组合荷载作用下腐蚀缺陷管道的极限承载力

腐蚀缺陷的存在会降低管道的承载力,影响管道的正常运行.考虑了管道轴向与环向材料强度的各向异性,提出了腐蚀缺陷压力管道在内压、轴力和弯矩组合荷载作用下极限承载力的一组广义解.推导了等深度腐蚀、椭圆腐蚀和抛物线三种形状腐蚀缺陷管道的解析解.通过算例验证了解析解与广义解结果具有很好的吻合性.腐蚀形状对极限承载力有显著影响,把...     

广义Maxwell体土模型条件下粘弹性桩纵向振动的半解析解及应用

研究考虑桩身材料阻尼，桩侧土采用广义Maxwell模型条件下，均质土中不均匀桩(截面面积或材料性质在桩长方向上突变)的纵向振动特性，求得了瞬态半正弦脉冲荷栽作用下，桩顶频域响应的解析解及时域响应的半解析解，分析了桩身材料阻尼及土质变化对桩顶时域、频域响应曲线的影响，得到了有关新的结论。通过本文理论结果与实际工程桩的实测曲线的拟合对比，表明本文所得结果能更好地反映客观实际。     

广义Voigt土模型条件下桩的纵向振动响应与应用

研究了桩侧土广义Voigt模型条件下，任意层桩土系统的振动特性，并求得了桩顶在瞬态半正弦脉冲荷载作用下，桩顶的时域纵向响应的半解析解，同时结合基桩完整性检测的机械阻抗法和反射波法研究了各主要模型参数以及土层界面、桩身缺陷等对桩顶时、频响应曲线的影响，得到了许多结论。结果表明，得到的理论成果相比于已有理论更加完善并能更好地反映客观实际，将为基桩完整性定量化检测创造条件。     

横观各向同性材料的三维断裂力学问题

从三维横观各向同性材料弹性力学理论出发, 使用Hadamard有限部积分概念, 导出了三维状态下单位位移间断(位错)集度的基 本解. 在此基础上, 进一步运用极限理论, 将任意载荷作用下, 三维无限大横观各向 同性材料弹性体中, 含有一个位于弹性对称面内的任意形状的片状裂纹问题, 归结为求 解一组超奇异积分方程的问题. 通过二维超奇异积分的主部分析方法, 精确地求得了裂纹前沿光滑点附近的应力奇异指数和奇异应力场, 从而找到了以裂纹表面位移间断表示的应力强度因子表达式及裂纹局部扩展所提供 的能量释放率. 作为以上理论的实际应用,最后给出了一个圆形片状裂纹问题 的精确解例和一个正方形片状裂纹问题的数值解例. 对受轴对称法向均布载荷作用下圆形片状裂纹问题, 讨论了超奇异积分方程的精确求解方法, 并获得了位移间断和应力强度因子的封闭解, 此结果与现有理论解完全一致.     

轴对称理想不可压缩流体和stokes流的广义解析函数解

本文利用轴对称共轭调和函数和广义解析函数的概念,推导出轴对称理想不可压流体和 stokes 流以广义解析函数表示的完备解.     

含刚性体可展开结构的准静态展开分析方法

包含具有一定几何形状刚性连续表面的可展结构可以有效提高展开效率,保证形状精度,具有较高的实用价值.刚性体按需要可为刚性曲板等,一般形状复杂且形式多样,展开分析中描述困难,目前还没有一种通用的处理方法.本文以节点坐标为变量建立一种通用的刚性体运动学方程,将运动学方程引入展开分析之中,利用广义逆矩阵法进行准静态展开过程分析.本文的方法数学描述简洁明快,包含的未知量少,且适用于含任意形状刚性体的可展开结构,数值计算算例验证了方法的有效性.     

