Inclusion of elastic deformation in rigid-plastic finite element analysis

A rigid-plastic finite element method combined with the effect of elastic deformation is proposed. In the present method, elastically and elastic-plastically deforming elements are mixed with rigid-plastically deforming elements in the deforming material. In this formulation based on an implicit scheme, the nodal forces for the rigid-plastic elements are equilibrated with those for the elastic and elastic-plastic elements at the end of each deformation step. The nodal forces for the elastic and elastic-plastic elements are derived by considering the effect of rigid-body rotation during deformation increment. The elastic-plastic element is transformed into the rigid-plastic one during the loading when the elastic strain increment is small. The reverse transformation is carried out in the unloading. This leads to a comparatively small computing time and the improvement of the calculated results. Plane-strain bending of a plate with a round punch is simulated by the present method under a mixed condition of elastic, elastic-plastic and rigid-plastic elements in the plate. Deformation behaviour in early stages of bending is successfully calculated. The calculated amounts of springback are in reasonable agreement with the experimental ones for aluminium plates because the stress distribution in the elastic regions without achieving yielding around the edges of the plate is taken into consideration.     

闭口式轧机牌坊的有限元分析

运用ANSYS 12软件对厚连铸板坯切割制造的闭口式轧机牌坊进行三维有限元分析,计算牌坊的应力和变形,计算结果为闭口式轧机牌坊的设计和制造提供了重要依据。     

Nodeless variable finite element method for stress analysis using flux-based formulation

A nodeless variable element is combined with an adaptive meshing technique to improve solution accuracy of the finite element method for analyzing two-dimensional elasticity problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without requiring additional actual nodes. The fluxbased formulation is developed for the nodeless variable finite element to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method. The superconvergent patch recovery procedure is implemented to compute accurate stresses from the nodeless variable finite element solutions. The effectiveness of the combined procedure for providing higher solution convergence rate from the proposed formulation is evaluated by two well-known examples.     

有限元与EXCEL结合计算大型梁单元结构

以某架桥机前支腿的结构分析为算例，介绍了用有限元软件与EXCEL相结合对大型梁单元结构进行强度、稳定性分析的过程，该方法能明显缩短计算时间、保证计算精确度。     

分析梁大变形问题的一种新算法

梁发生大变形时,在变形前的平衡位置建立平衡方程必然引起很大误差,因此除了考虑位移与变形之间的非线性关系外,几何非线性问题还需要考虑大变形所引起的平衡方程的变化。文中提出了一种在变形后的平衡位置分析几何非线性梁的新算法,建立梁发生大变形一阶微分控制方程的矩阵形式,结合迭代修正齐次扩容精细积分法和迭代优化算法进行求解。由于考虑大变形（挠度和转角）对平衡方程的影响,文中方法的模型较为精确,采用精细积分法可以实现高精度求解。以悬臂梁为例,验证方法的正确性和精确性。其方法求解简单,对于不同的边界条件,只需修改优化目标函数。     

有限元的因次分析法

利用因次分析法对用有限元法所分析的结构进行分析,求得了模型和原型之间相似准则,对于同种材料的结构,当结构几何比为λl,外加动载荷之比为λl^2,振动频率之比为时1／λl,结构满足相似准则,则结构的振动加速度之比为1／λl,辐射声功率之比为λl^2。     

离合器摩擦片热变形有限元分析

建立了摩擦离合器接合过程热分析数学模型,并利用有限元技术对离合器外摩擦片进行了热变形分析,结果显示离合器外摩擦片在一定工况条件下会发生翘曲变形,与实际外摩擦片变形情况一致,证明了热变形分析的正确性.该分析也为摩擦离合器安全工作提供了一定的理论依据.     

Matrix-presentation linear least square error method of inverse elastic-plastic large deformation finite element model for upsetting

The main purpose of this paper is to develop the matrix presentation linear least square error method of inverse elastic-plastic large deformation finite element model for upsetting to obtain the friction coefficients during the upsetting process. This inverse model assumed the linear material and based on the modified experimental loading increments using the linear modified experimental upsetting loading standard proposed in this paper. Then the friction coefficients of contact boundary between the workpiece and the die at specific finite element analysis stages can be derived. Finally, using the cubic spline fitting, the history of friction coefficient during the upsetting process can be obtained. It is demonstrated that the workpiece profile of upsetting experiment is quite identical to the workpiece profile of simulation using the result obtained in this paper as the history of friction coefficient of contact boundary, and furthermore the distribution of stress and strain of the workpiece during upsetting process can be understood.     

大型轴流压缩机焊接机壳的静态有限元分析

在建立大型轴流压缩机焊接机壳有限元模型的基础上,对联接螺栓台阶面与上机壳法兰面和上下机壳法兰面之间的接触问题,以及螺栓的预紧问题进行了处理,应用有限元分析软件对模型进行了分析计算.结果表明,所设计焊接机壳静态下的应力和变形均在允许范围内.可进一步对焊接机壳进行动态特性分析,以便为改进设计提供更可靠的理论依据.     

Mean dilatational based finite element formulation for a nearly incompressible nonlinear large deformation analysis

The finite element method (FEM) is one of the most powerful tools that can be used to solve engineering problems. Standard displacement-based isoparametric elements are the most popular in the engineering community for their simple implementation. However, low-order displacement-based elements exhibit locking in the incompressible. Our proposed formulation is a locking removing method that is free from the need to store any extra integration point. We calculate the modified deformation gradient from the mean dilatation of the element and also modify the finite element equations using the mean dilatation. This method is also different from the B-bar method as the B matrix is not modified, but rather the weak form is linearized for the modified deformation gradient. Therefore, this method is a unique implementation of the average dilatation of the element. Here we also present an implementation algorithm of the proposed formulation and compare the results with available methods.

