摩擦约束有限变形弹塑性广义变分不等原理

在弹塑性接触问题中,从变分原理出发来研究接触问题,可以将摩擦力纳入问题的能量泛函以便于问题的求解,尤其是数值解。研究了带摩擦约束的有限变形弹塑性接触问题,利用拉格朗日乘子法,证明了有限变形弹塑性接触问题的广义变分不等原理,导出了率形式的能量泛函,为摩擦约束有限变形弹塑性接触问题的数值解提供了理论基础。     

摩擦约束有限变形非线性弹性广义变分不等原理的半反推法

研究了有限变形非线性弹性接触问题变分不等方程的逆问题 ,用半反推法成功地导出了变分不等问题的势能型能量泛函 ,并巧妙地处理了由于变分不等式引起的困难。     

弹性理论中广义变分原理的研究及其在有限元计算中的应用

本文的目的在于说明怎样系统地建立各种广义变分原理,怎样合理地使用各种广义变分原理来改进有限元计算的成效。为了易于说明问题,本文只局限于弹性理论的各种广义变分原理,但其推广并不困难。本文指出,广义变分原理的泛函,可以系统地采用拉格朗日乘子法,把一般有条件的变分原理化为无条件的变分原理来唯一地决定的。拉格朗日所代表的物理量,可以通过变分求极值或驻值的过程求得,从而消除了在建立广义变分原理的泛函时,人们经常陷入的象猜谜一样的困境。本文也指出：我们同样可以用拉格朗日乘子法,把一般有多个条件的变分原理,化为条件个数较少的变分原理。我们称变分条件减少了的变分原理为各级不完全的广义变分原理。凡是全部变分条件都消除了的变分原理,称为完全的广义变分原理,或简称广义变分原理;实际上是完全无条件的变分原理。本文建立了弹性小位移变形理论中的各级不完全的广义位能原理和各级不完全的广义余能原理,包括从最小位能原理和最小余能原理分别导出的最完全的广义变分原理,且并证明了这两个弹性力学广义变分原理的泛函是等同的。在这些广义变分原理中,包括了HELLINGER REISSNER（1950）[1],[2],胡海昌－鹫津久一郎[3],[4]的广义变分原理。本文也建立了弹性大移位变形中的位能原理和余能原理,并建立了有关位能余能的各级不完全的广义变分原理,包括从大位移变形的最小余能原理分别导出的弹性力学广义变分原理,并且也证明了大位移变形情况下,这两个弹性力学的广义变分原理也是同等的。本文除了列举广义变分原理在有限元法上的众所周知的应用外,还补充三个比较重要的应用范围。     

基于邻域多边形特征和能量优化的网格参数化

针对复杂网格曲面提出了一种基于点邻域多边形特征和能量优化的网格曲面参数化方法。首先利用相邻两边夹角和长度比例建立节点邻域多边形特征方程组,通过求解一个约束优化问题将曲面网格展平到二维平面上;在网格曲面展平过程中不可避免会产生弹性变形能,然后采用能量优化方法释放曲面展平过程中的弹性变形能,最终得到网格曲面参数化结果。计算结果表明,该方法能得到较好的参数化结果,适用于复杂曲面的网格重划分等计算机辅助设计的应用。     

摩擦约束有限变形非线性弹性广义变分等原理的半反推法

研究了有限变形非线性弹性接触问题变分不等方程的逆问题,用半反推法成功地导出了变分不等问题的势能型能量泛函,并巧妙地处理了由于变分不等式引起的困难.     

弹性压杆稳定计算的方块脉冲函数法

弹性压杆特别是变截面压杆，要推导出其稳定方程和计算临界载荷是十分繁琐甚至是不可能的。这里利用方块脉冲函数(BPF)的良好运算性质直接求解弹性压杆稳定的能量泛函极值，将计算临界载荷转化为求矩阵的特征值问题，从而得到了计算弹性压杆失稳临界载荷的一种新的数值方法。该方法对于等截面压杆和变截面压杆均适用，具有计算简洁、便于计算机处理等优点，有很好的工程应用价值。     

有限单元法概述(第一讲)

有限单元法在最初是根据变分原理来求解数学物理问题的一种数值计算方法。到了60年代,许多学者对各种不同变分原理的有限单元法计算公式作了进一步的发展,曾有人从能量平衡原理出发,推出热弹性问题有限元解析的方程组,或者利用迦辽金法得出平面弹性问题     

