Casson Fluid Flow Due to Non-Coaxial Rotation of a Porous Disk and the Fluid at Infinity Through a Porous Medium

The flow of the Casson fluid due to non-coaxial rotation of a disk and the fluid at infinity is investigated. Partial differential equations are made dimensionless and coupled. The exact solution of the resultant nonlinear initial-boundary-value problem is solved by applying the Laplace transform. The shear stresses at the disk surface and the steady state stresses are computed. The effects of dimensionless parameters on the dimensionless primary and secondary velocities are analyzed.     

Non-steady-state elastic–plastic behavior of metal forming (rolling) with a generalized friction law

An analytical and generalized friction law is formulated and a three-dimensional large-strain non-steady-state elastic–plastic finite element analysis has been performed for rolling process. The contact/friction problem at the interface between the workpiece and the rolls is treated rigorously by using this new friction law. The numerical results, including the evolutions of roll torque and roll forces, and the interfacial normal and shear stresses, are presented and discussed.     

Contact stresses: a short survey of models and methods of computations

Contact stresses are identified as normal and tangential forces between contacting solids. The normal stresses are modeled using unilateral and complementary conditions, elastic response and normal compliance. Friction laws describe the tangential traction. Friction of materials depends on pressure, sliding velocity, surface temperature, time of contact, surface roughness and presence of wear debris. Phenomenological, micro-mechanical and atomic-scale models as well as non-classical models of anisotropic and heterogeneous friction are important steps in the development of friction modeling. Sophisticated friction models are desirable in vibrating systems, materials processing, rolling contacts, rubber and polymers, geomechanics, bioengineering and living systems. Main numerical methods in contact mechanics are: finite element method, boundary element method and discrete element method. To include specific contact constraints, the following computing techniques are applied: Lagrange multipliers, penalty function, perturbated and augmented Lagrangian methods, mathematical programming methods. The advances of adhesion and impact modeling are outlined in this paper.     

结构中微裂纹与超声波的混频非线性作用数值仿真研究

针对结构中微裂纹检测难题,本文对结构中微裂纹与超声波的混频非线性作用进行了数值仿真研究。基于经典非线性理论,得到了两列超声纵波相互作用产生混频效应的理论条件。通过有限元仿真,研究了两列纵波与微裂纹相互作用产生混频的条件,并分析了界面处静应力、摩擦系数和裂纹方向对混频效应的影响。研究发现,超声波与微裂纹相互作用产生混频非线性效应的发生条件仍符合经典非线性理论下的混频产生条件。裂纹界面处施加的静应力对差频横波幅值有明显影响;当施加静应力与无裂纹模型得到的最大应力值接近时,混频非线性效应最强;裂纹界面的摩擦系数对超声波的混频非线性效应影响较小;透射差频横波传播方向与经典非线性理论预测的理论差频分量方向基本一致,且几乎不受裂纹方向变化的影响,而反射差频横波的传播方向随裂纹方向的改变而有所不同。本文研究工作为微裂纹检出及方向识别做了有益探索。     

Nonlinear analysis of shear deformable beam-columns partially supported on tensionless three-parameter foundation

In this paper, a boundary element method is developed for the nonlinear analysis of shear deformable beam-columns of arbitrary doubly symmetric simply or multiply connected constant cross-section, partially supported on tensionless three-parameter foundation, undergoing moderate large deflections under general boundary conditions. The beam-column is subjected to the combined action of arbitrarily distributed or concentrated transverse loading and bending moments in both directions as well as to axial loading. To account for shear deformations, the concept of shear deformation coefficients is used. Five boundary value problems are formulated with respect to the transverse displacements, to the axial displacement and to two stress functions and solved using the Analog Equation Method, a BEM-based method. Application of the boundary element technique yields a system of nonlinear equations from which the transverse and axial displacements are computed by an iterative process. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress functions using only boundary integration. The proposed model takes into account the coupling effects of bending and shear deformations along the member as well as the shear forces along the span induced by the applied axial loading. Numerical examples are worked out to illustrate the efficiency, wherever possible, the accuracy and the range of applications of the developed method.     