     

采用有限元分析的圆柱齿轮磨齿机冷却系统优化

为在设计阶段对大型精密磨齿机的冷却系统进行优化,减小机床热变形,在对磨齿机整机边界条件进行分析的基础上,应用通用有限元软件,建立了磨齿机的热变形有限元模型,并对其进行热变形分析计算,仿真结果表明,通过优化冷却液流道,可以使机床温度分布更加均匀,有效地减小机床热变形;冷却液温度对于机床热变形影响很大,当机床的冷却液温度与环境温度之差在2℃以内时,机床热变形相对最小.分析结果对圆柱齿轮磨齿机的设计定型及改进具有重要的参考意义.     

工业构件塑变校正的非线性有限元分析

采用非线性有限元法,研究了杆类零件和板簧的塑性矫直过程,计算结果表明,对被矫直的工件施加合理的载荷,可以获得较高的矫直精度。     

Passat B5密封条大变形非线性有限元分析

利用非线性有限元分析软件MARC对Passat B5的车门密封条进行仿真分析,并借助测试装置对实际产品材料参数进行准确测定,解决了该复杂结构的几何非线性、材料非线性和压缩过程边界非线性的有限元分析难点,获得良好的定量分析结果。     

Extraction of wave characteristics from wavelet-based spectral finite element formulation

In this paper, a spectrally formulated wavelet finite element is developed and is used not only to study wave propagation in 1-D waveguides but also to extract the wave characteristics, namely the spectrum and dispersion relation for these waveguides. The use of compactly supported Daubechies wavelet basis circumvents several drawbacks of conventional FFT-based Spectral Finite Element Method (FSFEM) due to the required assumption of periodicity, particularly for time domain analysis. In this work, a study is done to use the formulated Wavelet-based Spectral Finite Element (WSFE) directly for such frequency domain analysis. This study shows that in WSFE formulation, a constraint on the time sampling rate is paced to avoid spurious dispersion being introduced in the analysis. Numerical experiments are performed to study frequency-dependent wave characteristics (dispersion and spectrum relations) in elementary rod, Euler–Bernoulli and Timoshenko beams. The effect of sampling rate on the accuracy of WSFE solution for both impulse and modulated sinusoidal loading with different frequency content is shown through different examples. In all above cases, comparison with FSFEM are provided to highlight the advantages and limitations of WSFE.     

Finite element methods for contact problems with friction

The numerical treatment of contact problems involves the formulation of the geometry, the statement of interface laws, the variational formulation and the development of algorithms. In this paper an overview with regard to the numerical simulation of frictional problems is presented when general constitutive equations are formulated in the contact interface. To be most general we will apply a geometrical model and its discretization for contact which is valid for large deformations. Furthermore the algorithms to integrate the interface laws will be discussed for the tangential stress components. Special emphasis is laid on the development of algorithms which allow an efficient treatment of frictional contact problems.     

有限元法在结构分析中的应用

主要介绍了有限元法的现状及发展趋势,有限元法的技术路线及有限元分析软件ANSYS。     

大型薄壁焊接卷筒有限元受力计算

结合具体算例,以有限元分析软件Ansys为工具,对大型薄壁焊接卷筒进行受力分析,并与常规校核计算应力结果进行比较,从中得到2种分析结果差异的原因。分析比较发现：弯扭合成应力计算时,引用材料力学空心轴弯扭理论并加以考虑离心力的影响,对分析计算结果尤为重要。     

Finite element method for rigid-plastic analysis of metal forming—Formulation for finite deformation

For the finite element analysis of metal forming processes, a method based on the equilibrium of nodal forces is proposed by assuming the deforming metal to be a slightly compressible rigid-plastic material. As an extension of the method, a formulation for finite deformation is derived on the basis of the equilibrium of nodal forces at the end of incremental deformation. The effects of work-hardening and shape change of element during incremental deformation are incorporated. This formulation is more accurate than that of the simple extension of infinitesimal deformation when dealing with non-steady problems, and is particularly effective for the processes in which the mode of deformation is sensitively changed by the distribution of flow stress and variation of shape. The effectiveness of the method is demonstrated by the examples of a tension test on an axi-symmetric specimen and of the plane-strain compression of blocks.     

考虑几何非线性的结构形状优化灵敏度分析

基于非线性增量有限元理论,给出了全拉格朗日描述下的空间结构优化设计有限元刚度表达式,导出了考虑几何非线性项的结构形状优化位移灵敏度和应力灵敏度的计算公式,并通过数值算例验证了公式的正确性和有效性,同时表明灵敏度分析中,考虑几何非线性项将显著提高优化设计的效率和精度。     

液动压悬浮抛光中磨粒与工件表面作用的数值模拟研究

针对液动压悬浮抛光固-液两相流中固相磨粒与工件表面撞击的过程中,对磨粒以不同的速度和不同的角度撞击工件表面后残余应力沿工件深度方向的分布规律进行了研究,利用ABAQUS软件建立了单颗磨粒撞击工件表面的三维有限元模型。对磨粒流撞击工件表面时的速度场进行了输出,利用PFC/3D软件建立了磨粒流撞击工件表面的三维离散元模型。研究结果表明:随着撞击角度和速度的增大,在工件表层形成的压应力场会增大,沿深度方向残余应力值急剧下降,磨粒流中磨粒间的撞击对磨粒撞击工件表面的速度场影响不大。