大型锻件内部空洞缺陷修复条件

介绍大型锻件内部空洞缺陷修复条件在理论研究和生产中的作用及研究现状.针对非线性粘性材料,建立以空洞周围速度场和远场应力、应变速率表示的泛函.对于由体积不可压缩材料构成的含有空洞的无限体而言,锻造过程中空洞周围的真实速度场总是使该泛函取极小值,借助泛函的变分可求得空洞边界速度与远场应力、应变的关系,锻造变形后空洞的形状.为使设计的速度场能表征空洞的变形特点,加快泛函极小化的收敛速度,采用叠加速度场.研究大型锻件镦粗工序中锻坯内部球形空洞的闭合情况.结果表明,随着空洞体积的减小,远场应力、应变迅速增大,仅靠远场应力的增大使空洞闭合是非常困难的,因此大锻件技术要求中应允许有未闭合的微小空洞存在.在理论分析的基础上进行试验研究,结果表明理论计算结果与实测结果相差不大.     

多目标不完全拆卸线平衡问题的建模与优化

针对实际生产中在满足约束条件下仅考虑拆卸需求零件和危害零件的特点,以工作站数目、空闲时间均衡指标和拆卸成本为优化目标,构建了不完全拆卸线平衡问题多目标模型。基于解的离散性和优化目标的多重性,提出一种Pareto解集思想的变邻域-粒子群融合算法。该算法通过建立拆卸任务和粒子群迭代搜索的对应关系,将变邻域搜索作为局部搜索策略,同时引入Pareto解集思想、拥挤距离机制处理多目标问题,以保证求解结果的多样性;通过Hyper-volume指标解决了多目标优化难以评价算法收敛性能及Pareto解集优劣等问题。采用所提算法求解不同规模完全拆卸线平衡问题测试算例,其中不同搜索深度的对比试验表明了变动搜索深度能很好地兼顾求解质量和求解效率,不同算法的对比试验表明了所提算法的优越性。最后,将所提模型与求解方法应用至某打印机不完全拆卸线的设计中。     

基于归一化超拉普拉斯先验项的运动模糊图像盲复原

基于变分方法提出了一种运动模糊退化图像的盲复原算法.考虑自然场景的图像梯度符合长拖尾概率分布,提出的方法采用归一化的超拉普拉斯先验项作为变分能量方程中的光滑项,从而有利于图像在去模糊的求解过程中正确解收敛.由于建立的能量方程不是严格凸的函数,故引入了分裂方法进行求解.整个运动模糊退化图像的盲复原过程在多尺度框架下由粗到细尺度渐进执行.最后利用估计出的点扩展函数计算清晰图像.相对于传统的盲复原算法,本文提出的算法不需要预测图像的梯度信息和对梯度进行筛选,直接求解能量方程就能够得到相应的正确解.得到的结果验证了本文算法的有效性.     

Proximal-point method for finite element model updating problem

The problem of finding the optimal approximation to analytical stiffness matrix modeled by the finite element method is considered in this paper. Desired matrix properties, including satisfaction of the dynamic equation, symmetry, positive semidefiniteness and physical connectivity, are imposed as side constraints of the minimization problem. To the best of the author's knowledge, the finite element model updating problem containing all these constraints simultaneously has not been proposed in the literature earlier. By partial Lagrangian multipliers technique, the optimization problem is transformed into a matrix linear variational inequality and the proximal-point method is first used to solve the equivalent problem. The results of numerical examples show that the proposed method works well even for incomplete measured data.     

A symplectic pseudospectral method for nonlinear optimal control problems with inequality constraints

A symplectic pseudospectral method based on the dual variational principle and the quasilinearization method is proposed and is successfully applied to solve nonlinear optimal control problems with inequality constraints in this paper. Nonlinear optimal control problem is firstly converted into a series of constraint linear-quadratic optimal control problems with the help of quasilinearization techniques. Then a symplectic pseudospectral method based on dual variational principle for solving the converted constrained linear-quadratic optimal control problems is developed. In the proposed method, inequality constraints which can be functions of pure state, pure control and mixed state-control are transformed into equality constraints with the help of parameteric variables. After that, state variables, costate variables and parametric variables are interpolated locally at Legendre-Gauss-Lobatto points. Finally, based on the parametric variational principle and complementary conditions, the converted problem is transformed into a standard linear complementary problem which can be solved easily. Numerical examples show that the proposed method is of high accuracy and efficiency.     

