Hilber-Hughes-Taylor-α法在接触约束多体系统动力学中的应用

以柔性梁在重力作用下绕转动铰做大范围定轴转动,并与刚性平面发生碰撞这一动力学过程为例,对Hilber-Hughes-Taylor(HHT-α)法在求解含接触约束的柔性多体系统动力学方程时的数值特性进行了研究.系统运动过程的全局动力学仿真由常微分方程组和微分-代数方程组的数值求解构成.柔性梁在无碰撞阶段系统动力学方程是一组常微分方程组.采用接触约束法模拟接触约束过程,系统的动力学方程为指标3的微分-代数方程组.采用HHT-α法对的该微分-代数方程组进行求解,并与Baumgarte违约修正法进行比较.分析了HHT-α法自由参数和违约修正常数对计算效率、动力学响应和系统机械能的影响,并对数值积分方法对模态截断数的敏感度以及速度约束和加速度约束的违约程度进行了分析.结果表明,违约修正常数对仿真结果影响非常明显,而HHT-α法的自由参数α对动力学响应的影响较小,从而避免了违约修正常数对数值积分结果的影响.HHT-α法的自由参数α可以消除碰撞高频模态的影响.     

基于平面问题的位移压力混合配点法

引入压力变量,将弹性力学控制方程表达为位移和压力的耦合偏微分方程组,采用重心插值近似未知量,利用重心插值微分矩阵得到平面问题控制方程的矩阵形式离散表达式.采用重心插值离散位移和应力边界条件,采用附加法施加边界条件,得到求解平面弹性问题的过约束线性代数方程组,采用最小二乘法求解过约束方程组,得到平面问题位移数值解.数值算例验证了所提方法的有效性和计算精度.     

弹性力学的复变量无网格局部 Petrov-Galerkin 法

复变量移动最小二乘法构造形函数, 其优点是采用一维基函数建立二维问题的试函数, 使得试函数中所含的待定系数减少, 从而有效提高计算效率. 文章基于复变量移动最小二乘法和局部Petrov-Galerkin弱形式, 采用罚函数法施加边界条件, 推导相应的离散方程, 提出弹性力学的复变量无网格局部Petrov-Galerkin法. 数值算例验证了该方法的有效性.     

热传导问题的比例边界等几何Mortar方法

将比例边界等几何Mortar方法用于求解热传导问题。该方法可将全域分解为若干子域,针对每个子域分别建模和剖分网格,交界面网格无需逐点匹配;各子域交界面之间的连续条件可被Mortar条件满足;只需对子域的边界采用NURBS基函数进行等几何建模与离散,使问题降低一维,并避免了几何模型与计算模型之间的误差。数值算例表明该方法具有收敛性有保证,计算精度高的特点。     

基于IB-LBFS和绝对节点坐标法的降落伞柔性结构流固耦合数值模拟

在空气动力学、水动力学和生物流体力学领域中,大变形柔性结构的流固耦合现象是一个重要的非线性力学问题.对该系统的数值模拟是分析这一问题的有效手段.将近年提出的一种Descartes流场求解器,即浸润边界-格子Boltzmann通量求解器(immersed boundary-lattice Boltzmann flux solver,IB-LBFS)作为流场求解方法,并引入绝对节点坐标法(absolute nodal coordinate formulation,ANCF)作为大变形结构分析手段,构建了流固耦合求解器以模拟三维流场中的大变形柔性体运动.使用三维来流中的旗帜摆动算例对该流固耦合求解器进行了验证计算.基于该流固耦合求解器对三维不可压流场中的矩形降落伞和十字形降落伞的展开过程进行了非定常流固耦合数值模拟.     

三维燃烧介质和壁面温度的非接触联合重建研究

温度分布在线实时测量对于燃烧过程优化和污染物控制具有重要意义, 针对以往非接触三维温度分布重建过程的耗时性问题和忽略壁面辐射的不足, 本文提出了一种新的离散重建模型, 用于三维吸收、 发射和散射性高温燃烧介质以及壁面温度的快速联合非接触测量. 该模型以四个CCD(Charge Coupled Device) 为测量传感器, 通过构建辐射逆问题求解方程, 从CCD输出的辐射投影图像重建温度分布. 介质中不同投影方向内的辐射传递过程通过离散传递法来描述, 介质的散射和壁面反射则通过离散坐标法来近似. 离散后计算局部辐射强度的病态方程通过最小二乘余量法来求解, 论文对其计算速度进行了优化. 通过非对称温度分布测量算例分析了该模型的有效性, 讨论了测量噪音、 介质和壁面辐射特性对重建精度的影响, 并与其他方法对比分析了模型的重建速度. 计算结果表明本文提出的离散模型可以有效地用于大型高温燃烧介质和壁面温度分布的联合非接触测量. 即使在有噪声的情况下, 该模型也能获得准确的测量结果, 与其他计算方法相比, 采用改进的最小二乘余量法, 能有效地提高温度分布的重建计算速度.     

