studied. The corresponding value of the critical friction coefficient is proved to be infinite in this case. In the particular case of the frictionless situation, our analysis incidentally unifies the approaches developed by Lions-Stampacchia (variational inequalities) and Hertz (harmonic analysis on the half-space) to contact problems in linear elasticity.     

求解Reissner板弯曲问题的一种新方法

运用摄动理论首次将Ｒｅｉｓｓｎｅｒ板理论分解为一系列Ｋｉｒｃｈｈｏｆ板理论的叠加。这样，Ｒｅｉｓｓｎｅｒ板问题的解答就可通过在具体边界条件下求解一系列Ｋｉｒｃｈｈｏｆ板问题来获得。算例表明，本文方法简单，只需摄动两次就能接近Ｒｅｉｓｓｎｅｒ板理论的精确解，适合在实际工程中推广     

A New Method for Solution of 3D Elastic-Plastic Frictional Contact Problems

ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｔａｃｔｐｒｏｂｌｅｍｉｓｏｆｐａｒｔｉｃｕｌａｒｉｎｔｅｒｅｓｔｉｎｎｕｍｅｒｏｕｓｅｎｇｉｎｅｅｒｉｎｇａｐｐｌｉｃａｔｉｏｎｓｒａｎｇｉｎｇｆｒｏｍｓｔｒｕｃｔｕｒｅ＿ｓｔｒｕｃｔｕｒｅｉｎｔｅｒａｃｔｉｏｎｔｏｍａｃｈｉｎｅｄｅｓｉｇｎａｎｄｍｅｔａｌｆｏｒｍｉｎｇｕｎｄｅｒｖａｒｉｏｕｓｌｏａｄｃａｓｅｓ.Ｃｏｎｔａｃｔｐｒｏｂｌｅｍｓａｒｅｎｏｎｌｉｎｅａｒｆｏｒｔｈｅｍｏｖｉｎｇｂｏｕｎｄａｒｙａｎｄｔｈｅｅｘｉｓｔｅｎｃｅｏｆｆｒｉｃｔｉｏｎａｌｏｎ…     

Global Solution to the Generalized Riemann Problem in the Presence of a Boundary and Contact Discontinuities

This work is a continuation of our previous work. In the present paper we study the global structure stability of the Riemann solution $u=U(\frac{x}{t})$ containing only contact discontinuities for general n×n quasilinear hyperbolic systems of conservation laws in the presence of a boundary. We prove the existence and uniqueness of a global piecewise C ¹ solution containing only contact discontinuities to a class of the generalized Riemann problems for general n×n quasilinear hyperbolic systems of conservation laws in a half space. Our result indicates that this kind of Riemann solution $u=U(\frac{x}{t})$ mentioned above for general n×n quasilinear hyperbolic systems of conservation laws in the presence of a boundary possesses a global nonlinear structure stability. Some applications to quasilinear hyperbolic systems of conservation laws occurring in physics and other disciplines, particularly to the system describing the motion of the relativistic string in Minkowski space R ^1?+?n , are also given.     

Asymptotic Solution of a Harmonic Contact Problem for a Permeable Stamp on a Liquid Saturated Base

A plane harmonic problem of vertical vibrations of a rigid permeable stamp on a liquid saturated poroelastic base is considered. The equations of two-phase Biot media, which take into account inertial and viscous interactions of phases, are used. The asymptotic properties of the contact stress at low vibration frequencies are studied.     

Axisymmetric Collision Problem for Two Identical Elastic Solids of Revolution

A direct central collision of two identical bodies of revolution is studied. A nonstationary mixed boundary-value problem with an unknown moving boundary is formulated. Its solution is represented by a series in term of Bessel functions. An infinite system of Volterra equations of the second kind for the unknown expansion coefficients is derived by satisfying the boundary conditions. The basic characteristics of the collision process are determined depending on the curvature of the frontal surface of the bodies     

A Non-linear Algorithm of Photoelastic Tomography for the Axisymmetric Problem

A non-linear algorithm of photoelastic tomography for the measurement of axisymmetric stress fields has been elaborated. It is free of any assumptions concerning the value of the birefringence or rotation of the principal stress axes along the light rays. The algorithm is based on the measurement of characteristic directions and phase retardation in two parallel sections of the test object. Stress components are presented in the form of power series along the radial coordinate. A differential evolution algorithm has been used for finding the stress field parameters, which fit the measurement data best. Application of the method is illustrated by residual stress measurement in a drinking glass.     

The Anti-Plane Shear Problem in Nonlinear Elasticity Revisited

A classical problem in the framework of nonlinear elasticity theory is the characterization of the materials that may sustain a pure state of anti-plane shear in the absence of body forces. This problem has been solved by Knowles and by Hill in the framework of isotropic and incompressible elasticity in the seventies. Here we provide a simpler and shorter proof of these classical results. Moreover, we extend these results to nonlinear elastodynamics and we provide some new special solutions.     

Nonstationary Axisymmetric Problem for a Half-Space of a Compressible Fluid*

International Applied Mechanics - The exact analytical solution to the axisymmetric problem for a half-space of an ideal compressible fluid under nonstationary pressure is found. The method of...     

Analytical Solution for Sliding Rounded-Edge Contact

Reliable analysis of the local stress fields in the vicinity of sliding frictional contacts of engineering components is a pre-requisite for the reliable assessment of structural integrity. In this paper we present the use of Muskhelishvili potentials to derive an analytical solution for a semi-infinite punch with a rounded edge pressed against a half-pane substrate, and a general numerical solution for a kind of Cauchy integral involved in the analytical contact solution. Using these solutions, the effect of the friction coefficient on the normal traction distribution is investigated. Numerical results show that the peak normal traction value is altered in comparison with the frictionless case solution, but this variation is mild (less than 5%), provided the friction coefficient does not exceed about 0.6. Finally, the adaptation of the analytical result to the solution of practical contact problems is addressed.     

Contact Problem for Porous Elastic Half-Plane

The paper is concerned with a static contact problem about a rigid punch on the free surface of a linear porous elastic half-plane. With the use of the Fourier transform the problem is reduced to a singular integral equation holding over the contact zone. This integral representation permits consideration of the Flamant problem (a line load on the half-plane) to be explicitly reduced to some quadratures. It is shown that in the classical linear elasticity limit the main integral equation has a Cauchy-type kernel, so distribution of the contact pressure is like in the Sadowsky punch-problem. For arbitrary porosity a numerical co-location technique is applied that allows one to analyze in detail the distribution of the contact pressure versus porosity. Both in the Flamant and Sadowsky problems we demonstrate a higher compliance of the porous foundation, with respect to the classical linear elastic results. This revised version was published online in July 2006 with corrections to the Cover Date.