广黏弹组合模型的等效性及其基本性质

对广义黏弹组合模型的等效性及其基本性质进行了研究,结果表明：广义Maxwell 模型由于并联结构,其蠕变柔量很难得到. 但提出了求解广义Maxwell模型蠕变柔量的 方法,给出了其具体表达式,且在此基础上证明了广义Maxwell模型与Kelvin链的等效性, 建立了这两个模型物理参数间的转换关系式. 证明了广义黏弹组合模型的一个基本性质：当 将模型的松弛时间谱和延迟时间谱由大到小顺序排列时,松弛时间与延迟时间互不相等,且 相互交织,两相邻松弛时间中间有且仅有一个延迟时间,同时,两相邻延迟时间中间有且仅有一个松 弛时间;当两者同阶相比时,延迟时间总是大于松弛时间. 这一基本性质明确了使用广义黏 弹组合模型来描述现实中某种特定材料的黏弹性行为时,该材料必须具备的基本条件,因此, 它可作为这类流变模型在工程应用中的一个实用判据. Wiechert模型和广义中村模型、广义 Jeffreys模型和广义N-K模型、Maxwell链和广义Kelvin模型之间的等效性可作为特例. 最后,实例验证了所提出的求解广义黏弹组合模型蠕变柔量方法及其基本性质.     

广义黏弹组合模型的等效性及其基本性质

对广义黏弹组合模型的等效性及其基本性质进行了研究,结果表明:广义Maxwell模型由于并联结构,其蠕变柔量很难得到. 但提出了求解广义Maxwell模型蠕变柔量的方法,给出了其具体表达式,且在此基础上证明了广义Maxwell模型与Kelvin链的等效性,建立了这两个模型物理参数间的转换关系式. 证明了广义黏弹组合模型的一个基本性质:当将模型的松弛时间谱和延迟时间谱由大到小顺序排列时,松弛时间与延迟时间互不相等,且相互交织,两相邻松弛时间中间有且仅有一个延迟时间,同时,两相邻延迟时间中间有且仅有一个松弛时间;当两者同阶相比时,延迟时间总是大于松弛时间. 这一基本性质明确了使用广义黏弹组合模型来描述现实中某种特定材料的黏弹性行为时,该材料必须具备的基本条件,因此,它可作为这类流变模型在工程应用中的一个实用判据. Wiechert模型和广义中村模型、广义Jeffreys模型和广义N-K模型、Maxwell链和广义Kelvin模型之间的等效性可作为特例.最后,实例验证了所提出的求解广义黏弹组合模型蠕变柔量方法及其基本性质.      

基于弹性解的结构弹塑性应力分析方法

以弹塑性力学的模型理论和塑性力学形变理论为基础，提出了一个由试验或计算获得的弹性解，按原型材料的广义应力与广义应变关系曲线，以及塑性力学伊留申理论，将弹性解转换为相应结构中的弹塑性应力解的分析方法。实验结果表明，本方法是正确、可行的。     

物性与温度相关材料广义热弹性模型及渐近分析

计及材料物性与温度的相关性,基于Clausius不等式和L-S广义热弹性理论,通过对自由能公式的高阶展开,构建了具有变物性特征的广义耦合热弹性动力学模型。推导了各向同性材料表面受热冲击问题的线性化控制方程组,利用热冲击的瞬时特征,借助于Laplace正、逆变换技术及其极限性质,给出了变物性条件下一维热冲击问题的温度场、位移场和应力场的渐近表达式。通过算例,得到了热冲击作用下各物理场的分布规律以及材料物性与温度相关性对于热弹性响应的影响规律。结果表明：材料物性与温度相关性对于各物理场的阶跃位置、阶跃间隔以及阶跃峰值均产生影响,但值得注意的是,相比于位移场和应力场的显著影响,其对温度场的影响效果并不明显。     

A unified treatment of axisymmetric adhesive contact problems using the harmonic potential function method

