基于LHS-Kriging法的正交异性钢桥面板疲劳可靠度分析

为解决随机车载下正交异性钢桥面板疲劳应力谱有限元求解耗时问题,采用拉丁超立方抽样（LHS）与Kriging方法,建立了快速获取随机车流作用下细节疲劳应力谱的LHS-Kriging有限元替代模型,并将此模型应用于南溪长江大桥正交异性钢桥面板疲劳可靠度计算。结果表明,基于LHS-Kriging方法的有限元替代模型, 不需要经过大量车辆荷载的有限元加载,可直接快速获取细节疲劳应力谱;与传统的响应面法（RSM）相比,Kriging法预测的细节等效疲劳应力更符合有限元计算结果;随着交通量增长率的增大,桥梁的疲劳可靠度显著减少;100年后,当交通量增长率为3%和5%时,正交异性桥面板与纵肋焊接处的细节疲劳可靠度小于2。     

Adaptive eigenfrequency analysis by improvedr- andh-adaptive finite element method based on perturbation and element energy ratio

A new adaptive technique ofr- andh-version for vibration problems utilizing the matrix perturbation theory and element energy ratio is proposed. In structural vibration analysis, through ther-convergence adaptive finite element process, mesh optimization can be realized. In the light of the judgement on the changes in the magnitude of the element energy ratio, local refinement can be achieved in the process ofh-convergence adaptive finite element so that more accurate finite element solutions can be obtained with as few meshes as possible. Many numerical examples are given and the proposed approach is shown to be feasible and effective. Project supported by the National Natural Science Foundation of China (No. 19872029).     

利用间隙元的方法计算和分析疲劳寿命

提出了一个利用结构有限元方法中间隙元的原理来计算和分析疲劳寿命的新的累积损伤模型和方法。该方法利用间隙来模拟裂纹的形成和扩展 ,并提出新的累积损伤理论。不仅可以得到构件的疲劳总寿命 ,而且还可以用于计算裂纹的生成寿命、扩展寿命。同时又描述了裂纹的开裂过程 ,即裂纹的开裂尺寸和开裂方向。这为进行各种疲劳强度设计提供了一个新的思路和方法     

粉末冶金涡轮盘简单模拟件低周疲劳寿命研究

采用光滑圆棒试样和带孔平板试样,对不同温度下的镍基粉末高温合金(FGH95)的低周疲劳(LCF)寿命进行了试验研究和有限元分析。在详细分析试验和有限元计算结果的基础上,提出了复杂应力状态下的低周疲劳寿命模型。模型寿命表达为真实应力幅的函数,模型参数由不同应力水平加载作用下的光滑圆棒试样试验结果给定,进一步采用涡轮盘简单模拟件即带孔平板试样对比验证LCF寿命模型的有效性。有限元计算结果显示,理论预测寿命与试验结果能很好地吻合。     

基于应变能的复杂应力场低周疲劳分析

塑性应变能使材料微观组织结构发生不可逆变化,从而引起等效宏观应力,该应力随循环加载而增大．假定材料疲劳源处破坏是由最大拉应力引起的,最大等效宏观应力与外加应力叠加达到材料本征断裂应力时形成微裂纹．微裂纹引起上述两部分应力变化,继续加载直至宏观裂纹出现,从而得到材料的疲劳寿命．本文所建立的多轴疲劳寿命公式包含材料参数、拉应力以及塑性应变能等,以上数据可通过单轴疲劳数据和有限元方法获得．通过对SM45C材料的计算验证,表明该模型对多轴随机应变加载低周疲劳寿命,具有良好的预测结果．     

一个修正的金属材料低周疲劳损伤模型

疲劳破坏是金属最常见的失效形式之一.基于连续损伤力学理论和能量原理,论文提出了一个修正的金属材料低周疲劳损伤演化方程,该方程综合考虑了材料的塑性强化、微裂纹闭合效应等因素对损伤累积的影响.将修正后的损伤演化方程以UMAT子程序的形式导入有限元计算软件ABAQUS之中,建立了疲劳损伤的计算模型,并以铝合金7050-T7451为例对该模型的有效性和适用性进行了验证.     