回转支承构件牵引滚动接触应力解析

回转支承构件是重型机械的重要基础元件,其失效往往导致灾难性的设备事故和人身事故以及巨大的经济损失.及时、充分地了解回转支承构件牵引滚动接触应力分布特点,对于保证整机安全生产和提高企业经济效益具有非常重要的意义.本文将回转支承构件接触模型简化为轴线平行的圆柱体二维平面应变模型,从接触力学理论中McEwen关于轴线平行的圆柱体二维法向接触理论出发,重点讨论牵引滚动与常规法向接触状态的切向分布力的相同点和不同点,从而推导出牵引滚动接触状态下接触区应力场各应力分量解析式,将McEw-en法向理论公式推广到法、切向复合分布力综合作用下.在此基础上,探讨了表面拉应力与摩擦系数的关系,摩擦系数越大则表面拉应力水平越高.最后,运用材料力学二向应力状态受力分析方法,计算了接触应力场最大剪应力位置、大小和方向角与深度的关系,发现与无表面摩擦情况相比,最大主剪应力发生位置变浅,幅值反而变小.     

Numerical investigation of effect of rolling manipulation of traditional Chinese medical massage on blood flow

The hemodynamic mechanism of rolling manipulation (RM) of traditional Chinese medical massage (TCMM) is investigated. An axisymmetrical nonlinear model and an arbitrary Lagrangian-Eulerian finite element method (ALE-FEM) with rezoning algorithm were introduced to study the viscous flow through an axisymmetrical rigid tube with axially moving stenosis to simulate the rolling manipulation. Flow rate and wall shear stress were obtained by solving complete Navier-Stokes equations numerically. The numerical results show that the stenosis moving frequency, namely the frequency of rolling manipulation, has great effect on the disturbance of flow and the wall shear stress. The stenosis coefficient, which characterizes the severity of the stenosis, another adjustable parameter in rolling manipulation, also shows the significant effect on flow rate and wall shear stress. These numerical results may provide some data that can be taken into consideration when massage is used in clinic.     

Near field behavior of in-plane crack extension in nonlinear incompressible material

The nonlinear theory of finite elasticity is applied to obtain the in-plane displacement and stresses in the immediate vicinity of the crack tip. Incompressibility, homogeneity, elasticity and isotropy are assumed for the material while the resultant shear stress and shear strain are assumed to follow a nonlinear hardening/softening behavior. The system of governing differential equations becomes nonelliptical when the strains are sufficiently large.     

Extended Kantorovich method for local stresses in composite laminates upon polynomial stress functions

The extended Kantorovich method is employed to study the local stress concentrations at the vicinity of free edges in symmetrically layered composite laminates subjected to uniaxial tensile load upon polynomial stress functions. The stress fields are initially assumed by means of the Lekhnitskii stress functions under the plane strain state. Applying the principle of complementary virtual work, the coupled ordinary differential equations are obtained in which the solutions can be obtained by solving a generalized eigenvalue problem. Then an iterative procedure is estab-lished to achieve convergent stress distributions. It should be noted that the stress function based extended Kantorovich method can satisfy both the traction-free and free edge stress boundary conditions during the iterative processes. The stress components near the free edges and in the interior regions are calculated and compared with those obtained results by finite element method (FEM). The convergent stresses have good agreements with those results obtained by three dimensional (3D) FEM. For generality, various layup configurations are considered for the numerical analysis. The results show that the proposed polynomial stress function based extended Kan-torovich method is accurate and efficient in predicting the local stresses in composite laminates and computationally much more efficient than the 3D FEM.     

Linear and higher order displacement theories for adhesively bonded lap joints

This work presents an adhesive model for stress analysis of bonded lap joints, which can be applied to model thin and thick adhesive layers. In this theory, linear variations of displacement components along the adhesive thickness are firstly assumed, and the longitudinal strain and the Poisson's effect of the adhesive are modeled. A differential form of the equilibrium equations for the adherends is analytically solved by means of compatible relations of the adhesive deformation. The derived shear and peel stresses are compared with the classical adhesive model of continuous springs with constant shear and peel stresses, and validated with two-dimensional finite element results of the geometrically nonlinear analysis using a commercial package. The numerical results show that the present linear displacement theory can be applied to both thin and moderately thick adhesive layers. The present formulation of the linear displacement theory is then extended to the higher order displacement theory for stress analysis of a thick adhesive, whose numerical results are also compared with those of the finite element computation.     