Springback prediction and optimization of variable stretch force trajectory in three-dimensional stretch bending process

Most of the existing studies use constant force to reduce springback while researching stretch force. However, variable stretch force can reduce springback more efficiently. The current research on springback prediction in stretch bending forming mainly focuses on artificial neural networks combined with the finite element simulation. There is a lack of springback prediction by support vector regression(SVR). In this paper, SVR is applied to predict springback in the three-dimensional stretch bending forming process, and variable stretch force trajectory is optimized. Six parameters of variable stretch force trajectory are chosen as the input parameters of the SVR model. Sixty experiments generated by design of experiments(DOE) are carried out to train and test the SVR model. The experimental results confirm that the accuracy of the SVR model is higher than that of artificial neural networks. Based on this model, an optimization algorithm of variable stretch force trajectory using particle swarm optimization(PSO) is proposed. The springback amount is used as the objective function. Changes of local thickness are applied as the criterion of forming constraints. The objection and constraints are formulated by response surface models. The precision of response surface models is examined. Six different stretch force trajectories are employed to certify springback reduction in the optimum stretch force trajectory, which can efficiently reduce springback. This research proposes a new method of springback prediction using SVR and optimizes variable stretch force trajectory to reduce springback.     

Optimum design of structures with stress and displacement constraints using the force method

A new structural analysis and optimization algorithm is developed to determine the minimum weight of structures with the truss and beam-type members under displacement and stress constraints. The algorithm combines the mathematical programming based on the sequential quadratic programming (SQP) technique and the finite element technique based on the integrated force method. The equilibrium matrix is generated automatically through the finite element analysis while the compatibility matrix is obtained directly using the displacement–deformation relations and the single value decomposition (SVD) technique. By combining the equilibrium and compatibility matrices with the force–displacement relations, the equations of equilibrium with the element forces as variables are obtained. The proposed method is extremely efficient to analyze and optimize the truss and beam structures under stress and displacement constraints. The computational effort required by the force method is found to be significantly lower than that of the displacement method. The effect of the geometric nonlinearity in the structural optimization problems under the stress and displacement constraints were also investigated and it is illustrated that the geometric nonlinearity is not an important issue in these types of problems and hence, it does not affect the final optimum solution significantly. Four examples illustrate the procedure and allow the results to be compared with those reported in the literatures.     

Finite plastic deformation of a circular membrane under hydrostatic pressure—II : Strain-rate effects

The large strain behaviour of a circular membrane under uniform hydrostatic pressure is examined for materials with transversely isotropic plastic properties. Time-independent material response is assumed, and both flow theory and deformation theory of plasticity are considered.A variational principle is first applied to derive the governing equations for the pressurized membrane. It is shown that a special solution previously given by Hill[7] for isotropic materials can readily be extended to certain transversely isotropic membranes.A finite element solution based on Hill's extremum principle[24] is then developed to study the influence of anisotropy on the finite deformation behaviour of the membrane. Conditions where localized-necking bifurcations become possible are also discussed.     

二维草图变量化设计中的混合法求解

变量化技术是当代ＣＡＤ技术的核心,以实现变量化设计为目的的几何约束求解有多种方法,但它们都存在一定的局限性。本文在讨论草图设计模型与基于几何约束图形表达方式的基础上,综合变量几何法和人工智能法的优点,提出了二维草图变量化设计中的几何约束混合法求解策略,该方法能够快速地进行约束求解及一致性检查,同时充分利用原图信息解决图形的二义性问题。     

Finite plastic deformation of a circular membrane under hydrostatic pressure—I: Rate-independent behaviour

The large strain behaviour of a circular membrane under uniform hydrostatic pressure is examined for materials with transversely isotropic plastic properties. Time-independent material response is assumed, and both flow theory and deformation theory of plasticity are considered.A variational principle is first applied to derive the governing equations for the pressurized membrane. It is shown that a special solution previously given by Hill[7] for isotropic materials can readily be extended to certain transversely isotropic membranes.A finite element solution based on Hill's extremum principle[24] is then developed to study the influence of anisotropy on the finite deformation behaviour of the membrane. Conditions where localized-necking bifurcations become possible are also discussed.     

滑动轴承非线性油膜力的一维直接解法

滑动轴承的油膜力,特别在雷诺边界条件下,并不存在解析解。一般采用有限差分方法或迭代算法求解方 程,因计算量偏大不适合轴承非线性动力分析。针对滑动轴承轴瓦形状比较规则和轴向压力分布较为简单的特点, 把二维变分不等方程降阶为一维形式,并提出一维变分不等方程的直接解法,无需迭代便可求出节点压力及油膜 破裂边界。与二维有限元互补算法相比,直接解法误差小于百分之一,而且其运算时间也仅为其百分之一。