具有弹性层的两圆管间夹入弹性薄膜时的回转接触

应用弹性接触理论及Fourier变换,考虑接触域的粘着及微小滑状态,对具有弹性层的两圆筒间夹入弹性薄膜的非对称回转接触问题进行了0研究,讨论了接触宽度,弹性层厚度及摩擦系数等对弹性薄膜传送速度和圆筒公称圆周速度之比的影响。     

Analytical solutions of steady vibration of free rectangular plate on semi-infinite elastic foundation

The method of double Fourier transform was employed in the analysis of the semi-infinite elastic foundation with vertical load.And an integral representations for the displacements of the semi-infinite elastic foundation was presented.The analytical solution of steady vibration of an elastic rectangle plate with four free edges on the semi-infinite elastic foundation was also given by combining the analytical solution of the elastic rectangle plate with the integral representation for displacements of the semi- infinite elastic foundation.Some computational results and the analysis on the influence of parameters were presented.     

一种通过改进Canny算子提取光弹条纹骨架线的方法

光弹性法是确定应力集中系数的有效手段，在实际工程中应力参数都是通过分析光弹干涉条纹图获得的，由于光弹干涉条纹图的复杂性，且影响成像质量的因素较多，因此如何从光弹干涉条纹图中撇开其复杂性，较高精度的提取骨架线，是一项较困难的工作，本文提出一种由改进的Canny算子对条纹方位图进行直接运算提取光弹条纹骨架线的算法，实验表明此方法对光弹条纹图很有效。     

Theory of rolling: Solution of the Coulomb problem

A theory of rolling of round bodies in the normal mode with adhesion conditions satisfied on the entire contact area is proposed. This theory refines the classical Coulomb’s theory of rolling in which the rolling moment is directly proportional to the pressing force (e.g., the weight of the rolling body). The rolling moment of cylinders is found to be directly proportional to the pressing force raised to a power of 3/2, and the rolling moment of balls and tori is proportional to the pressing force raised to a power of 4/3. It is shown that the normal mode of uniform rolling can only be provided for a certain ratio of the elastic constants of the materials of the round body and the base forming an ideal pair. The Coulomb problem is solved for the cases of rolling of an elastic cylinder over an elastic half-space, of an elastic ball over an elastic half-space, of an elastic torus over an elastic half-space, and of a cylinder and ball over a tightly stretched membrane. The rolling law is derived for such cases. The rolling friction coefficients, the rolling moment, and the rolling friction force are calculated.     

APPROXIMATE FORMULASOF IMPACT FORCE FOR NORMAL IMPACT OF A FINITE ELASTIC BEAM OF ELASTIC FOUNDATION BY A FINITE ROD

ＲｅｎＷｅｎｍｉｎ（任文敏）；ＨｕａｎｇＪｉａｎｍｉｎ（黄剑敏）；ＣｈｅｎＷｅｎ（陈文）（ＲｅｃｅｉｖｅｄＤｅｃ．２５，１９９４；ＣｏｍｍｕｎｉｃａｔｅｄｂｙＹａｎｇＧｕｉｔｏｎｇ）ＡＰＰＲＯＸＩＭＡＴＥＦＯＲＭＵＬＡＳＯＦＩＭＰＡＣＴＦＯＲＣＥＦＯ...     

Nonlinear vibration isolation of a viscoelastic beam

In this paper, the transmissibility of a viscoelastic beam supported by vertical springs is defined by proposing a new vertical elastic support boundary. By contrasting with the viscoelastic beam with rigid vertical supports and the rigid rod with vertical elastic support ends, the necessity of the transmissibility of an elastic structure with vertical elastic supports is proved. In order to approximately solve the steady-state responses of the nonlinear transverse vibration of the viscoelastic beam under periodic excitation, the harmonic balance method in conjunction with the pseudo arc-length method is adopted. The numerical results are calculated to confirm the approximate analytic results. The comparison between the rigid rod and the elastic beam shows that neglecting the bending vibration of the structures will underestimate the frequency range in which the elastic support produces an effective vibration isolation. On the other hand, the comparison between the rigid support and the spring support demonstrates that ignoring the elasticity of the support ends will create a false understanding of the force transmission of elastic structures. In general, this paper presents the necessity of studying the force transmission of elastic structures with elastic supports. Moreover, this paper will become the beginning of the study of the vibration isolation of the elastic structure.     