A unified treatment of axisymmetric adhesive contact problems is provided using the harmonic potential function method for axisymmetric elasticity problems advanced by Green, Keer, Barber and others. The harmonic function adopted in the current analysis is the one that was introduced by Jin et al. (2008) to solve an external crack problem. It is demonstrated that the harmonic potential function method offers a simpler and more consistent way to treat non-adhesive and adhesive contact problems. By using this method and the principle of superposition, a general solution is derived for the adhesive contact problem involving an axisymmetric rigid punch of arbitrary shape and an adhesive interaction force distribution of any profile. This solution provides analytical expressions for all non-zero displacement and stress components on the contact surface, unlike existing ones. In addition, the newly derived solution is able to link existing solutions/models for axisymmetric non-adhesive and adhesive contact problems and to reveal the connections and differences among these solutions/models individually obtained using different methods at various times. Specifically, it is shown that Sneddon’s solution for the axisymmetric punch problem, Boussinesq’s solution for the flat-ended cylindrical punch problem, the Hertz solution for the spherical punch problem, the JKR model, the DMT model, the M-D model, and the M-D-n model can all be explicitly recovered by the current general solution.     

Adhesive contact of an elastic semi-infinite solid with a rigid rough surface: Strength of adhesion and contact instabilities

The effect of adhesion on the contact behavior of elastic rough surfaces is examined within the framework of the multi-asperity contact model of Greenwood and Williamson (1966), known as the GW model. Adhesive surface interaction is modeled by nonlinear springs with a force–displacement relation governed by the Lennard–Jones (LJ) potential. Constitutive models are presented for contact systems characterized by low and high Tabor parameters, exhibiting continuous (stable) and discontinuous (unstable) surface approach, respectively. Constitutive contact relations are obtained by integrating the force–distance relation derived from the LJ potential with a finite element analysis of single-asperity adhesive contact. These constitutive relations are then incorporated into the GW model, and the interfacial force and contact area of rough surfaces are numerically determined. The development of attractive and repulsive forces at the contact interface and the occurrence of instantaneous surface contact (jump-in instability) yield a three-stage evolution of the contact area. It is shown that the adhesion parameter introduced by Fuller and Tabor (1975) governs the strength of adhesion of contact systems with a high Tabor parameter, whereas the strength of adhesion of contact systems with a low Tabor parameter is characterized by a new adhesion parameter, defined as the ratio of the surface roughness to the equilibrium interatomic distance. Applicable ranges of aforementioned adhesion parameters are interpreted in terms of the effective surface separation, obtained as the sum of the effective distance range of the adhesion force and the elastic deformation induced by adhesion. Adhesive strength of rough surfaces in the entire range of the Tabor parameter is discussed in terms of a generalized adhesion parameter, defined as the ratio of the surface roughness to the effective surface separation.     

Adhesion-induced instabilities in elastic and elastic-plastic contacts during single and repetitive normal loading

Adhesive interaction in spherical contacts was modeled with the Lennard-Jones (L-J) potential. Elastic adhesive contact was analyzed by the equivalent system of a rigid sphere with reduced radius of curvature and a half-space of effective elastic modulus. The critical gap at the instant of abrupt surface contact (jump-in) and separation (jump-out) was determined from the deformed surface profile of the elastic half-space and geometrical relationships. A finite element model of a rigid sphere and an elastic-plastic half-space was used to examine elastic-plastic adhesive contact. Surface adhesion was modeled by nonlinear springs with a force-displacement relationship governed by the L-J potential. The evolution of the interfacial force and the central gap distance as well as the occurrence of jump-in and jump-out instabilities were investigated in terms of the Tabor parameter, plasticity parameter, and dimensionless maximum normal displacement. The force-displacement response due to several approach-retraction cycles was interpreted in the context of elastic and plastic shakedown behaviors using dimensionless parameters.     

The displacement solution of conical shell and its application

In this paper,the displacement solution method of the conical shell is presented.Fromthe differential equations in displacement form of conical shell and by introducing adisplacement function,U(s,θ),the differential equations are changed into an eight-ordersoluble partial differential equation about the displacement function U(s,θ)in which thecoefficients are variable.At the same time,the expressions of the displacement and internalforce components of the shell are also given by the displacement function.As special casesof this paper,the displacement function introduced by V.Z.Vlasov in circular cylindricalshell,the basic equation of the cylindrical shell and that of the circular plate are directlyderived.Under the arbitrary loads and boundary conditions,the general bending problem of theconical shell is reduced to finding the displacement function U(s,θ),and the generalsolution of the governing equation is obtained in generalized hypergeometric function,Forthe axisymmetric bending deformation of the     