Slip flow due to a stretching cylinder

The slip flow due to a stretching cylinder is studied. A similarity transform reduces the Navier-Stokes equations to a set of non-linear ordinary differential equations. Asymptotic solutions for large Reynolds number and small slip show the problem can be related to the existing two-dimensional stretching cases. Due to algebraic decay, the equations are further transformed through a compressed variable, and then integrated numerically. It is found that slip greatly reduces the magnitudes of the velocities and the shear stress.     

Dynamics of spatial structure-varying rigid multibody systems

Summary Couplings in machines and mechanisms exhibiting backlash and friction phenomena can be modeled as multibody systems with unilateral constraints and Coulomb friction. The structure of the differential-algebraic equations describing the system depends on the state of the constraints. The contact forces occurring at active constraints are taken into account in the equations of motion as Lagrange multipliers. Additionally, the kinematic conditions of all active constraints are formulated on the acceleration level. Contact and friction laws are sufficient conditions for state transitions of active constraints, and are represented by nonsmooth characteristics. Several formulations, like the linear complementarity problem, and two different nonlinear systems of equations are presented together with their solution method. The theory is applied to a mechanical system containing three-dimensional and coupled unilateral constraints with friction. Received 14 May 1998; accepted for publication 5 January 1999     

Mechanics of advancing pin-loaded contacts with friction

This paper considers finite friction contact problems involving an elastic pin and an infinite elastic plate with a circular hole. Using a suitable class of Green's functions, the singular integral equations governing a very general class of conforming contact problems are formulated. In particular, remote plate stresses, pin loads, moments and distributed loading of the pin by conservative body forces are considered. Numerical solutions are presented for different partial slip load cases. In monotonic loading, the dependence of the tractions on the coefficient of friction is strongest when the contact is highly conforming. For less conforming contacts, the tractions are insensitive to an increase in the value of the friction coefficient above a certain threshold. The contact size and peak pressure in monotonic loading are only weakly dependent on the pin load distribution, with center loads leading to slightly higher peak pressure and lower peak shear than distributed loads. In contrast to half-plane cylinder fretting contacts, fretting behavior is quite different depending on whether or not the pin is allowed to rotate freely. If pin rotation is disallowed, the fretting tractions resemble half-plane fretting tractions in the weakly conforming regime but the contact resists sliding in the strongly conforming regime. If pin rotation is allowed, the shear traction behavior resembles planar rolling contacts in that one slip zone is dominant and the peak shear occurs at its edge. In this case, the effects of material dissimilarity in the strongly conforming regime are only secondary and the contact never goes into sliding. Fretting tractions in the forward and reversed load states show shape asymmetry, which persists with continued load cycling. Finally, the governing integro-differential equation for full sliding is derived; in the limiting case of no friction, the same equation governs contacts with center loading and uniform body force loading, resulting in identical pressures when their resultants are equal.     

Nonlinear stress and deformation analysis of thin current-carrying strip shells

The paper analyzes the nonlinear deformation of a current-carrying thin shell in coupled electromagnetic and mechanical fields. The nonlinear magnetoelastic kinetic equations, physical equations, geometric equations, electrodynamic equations, expressions for the Lorentz force of a current-carrying thin shell in a coupled field are given. The normal Cauchy form nonlinear differential equations that include ten basic unknown functions are obtained by the variable replacement method. The difference and quasi-linearization methods are used to reduce the nonlinear magnetoelastic equations to a sequence of quasilinear differential equations that can be solved by discrete orthogonalization. Numerical solutions for the stresses and strains in a current-carrying thin strip shell with two edges simply supported are obtained as an example. The dependence of the stresses and strains in the current-carrying thin strip shell on the electromagnetic parameters is discussed. In a special case, it is shown that the deformation of the shell can be controlled by changing the electromagnetic parameters     

Nonlinear elastic effects in graphite/epoxy: An analytical and numerical prediction of energy flux deviation