Free vibration analysis of general stepped circular plates with internal elastic ring support resting on Winkler foundation by green function method

Natural frequencies are important dynamic characteristics of a structure. Therefore, the exact solution pertaining to free vibration of stepped circular plate elastically restrained against rotation, translation, and internal elastic ring support resting on an arbitrary variable elastic foundation using Green Function is presented in this paper. Thus, an accurate and direct modeling technique is introduced for modeling stepped circular plate on an arbitrary variable elastic foundation with arbitrary boundary conditions and internal elastic ring support. The effect of the translational along with rotational support flexibilities, as well as, the elastic coefficient of Winkler foundation and other parameters are assessed. Finally, some numerical examples are shown in order to present the efficiency and simplicity of the Green Function in the new formulation.     

Construction of Exact Solutions to Three-Dimensional Elastic Problems in Stresses

A method is proposed to construct solutions to differential elastic equations in stresses (Beltrami compatibility equations and equilibrium equations). The method is based on potential theory and allows us to solve efficiently boundary-value problems of elastic theory. As an example, the second boundary-value problem for an elastic half-space is considered     

Nonlinear analysis and buckling of elastically supported circular shallow arches

Arches are often supported elastically by other structural members. This paper investigates the in-plane nonlinear elastic behaviour and stability of elastically supported shallow circular arches that are subjected to a radial load uniformly distributed around the arch axis. Analytical solutions for the nonlinear behaviour and for the nonlinear buckling load are obtained for shallow arches with equal or unequal elastic supports. It is found that the flexibility of the elastic supports and the shallowness of the arch play important roles in the nonlinear structural response of the arch. The limiting shallownesses that distinguish between the buckling modes are obtained and the relationship of the limiting shallowness with the flexibility of the elastic supports is established, and the critical flexibility of the elastic radial supports is derived. An arch with equal elastic radial supports whose flexibility is larger than the critical value becomes an elastically supported beam curved in elevation, while an arch with one rigid and one elastic radial support whose flexibility is larger than the critical value still behaves as an arch when its shallowness is higher than a limiting shallowness. Comparisons with finite element results demonstrate that the analytical solutions and the values of the critical flexibility of the elastic supports and the limiting shallowness of the arch are valid.     

Solution of the plane Hertz problem

The paper considers the problem of onesided frictionless compression of plane elastic bodies that are initially in contact with each other at a point. The first terms of an asymptotic solution of the problem are constructed by the method of joined asymptotic expansions. Determination of the approach of the bodies as a function of the pressing force reduces to calculating socalled of local compliance. The problems of contact of an elastic ring and elastic circular disks with punches and an elastic disk compressed between two elastic strips are considered. An asymptotic model for the quasistatic collision of plane elastic bodies is proposed.     

Identification of an ellipsoidal defect in an elastic solid using boundary measurements

Elastostatic problem of identification of an ellipsoidal cavity or inclusion (rigid or linear elastic) in an isotropic, linear elastic solid is considered. The reciprocity gap functional method is used for solving the problem. It is shown that the parameters of the ellipsoidal defect (coordinates of its center, the directions and magnitudes of the semiaxes and elastic moduli in the case of isotropic, linear elastic inclusion), located in an infinite elastic solid are expressed by means of the values of the reciprocity gap functional. The values of the reciprocity gap functional can be calculated if the loads and displacements corresponding to uniaxial tension (compression) of an infinite solid are known on the closed surface containing the defect inside. Applications of the results to the problem of ellipsoidal defect identification in a bounded body are discussed. A number of numerical examples showing the efficiency of the developed identification method are considered.     

Structural modeling of beams on elastic foundations with elasticity couplings

A new simplified structural model and its governing equations for beams on elastic foundations with elastic coupling are proposed. This modeling system is simple but appropriate for the initial structural design of large-scale submerged floating-beam structures moored by tension legs spaced at uniform interval along the beam. The model is actually for beam on discrete elastic supports rather than on continuous elastic foundations. Therefore, the governing equations are based on finite difference calculus and solutions for beams on discrete elastic supports with elasticity coupling are also proposed. To clarify the applicability limit of the proposed model, the equivalence between a beam on discrete elastic supports and that on continuous elastic foundation is investigated by comparisons of characteristic solutions.     