Elastic–plastic FE analysis of a notched shaft under multiaxial nonproportional synchronous cyclic loading

An elastic–plastic finite element analysis is presented for a notched shaft subjected to multiaxial nonproportional synchronous cyclic tension/torsion loading. The elastic–plastic material property is described by the von Mises yield criterion and the kinematic hardening rule of Prager/Ziegler. The finite element program system ABAQUS is used to solve the boundary value problem. Special emphasis is given to explore the effects of the stress amplitude, the mean-stress, and the mutual interactions on the local stress–strain responses at the notch root.     

A note on the stability and accuracy of Cn finite elements in steady diffusion-convection problems

The paper is concerned with stability and accuracy of an nth order Lagrangian family of finite element steady-state solutions of the diffusion-convection equation, and furthermore is concerned with the stability and the accuracy of on mth kind Hermitian family of finite element solutions. We discuss the stability of the numerical solution based on the fact that the characteristic finite element solution can be expressed approximately as a rational function of cell Peclet number Pe_c ( = uh/k). Moreover, it is shown that by eliminating derivatives and by using the interpolation method over elements a stable solution is obtained over the domain independent of Pe_c for P^1,3, and for P^2,5 the stable solution is obtained for Pe_c less than 44.4.     

Solution of the connection problems between a finite holed plate and a stiffener by using the partitioning concept of the generalized variational method

In this paper a new finite element method is presented, in which complex functions are chosen to be the finite element model and the partitioning concept of the generalized variational method is utilized. The stress concentration factors for a finite holed plate welded by a stiffener are calculated and the analytical solutions in series form are obtained. From some computer trials it is demonstrated that the problem of displacement compatibility and continuity of tractions between the holed plate and the stiffener is successfully analysed by using this method. Since only three elements need to be formulated, relatively less storage is required than the usual finite element methods. Furthermore, the accuracy of solutions is improved and the computer time requirements are considerably reduced. Numerical results of stress concentration factors and stresses along the welded-line which may be referential to engineers are shown in tables.     

A finite element variational multiscale method for incompressible flows based on the construction of the projection basis functions

In this article, we present a finite element variational multiscale (VMS) method for incompressible flows based on the construction of projection basis functions and compare it with common VMS method, which is defined by a low‐order finite element space L_h on the same grid as X_h for the velocity deformation tensor and a stabilization parameter α. The best algorithmic feature of our method is to construct the projection basis functions at the element level with minimal additional cost to replace the global projection operator. Finally, we give some numerical simulations of the nonlinear flow problems to show good stability and accuracy properties of the method. Copyright © 2011 John Wiley & Sons, Ltd.     

椭圆孔三维应力集中及其对疲劳强度的影响

应用有限单元法对有限厚中心椭圆孔板的三维应力集中进行了分析。发现厚板的最大应力集中总是与自由表面保持一固定的距离而不随板厚的增加而变化;椭圆形状因子越小,距离自由表面越近。得到了最大三维应力集中、表面应力集中与相应平面解之间的近似关系和经验公式;研究了厚度对疲劳强度的影响,并给出相应的影响系数。     

A Bubble Element for the Compressible Euler Equations

In this paper, we present a new Galerkin finite element method with bubble function for the compressible Euler equations. This method is derived from the scaled bubble element for the advection-diffusion problems developed by Simo and his colleagues, which is based on the equivalence between the Galerkin method employing piecewise linear interpolation with bubble functions and the Streamline-Upwind/Petrov Galerkin (SUPG) finite element method using P₁ approximation in the steady advection-diffusion problem. Simo and this author have applied this approach to transient advection-diffusion problems by using a special scaled bubble function called P-scaled bubble, which is designed to work in the transient advection-diffusion problems for any Peclet number from 0 to ∞. The method presented in this paper is an application of this p-scaled bubble element to a pure hyperbolic system.     

Two-level stabilized finite element method for Stokes eigenvalue problem

A two-level stabilized finite element method for the Stokes eigenvalue problem based on the local Gauss integration is considered.This method involves solving a Stokes eigenvalue problem on a coarse mesh with mesh size H and a Stokes problem on a fine mesh with mesh size h = O(H 2),which can still maintain the asymptotically optimal accuracy.It provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution,which involves solving a Stokes eigenvalue problem on a fine mesh with mesh size h.Hence,the two-level stabilized finite element method can save a large amount of computational time.Moreover,numerical tests confirm the theoretical results of the present method.     