瞬态热传导问题的复变量重构核粒子法

在重构核粒子法的基础上,引入复变量,讨论了复变量重构核粒子法.复变量重构核粒子法的优点是在构造形函数时采用一维基函数建立二维问题的修正函数.然后,将复变量重构核粒子法应用于瞬态热传导问题的求解,结合瞬态热传导问题的Galerkin积分弱形式,采用罚函数法引入本质边界条件,建立了瞬态热传导问题的复变量重构核粒子法,推导了相应的计算公式.与传统的重构核粒子法相比,复变量重构核粒子法具有计算量小、精度高的优点.最后通过数值算例证明了该方法的有效性. 关键词： 重构核粒子法 复变量重构核粒子法 修正函数 瞬态热传导问题     

数值求解瞬态温度场的有限体积法

本文介绍了求解三维瞬态热传导的有限体积法,给出了控制方程和数值方法。通过一些算例对该方法进行了验证,数值试验结果表明该方法计算稳定、可靠。     

洁净机器人反应转矩观测与碰撞保护研究

提出一种基于反应转矩观测器的机器人碰撞保护方法。机器人的反应转矩由基于模型的干扰观测器估值得到,模型的建立包括电机系统转矩模型与机器人系统动力学模型两部分。由于洁净机器人特殊的构型及关节耦合关系,机器人的动力学建模被大大简化,同时对简化后的模型采用最小二乘法对惯性参数和摩擦参数进行辨识,提高了模型的精度。根据永磁同步电机的转矩模型与机器人动力学模型,可以得到基于电机电流的机器人关节转矩。机器人与外界环境接触时,关节转矩的增加量即为反应转矩。通过设计反应转矩观测器并采用力/位混合控制结构,实现基于电流的机器人主动柔顺控制功能,并在洁净机器人进行碰撞保护实验,实际运行结果验证了该方法的有效性。     

谐和与随机噪声联合作用Duffing单边约束系统的响应

研究了Duffing单边约束系统在谐和与随机噪声联合激励下的响应问题. 用谐波平衡法和摄动法分析了系统在确定性谐和激励和随机激励联合作用下的响应,用随机平均法讨论了随机扰动项对系统响应的影响. 在一定条件下,当约束距离较大时对应于不同的初始条件,系统具有两个非碰撞的稳态响应;而当约束距离不大时,对应于不同的初始条件,系统也可以有两个不同的稳态响应,其中一个是发生碰撞的响应,而另外一个则不发生碰撞. 数值模拟表明该方法是有效的. 关键词： Duffing单边约束系统 随机响应 谐波平衡法 摄动法     

Rayleigh-Taylor不稳定性的Runge-Kutta间断有限元模拟

 采用发展后的间断有限元方法,对Rayleigh-Taylor不稳定性进行了数值模拟。在计算中采用Level-Set方法进行界面追踪,用虚拟流体方法（Ghost Fluid Method,GFM）对界面附近物理量进行等压装配。对两个典型的Rayleigh-Taylor不稳定性算例的数值研究结果表明,采用该方法计算含有接触间断的多介质流体力学问题是有效的,在交界面附近不出现伪振荡,具有较高的分辨率。     

局部间断Petrov-Galerkin方法在大气污染模型中的应用

构造数值模拟两类大气污染模型的局部间断Petrov-Galerkin方法.首先通过变量代换将大气污染模型方程转化为与之等价的一阶微分方程组,再利用间断Petrov-Galerkin方法求解微分方程组.该方法既可以选取不同的检验函数和试探函数空间,又可以保持间断Petrov-Galerkin方法的优势.同局部间断有限元方...     

An improved penalty immersed boundary method for fluid–flexible body interaction

An improved penalty immersed boundary (pIB) method has been proposed for simulation of fluid–flexible body interaction problems. In the proposed method, the fluid motion is defined on the Eulerian domain, while the solid motion is described by the Lagrangian variables. To account for the interaction, the flexible body is assumed to be composed of two parts: massive material points and massless material points, which are assumed to be linked closely by a stiff spring with damping. The massive material points are subjected to the elastic force of solid deformation but do not interact with the fluid directly, while the massless material points interact with the fluid by moving with the local fluid velocity. The flow solver and the solid solver are coupled in this framework and are developed separately by different methods. The fractional step method is adopted to solve the incompressible fluid motion on a staggered Cartesian grid, while the finite element method is developed to simulate the solid motion using an unstructured triangular mesh. The interaction force is just the restoring force of the stiff spring with damping, and is spread from the Lagrangian coordinates to the Eulerian grids by a smoothed approximation of the Dirac delta function. In the numerical simulations, we first validate the solid solver by using a vibrating circular ring in vacuum, and a second-order spatial accuracy is observed. Then both two- and three-dimensional simulations of fluid–flexible body interaction are carried out, including a circular disk in a linear shear flow, an elastic circular disk moving through a constricted channel, a spherical capsule in a linear shear flow, and a windsock in a uniform flow. The spatial accuracy is shown to be between first-order and second-order for both the fluid velocities and the solid positions. Comparisons between the numerical results and the theoretical solutions are also presented.     