Equilibrium of a Prestressed Strip Reinforced with Elastic Plates

The contact problem for a prestressed elastic strip reinforced with equally spaced elastic plates is considered. The Fourier integral transform is used to construct an influence function of a unit concentrated force acting on the infinite elastic strip with one edge constrained. The transmission of forces from the thin elastic plates to the prestressed strip is analyzed. On the assumption that the beam bending model and the uniaxial stress model are valid for an elastic plate subjected to both vertical and horizontal forces, the problem is mathematically formulated as a system of integro-differential equations for unknown contact stresses. This system is reduced to an infinite system of algebraic equations solved by the reduction method. The effect of the initial stresses on the distribution of contact forces in the strip under tension and compression is studied     

On a Displacement Based Solution to an Antiplane Crack Problem for Inhomogeneous Anisotropic Elastic Materials

This paper employs a displacement based method to examine an antiplane crack problem for an inhomogeneous elastic material in which the elastic moduli vary continuously with the spatial coordinates. Expressions for the crack tip stress intensity factors and the crack displacement are obtained in terms of Chebyshev polynomials. Numerical results are obtained for some particular inhomogeneous elastic materials.     

Characteristics of local compliance of an elastic body under a small punch indented into the plane part of its boundary

An asymptotic solution of the contact problem of an elastic body indented (without friction) by a circular punch with a flat base is obtained under the assumption of a small relative size of the contact zone. The resulting formulas involve integral characteristics of the elastic body, which depend on its shape, dimensions, fixing conditions, Poisson's ratio, and location of the punch center. These quantities have the mechanical meaning of the coefficients of local compliance of the elastic body. Relations that, generally, reduce the number of independent coefficients in the asymptotic expansion are obtained on the basis of the reciprocal theorem. Some coefficients of local compliance at the center of an elastic hemisphere are calculated numerically. The asymptotic model of an elastic body loaded by a point force is discussed.     

SH波对浅埋弹性圆柱及裂纹的散射与地震动

采用Green函数、复变函数和多极坐标等方法研究含圆柱形弹性夹杂的弹性半空间中任意位置、任意方位有限长度裂纹对SH波的散射与地震动. 构造了含圆柱形弹性夹杂的半空间对SH波的散射波,并求解了适合本问题Green函数,即含有圆柱形弹性夹杂的半空间内(表面)任意一点承受时间谐和的出平面线源载荷作用时位移函数的基本解答. 利用裂纹``切割'方法在任意位置构造任意方位的裂纹,可以得到基体中圆柱形弹性夹杂和裂纹同时存在条件下的位移场与应力场. 通过数值算例,讨论各种参数对夹杂上方地表位移的影响.      

Systems with Discontinuous Quasi-Zero Reconstructing Force

The paper deals with the problem of constructing systems with discontinuous quasizero reconstructing force on the basis of structures where an elastic element moves between two directrices of prescribed design shape perpendicularly to their axis of symmetry. A spring is considered as an elastic element. The cases where the elastic element works only in compression or only in tension are considered.     

半无限长弹性杆与有限长弹性地基梁横向冲击的冲击力近似公式

本文对具有初速的半无限长弹性杆与初始静止的有限长弹性地基梁的横向冲击问题进行了研究，用伽辽金原理求出了冲击力的近似公式，并对结果进行了，得出有关结论。     

Derivation of the Linear Elastic String Model from Three-Dimensional Elasticity

We derive a one-dimensional model for the displacement and torsion of an elastic string starting from a cylindrical three-dimensional linearized prestressed elastic body with small diameter. The prestress is due to the prior elastic deformation of an isotropic, homogenous, elastic body. We deduce the scaling of forces by a formal asymptotic expansion. Then we prove that the family of solutions of three-dimensional problems converges to a limit that is the unique solution of the string model. Coefficients of the string model depend on the three-dimensional elasticity coefficients and the tension due to the predeformation.     

ON THE ORIENTATION OF BUCKLING DIRECTION OF ANISOTROPIC ELASTIC PLATE UNDER UNIAXIAL COMPRESSION

The theory of small deformation superimposed on a large deformation of an elastic solid is used to investigate the buckling of anisotropic elastic plate under uniaxial compression. The buckling direction (the direction of buckling wave) is generally not aligned with the compression direction. The equation for determining the buckling direction is obtained. It is found that the out-of-plane buckling of anisotropic elastic plate is possible and both buckling conditions for flexural and extensional modes are presented. As a specific case of buckling of anisotropic elastic plate, the buckling of an orthotropic elastic plate subjected to a compression in a direction that forms an arbitrary angle with an elastic principal axis of the materials is analyzed. It is found that the buckling direction depends on the angle between the compression direction and the principal axis of the materials, the critical compressive force and plate-thickness parameters. In the case that the compression direction is aligned with the principal axis of the materials, the buckling direction will be aligned with the compression one irrespective of critical compressive force and plate-thickness. Project supported by the National Natural Science Foundation of China (No. 19772032).