Manipulating acoustic wave propagation through a material have several interdisciplinary applications. Here we predict shift in energy flux deviation for acoustic waves propagating in unidirectional graphite/epoxy due to applied normal and shear stresses using both an analytical model, using acoustoelastic continuum theory, and a finite element discrete numerical model. The acoustoelastic theory predicts that the quasi-transverse (QT) wave exhibits larger shifts in energy flux deviation compared to quasi-longitudinal (QL) or the pure transverse (PT) due to an applied shear stress for fiber orientation angle ranging from 0° to 60°. Due to an applied shear stress the QT wave exhibits a shift in energy flux deviation at 0° fiber orientation angle as compared to normal stress case where the flux deviation and its load induced shift are both zero. A finite element model (FEM) is developed where equations of motion include the effect of nonlinear elastic coefficients. Element equations were integrated in time using Newmark’s method to determine the shift in energy flux deviations in graphite/epoxy for different loading cases. The energy flux shift of QT waves predicted by FEM for fiber orientation angles from 0° to 60° for applied shear stress case is in excellent agreement with acoustoelastic theory. Because energy shift magnitudes are not small, it is possible to experimentally measure these shifts and calibrate shifts with respect to load type (normal/shear) and magnitude.     

弹塑性流变模型在弹流脂润滑特性分析中的应用

采用自行研制的高速润滑脂拖动力试验装置测量了7007国产润滑脂的拖动力;以7007润滑脂为例,建立了该类高速润滑脂的平均剪切弹性模量和平均极限剪切应力的计算公式,基于Tevaarwerk-Johnson弹塑模型给出了拖动力的计算方法,并分析了其流变特性.结果表明:该润滑脂在本文试验条件下表现出弹塑性,其拖动力的理论预测值与试验测量值具有很好的一致性;所建立的拖动力计算公式可用于指导润滑分析领域的工程计算.     

A 3D FEM–BEM rolling contact formulation for unstructured meshes

This work presents a new formulation for solving 3D steady-state rolling contact problems. The convective terms for computing the tangential slip velocities involved in the rolling problem, are evaluated using a new approximation inspired in numerical fluid dynamics techniques for unstructured meshes. Moreover, the elastic influence coefficients of the surface points in contact are approached by means of the finite element method (FEM) and/or the boundary element method (BEM). The contact problem is based on an Augmented Lagrangian Formulation and the use of projection functions to establish the contact restrictions. Finally, the resulting nonlinear equations set is solved using the generalized Newton method with line search (GNMls), presenting some acceleration strategies as: a new and more simplified projection operator, which makes it possible to obtain a quasi-complementarity of the contact variables, reducing the number of contact problem unknowns, and using iterative solvers. The presented methodology is validated solving some rolling contact problems and analyzed for some unstructured mesh examples.     

Nonlinear dynamic analysis of Timoshenko beams by BEM. Part I: Theory and numerical implementation

In this two-part contribution, a boundary element method is developed for the nonlinear dynamic analysis of beams of arbitrary doubly symmetric simply or multiply connected constant cross section, undergoing moderate large displacements and small deformations under general boundary conditions, taking into account the effects of shear deformation and rotary inertia. Part I is devoted to the theoretical developments and their numerical implementation and Part II discusses analytical and numerical results obtained from both analytical or numerical research efforts from the literature and the proposed method. The beam is subjected to the combined action of arbitrarily distributed or concentrated transverse loading and bending moments in both directions as well as to axial loading. To account for shear deformations, the concept of shear deformation coefficients is used. Five boundary value problems are formulated with respect to the transverse displacements, to the axial displacement and to two stress functions and solved using the Analog Equation Method, a BEM based method. Application of the boundary element technique yields a nonlinear coupled system of equations of motion. The solution of this system is accomplished iteratively by employing the average acceleration method in combination with the modified Newton–Raphson method. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress functions using only boundary integration. The proposed model takes into account the coupling effects of bending and shear deformations along the member, as well as the shear forces along the span induced by the applied axial loading.

     

下限原理在岩土工程中的应用

采用极限分析下限原理求解了岩土工程中基础的极限载力和边坡的安全系数。求解过程中把有限元法和非线性规划相结合,把整个结构离散化,设定每个结点的应力,把原问题变成一个以边坡的稳定安全系数或基础的极限承载力为目标函数,以结点应力为优化变量,以对可静应力场的各种制约为约束条件的非线性规划问题。采用序列二次规划法求解该非线性规划问题,得到了人为构造的严格满足应力边界条件、平衡微分方程、不违反Mohr-Coulomb或Drucker-Prager屈服准则的应力场,解决了三维可静应力场的构造问题。算例分析表明,本文的方法是正确、可行的。