Finite element simulation on the mechanical properties of MHS materials

Finite element simulations are carried out to examine the mechanical behavior of the metallic hollow sphere (MHS) material during their large plastic deformation and to estimate the energy absorbing capacity of these materials under uniaxial compression. A simplified model is proposed from experimental observations to describe the connection between the neighboring spheres, which greatly improves the computation efficiency. The effects of the governing physical and geometrical parameters are evaluated; whilst a special attention is paid to the plateau stress, which is directly related to the energy absorbing capacity. Finally, the empirical functions of the relative material density are proposed for the elastic modulus, yield strength and plateau stress for FCC packing arrangement of hollow spheres, showing a good agreement with the experimental results obtained in our previous study.     

塑性成型弹塑性有限元模拟的静水压力间接计算法

在单元内偏应力导数精度分析的基础上，了偏应力导数佳点逐层积分建立了修正的静水压力间接算法，将该方法应用于金属成型过程的弹塑性有限元模拟中，较好了解决了大步长时应力计算精度低的问题，提高了计算效率，算例表明，在变形总量和应变步长都较大的情况下。用庐方法计算得到的应力和变形载荷仍具有较好的精度。     

流体饱和下高孔隙率储油砂岩力学特性及本构模型

通过对其力学实验结果的分析,以两种破坏理论对油及水饱和下大孔隙率储油砂岩的破坏特征进行了解释,并应用塑性力学的盖帽模型建立了油及水饱和下大孔隙率储油砂岩的本构模型,并应用非线性有限元法进行了数值试验,结果表明,该文提出的模型与实验资料吻合良好,且能较好地模拟大孔隙率砂岩的几种破坏机理及模拟注水采油引起的砂岩附加沉降.     

EXACT SOLUTION OF LARGE DEFORMATION BASIC EQUATIONS OF CIRCULAR MEMBRANE UNDER CENTRAL FORCE

Exact solution of the nonlinear boundary value problem for the basic equation and boundary condition of circular membrane under central force was obtained by using new simple methods. The existence and uniqueness of the solution were discussed by using of modern immovable point theorems. Although specific problem is treated, the basic principles of the methods can be applied to a considerable variety of nonlinear problems.     

基于有限元理论绘制等高线的新方法

由于传统绘制等高线的方法存在很多的缺点，如相邻等高线不协调，等高线交叉重叠等．为了克服这些现象，提出了一种根据地形特征点自动绘制等高线的高效、简便、实用的新方法，其基本思想是建立在样条函数的力学模型基础上，利用弹性薄板的竖向位移比拟地形特征点的标高，从而利用有限元，高精度地绘制出等高线．还通过两个算例，利用有限元通用程序ANSYS进行绘制等高线，来进一步说明该方法的实用性．     

双参数弹性地基上圆板的轴对称大挠度问题

提出将摄动法和积分方程法联合应用于Ｐａｓｔｅｒｎａｋ弹性地基上圆板的轴对称大挠度问题。该方法简明、计算量小、结果可靠。     

Euler杆大挠度屈曲的解析逼近

研究Euler杆大挠度屈曲问题，将控制方程的线性化与谐波平衡法组合起来，分别建立以杆端转角形式表示的屈曲荷载及最大挠度的解析逼近公式，这些公式既适用于小变形又适用于大变形。     

低速冲击载荷下加筋板弹塑动力响应分析

给出了一种半解析方法求解加筋板在横向低速冲击载荷下的非线性弹塑动力响应分析。考虑大变形的影响，采用增量型本构关系，得到膜力、弯矩增量与应变增量的关系，忽略面内惯性力的影响，运用Hamilton变分原理，得到加筋板增量形式动响应控制方程，最后采用增量形式的迦辽金法来求解。     

On the Use of Implicit Integration Methods and the Absolute Nodal Coordinate Formulation in the Analysis of Elasto-Plastic Deformation Problems

In the general theory of continuum mechanics, the state of rotation and deformation of material points can be uniquely defined from the displacement field by using the nine independent components of the displacement gradients. For this reason, the use of the absolute rotation parameters as nodal coordinates, without relating them to the displacement gradients, leads to coordinate redundancy that leads to numerical and fundamental problems in many existing large rotation finite element formulations. Because of this fundamental problem, special measures that require modifications of the numerical integration methods were proposed in the literature in order to satisfy the principle of work and energy. As demonstrated in this paper, no such measures need to be taken when the finite element absolute nodal coordinate formulation is used since the principle of work and energy are automatically satisfied. This formulation does not suffer from the problem of coordinate redundancy and ensures the continuity of stresses and strains at the nodal points. In this study, the use of the implicit integration methods with the consistent Lagrangian elasto-plastic tangent moduli is examined when the absolute nodal coordinate formulation is used. The performance of different numerical integration methods in the dynamic analysis of large elasto-plastic deformation problems is investigated. It is shown that all these methods, in the case of convergence, yield a solution that satisfies the principle of work and energy without the need of taking any special measures. Semi-implicit integration methods, however, can lead to numerical difficulties in the case of very stiff problems due to the linearization made in these methods in order to avoid the iterative Newton--Raphson procedure. It is also demonstrated that the use of the consistent Lagrangian-plastic tangent moduli derived in this investigation using the absolute nodal coordinate formulation leads to better convergence of the iterative Newton--Raphson procedure used in the implicit integration methods.