Augmented mixed finite element methods for a vorticity‐based velocity–pressure–stress formulation of the Stokes problem in 2D

In this paper, we consider an augmented velocity–pressure–stress formulation of the 2D Stokes problem, in which the stress is defined in terms of the vorticity and the pressure, and then we introduce and analyze stable mixed finite element methods to solve the associated Galerkin scheme. In this way, we further extend similar procedures applied recently to linear elasticity and to other mixed formulations for incompressible fluid flows. Indeed, our approach is based on the introduction of the Galerkin least‐squares‐type terms arising from the corresponding constitutive and equilibrium equations, and from the Dirichlet boundary condition for the velocity, all of them multiplied by stabilization parameters. Then, we show that these parameters can be suitably chosen so that the resulting operator equation induces a strongly coercive bilinear form, whence the associated Galerkin scheme becomes well posed for any choice of finite element subspaces. In particular, we can use continuous piecewise linear velocities, piecewise constant pressures, and rotated Raviart–Thomas elements for the stresses. Next, we derive reliable and efficient residual‐based a posteriori error estimators for the augmented mixed finite element schemes. In addition, several numerical experiments illustrating the performance of the augmented mixed finite element methods, confirming the properties of the a posteriori estimators, and showing the behavior of the associated adaptive algorithms are reported. The present work should be considered as a first step aiming finally to derive augmented mixed finite element methods for vorticity‐based formulations of the 3D Stokes problem. Copyright © 2010 John Wiley & Sons, Ltd.     

The effect of the sheet rigidity on strength of the spot weld tension shear joint

This paper presents some test and analysis results for a spot welded joint subjected to tensile and alternate load. The effect of sheet rigidity on the tensile strength and fatigue life of the spot welded joint is studied by using the stress intensity factorsK _I,K _II,K _III and an effective stress intensity factor K_max calculated by the finite element method for crack around the nugget. The results show that the effective stress intensity factor K_max is an essential parameter for estimating the fatigue life of the spot welded joint.     

Numerical simulation of transient planar flow of a viscoelastic material with two moving free surfaces

In this study, we examine the numerical simulation of transient viscoelastic flows with two moving free surfaces. A modified Galerkin finite element method is implemented to the two-dimensional non-steady motion of the fluid of the Oldroyd-B type. The fluid is initially placed between two parallel plates and bounded by two straight free boundaries. In this Lagrangian finite element method, the spatial mesh deforms in time along with the moving free boundaries. The unknown shape of the free surfaces is determined with the flow field u, v, τ, p by the deformable finite element method, combined with a predictor-corrector scheme in an uncoupled fashion. The moving free surfaces and fluid motion of both Newtonian and non-Newtonian flows are investigated. The results include the influence of surface tension, fluid inertia and elasticity.     

A finite element method for the one‐dimensional extended Boussinesq equations

A new finite element method for Nwogu's (O. Nwogu, ASCE J. Waterw., Port, Coast., Ocean Eng., 119 , 618–638 (1993)) one‐dimensional extended Boussinesq equations is presented using a linear element spatial discretisation method coupled with a sophisticated adaptive time integration package. The accuracy of the scheme is compared to that of an existing finite difference method (G. Wei and J.T. Kirby, ASCE J. Waterw., Port, Coast., Ocean Eng., 121 , 251–261 (1995)) by considering the truncation error at a node. Numerical tests with solitary and regular waves propagating in variable depth environments are compared with theoretical and experimental data. The accuracy of the results confirms the analytical prediction and shows that the new approach competes well with existing finite difference methods. The finite element formulation is shown to enable the method to be extended to irregular meshes in one dimension and has the potential to allow for extension to the important practical case of unstructured triangular meshes in two dimensions. This latter case is discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

A unified mesh refinement method with applications to porous media flow

A unified algorithm is presented for the refinement of finite element meshes consisting of tensor product Lagrange elements in any number of space dimensions. The method leads to repeatedly refined n-irregular grids with associated constraint equations. Through an object-oriented implementation existing solvers can be extended to handle mesh refinements without modifying the implementation of the finite element equations. Various versions of the refinement procedure are investigated in a porous media flow problem involving singularities around wells. A domain decomposition-type finite element method is also proposed based on the refinement technique. This method is applied to flow in heterogeneous porous media. © 1998 John Wiley & Sons, Ltd.