Effective elastic modulus of film-on-substrate systems under normal and tangential contact

Load and depth sensing indentation methods have been widely used to characterize the mechanical properties of the thin film-substrate systems. The measurement accuracy critically depends on our knowledge of the effective elastic modulus of this heterogeneous system. In this work, based on the exact solution of the Green's function in Fourier space, we have derived an analytical relationship between the surface tractions and displacements, which depends on the ratio of the film thickness to contact size and the generalized Dundurs parameters that describe the modulus mismatch between the film and substrate materials. The use of the cumulative superposition method shows that the contact stiffness of any axisymmetric contact is the same as that of a flat-ended punch contact. Therefore, assuming a surface traction of the form of [1−(r/a)²]^−1/2 with radial coordinate r and contact size a, we can obtain an approximate representation of the effective elastic moduli, which agree extremely well with the finite element simulations for both normal and tangential contacts. Motivated by a recently developed multidimensional nanocontact system, we also explore the dependence of the ratio of tangential to normal contact stiffness on the ratio of film thickness to contact radius and the Dundurs parameters. The analytical representations of the correction factors in the relationship between the contact stiffness and effective modulus are derived at infinite friction conditions.     

On the radial oscillations of incompressible, isotropic, elastic and limited elastic thick-walled tubes

The finite amplitude, free radial oscillations of a thick-walled circular cylindrical tube are studied for an arbitrary incompressible, isotropic and homogeneous rubber-like material having limiting molecular chain extensibility. First, based on classical results for hyperelastic tubes, some results for thick-walled Mooney-Rivlin tubes are described graphically in the phase plane. Then the periodicity of the finite amplitude, free oscillations of a general limited elastic, thick-walled tube is studied; and some analytical results for the Gent model are illustrated in several numerical examples. Results for thick-walled Gent tubes are compared with those for corresponding Mooney-Rivlin tubes; and the motion of thin-walled Gent tubes is illustrated in the phase plane. Physical conclusions are presented. The period of small amplitude oscillations of an arbitrary elastic or limited elastic tube is derived from relations obtained by a linearization of a general class of equations of which the tube problem is a special case. Classical results of the linear theory are thereby recovered and compared with results for Mooney-Rivlin and Gent tubes.     

不同模量壳体理论广义弹性定律的普遍表达式

本文研究了拉伸和压缩不同模量材料制成的壳体弱矩理论的本构关系,导出了广义弹性定律的普遍表达式,即中曲面法向坐标的各任意幂次项系数的公式,并指出文献[1]中最终公式保留的线性项,仅为本文普遍表达式的一个较简单的特殊情形,因此,可以不顾文献[1]中关于应力沿壳厚按线性规律变化的基本假设。     

THE FIRST ORDER APPROXIMATION OF NON-KIRCHHOFF-LOVE THEORY FOR ELASTIC CIRCULAR PLATE WITH FIXED BOUNDARY UNDER UNIFORM SURFACE LOADING (Ⅰ)

Based on the approximation theory adopting non-kirchhoff-Love assumption for three dimensional elastic plates with arbitrary shapes^[1],[2], the author derives a functional of generalized variation for three dimensional elastic circular plates, thereby obtains a set of differential equations and the relate boundary conditions to establish a first order approximation theory for elastic circular plate with fixed boundary and under uniform loading on one of its surface. The analytical solution of this problem will present in another paper.     

THE FIRST ORDER APPROXIMATION OF NON-KIRCHHOFF-LOVE THEORYFOR ELASTIC CIRCULAR PLATE WITH FIXED BOUNDARY UNDERUNIFORM SURFACE LOADING (Ⅰ)

I.1ntroductionTheaxisymmetricproblemofthreedimensionalelasticcircularplatecanbetreatedasthreedimensionalaxisymmetricproblemofelasticity.Weconsideracircularplatewithauniformthicknessh,andsetupacircumferentialcoordinates(r,o)onitsmidd1esurfacewithabscissazp…