多分量流计算的高分辨KFVS有限体积方法

论及高分辨分子动力学通向量分裂（ＫＦＶＳ）有限体积方法的推广。在方法中提出了适当修改Ｍａｘｗｅｌｌ平衡分布用以修复Ｅｕｌｅｒ方程。基于熟知的Ｅｕｌｅｒ方程与Ｂｏｌｔｚｍａｎｎ方程的关系提出了一类求解多分量Ｅｕｌｅｒ方程的高分辨分子动力爱向量分裂（ＫＦＶＳ）有限体积方法,应用该方法不需要求解任何Ｒｉｅｍａｎｎ问题或求附加的非守恒压力方程也需要任何非守恒修正。数值计算表明,数值解在物质界面附近无振荡,     

光滑粒子流体动力学有限元法接触算法研究

 耦合光滑粒子流体动力学（SPH）方法和有限元法（FEM）,是研究冲击动力学问题的一种有效途径。为解决SPH粒子和有限单元间的接触问题,提出了SPH-FEM接触算法。该算法是在有限元节点处设置背景粒子,采用SPH接触算法的思想,计算施加在SPH粒子和有限元节点上的接触力,并且以外力的形式分别加入到SPH动量方程和有限元动力学方程中。利用SPH-FEM接触算法,对两杆撞击以及圆柱形钢弹正冲击钢板发生的冲塞破坏过程进行了三维数值模拟,靶板采用含损伤的Johnson-Cook模型和Grüneisen状态方程,模拟结果与实验结果吻合较好。     

Variational collision integrator for polymer chains

The numerical simulation of many-particle systems (e.g. in molecular dynamics) often involves constraints of various forms. We present a symplectic integrator for mechanical systems with holonomic (bilateral) and unilateral contact constraints, the latter being in the form of a non-penetration condition. The scheme is based on a discrete variant of Hamilton’s principle in which both the discrete trajectory and the unknown collision time are varied (cf. [R. Fetecau, J. Marsden, M. Ortiz, M. West, Nonsmooth Lagrangian mechanics and variational collision integrators, SIAM J. Appl. Dyn. Syst. 2 (2003) 381–416]). As a consequence, the collision event enters the discrete equations of motion as an unknown that has to be computed on-the-fly whenever a collision is imminent. The additional bilateral constraints are efficiently dealt with employing a discrete null space reduction (including a projection and a local reparametrisation step) which considerably reduces the number of unknowns and improves the condition number during each time-step as compared to a standard treatment with Lagrange multipliers. We illustrate the numerical scheme with a simple example from polymer dynamics, a linear chain of beads, and test it against other standard numerical schemes for collision problems.     

非定常Navier-Stokes方程基于两重网格离散的有限元并行算法

基于两重网格离散和区域分解技巧,提出三种求解非定常Navier-Stokes方程的有限元并行算法.算法的基本思想是在每一时间迭代步,在粗网格上采用Oseen迭代法求解非线性问题,在细网格上分别并行求解Oseen、Newton、Stokes线性问题以校正粗网格解.对于空间变量采用有限元离散,时间变量采用向后Euler格式离散.数值实验验证了算法的有效性.     

Mathematical programming methods for the optimal design of turbine blade shapes

This paper describes some optimization techniques for the design of turbine blade profiles with a vibration constraint. The vibration characteristics were modelled by a Timoshenko beam with idealized boundary conditions permitting the system dynamics to be simulated by differential equations. Elliptical cross-sectional shapes were assumed, resulting in an optimization problem in a finite number of variables. The methods used were (1) a direct handling of the differential equations describing the system, in which penalty function transformations were used, and (2) a finite difference discretization with the system equations replaced by finite difference approximations. In the latter formulation the vibrational frequencies are the eigenvalues of the system while in the former case they are regarded as control parameters.This paper includes a numerical study of these methods and their implementation together with a discussion of results.     

Numerical-experimental hybrid method for stress separation in digital gradient sensing method

A numerical-experimental hybrid method for the stress separation in the digital gradient sensing (DGS) method is proposed in this study. In the proposed hybrid method, boundary conditions for a local finite element model, that is, nodal force along boundaries are inversely determined from experimental values obtained by the digital gradient sensing method. The hybrid method follows two stages. In stage 1, the DGS method measures the Cartesian stress gradient components directly and, subsequently, the sum in Cartesian stresses at all interesting points on the surface; stress sum are used to compute the unknown boundary conditions for the local model. In stage 2, the individual stress components are calculated by the direct finite element method using the computed boundary conditions from stage 1. The effectiveness is demonstrated by applying the proposed method to a stress concentration problem involving concentrated load acting on an edge of a large planar sheet. The individual stress components thus determined are summed and compared with analytical stress sum, confirming the effectiveness and accuracy of the proposed technique.