Rotationless formulation for large deformations in flexible multibody dynamics

Especially for specific applications, such as contact problems, computer methods for flexible multibody dynamics that are able to treat large deformation phenomena are important. Classical formalisms for multibody dynamics are based on rigid bodies. Their extension to flexible multibody systems is typically restricted to linear elastic material behavior whereas large deformation phenomena are formulated in the framework of the nonlinear finite element method. In the talk we address computer methods that can handle large deformations in the context of multibody systems. In particular, the link between nonlinear continuum mechanics and multibody systems is facilitated by a specific formulation of rigid body dynamics [1]. It makes possible the incorporation of state-of-the-art computer methods for large deformation problems. In the talk we focus on the treatment of large deformation contact whithin flexible multibody dynamics [2]. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于EEP法的一维有限元自适应求解

基于新近提出的一维有限元后处理超收敛算法——单元能量投影（EEP）法,将有限元自适应求解问题转化为对超收敛解答的自适应分段多项式插值问题;对于大多数问题,一步便可获得满意的有限元网格划分,在该网格上再次进行有限元计算,一般即可获得满足用户给定的误差限的有限元解答．即便未能完全满足精度要求,一般只需局部细分加密网格一至二步即可．该法简单实用、高效可靠,是一个颇具优势和潜力的自适应方法．以二阶椭圆型常微分方程模型问题为例,对该法的基本思想、实施策略及具体算法做一介绍,并给出有代表性的数值算例用以展示该法的优良性能和效果．     

Combined unstructured and hanging-node-based remeshing with boundary control for metal forming simulations

During finite element simulation of metal forming process, the mesh which represents the workpiece undergoes extreme large deformation, which could result in highly distorted mesh and numerical failure in simulation. To overcome the problem and improve computation efficiency, advancing front quad meshing technique and non–conforming mesh refinement approach are combined to generate new mesh according to desired mesh size distribution. Application of the combined remeshing strategy to rolling simulation will be presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling and simulation of multiple impacts of falling rigid bodies

When an electronic device drops at an inclination angle to the floor, the rapid successions of clattering sequence are important for their shock response to circuits, displays and disk drives. This article deals with both analytical and numerical analysis of multiple impacts. A three-dimensional computational dynamics code with a continuous contact impact model has been developed to simulate the multiple impacts of a falling rigid body with the ground. Results from the computational model as well as analytic analysis from a discrete contact impact model indicate that subsequent impacts might be larger than the initial impact in some situations. The differential equation based three-dimensional model is shown to be realistic in simulating a multiple-impact sequence and laid a foundation for detailed finite element analysis of the interior impact response of an electronic device.     

A Holistic Simulation Approach from a Measured Load to Element Stress Using Combined Multi-body Simulation and Finite Element Modelling

The design of vehicle bodies requires the knowledge of the vehicle's structural response to external loads and disturbances. In rigid multi-body simulation the dynamic behaviour of complex systems is calculated with rigid bodies and neglect of body elasticity. On the other hand, in finite element models large degree of freedom numbers are used to represent the elastic properties of a single body. Both simulation methods can be combined, if the finite element model size is reduced to a degree of freedom number feasible to multi-body simulation. The application to practical purposes requires the use and interconnection of several different software tools. In this contribution a holistic method is presented, which starts with the measurement or synthesis of loads and excitations, continues with the integration of a reduced finite element model into a multi-body system, the dynamic response calculation of this combined model, and concludes with the result expansion to the full finite element model for calculating strain and stress values at any point of the finite element mesh. The applied software tools are Simpack, Nastran, and Matlab. An example is given with a railway vehicle simulated on measured track geometry. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A time finite element method for structural dynamics

A time (Galerkin) finite element method (time FEM) for structural dynamics is proposed in this paper. The key lies in a variational formulation that is well-posed and equivalent to the conventional strong form of governing equations of structural dynamics. Based on the variational formulation, a time finite element formulation is naturally established and its convergence property is easily derived through an a priori error analysis. Technical details on practical implementation of the time FEM are presented. Numerical examples are studied to verify the proposed time FEM.     

Real-Time Simulation of Elastic Multibody Systems with Application in Vehicle Dynamics

Real-time simulation models are widely used for vehicle development, usually built up as rigid multibody systems. However, since lightweight structures are commonly used, body deformation is no longer negligible and rigid multibody simulations may be inaccurate. This work presents a real-time capable full vehicle model with a flexible car body, derived from a finite element model, whose performance has been improved by model order reduction. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

3D dynamic modeling of powder forming processes via a simple and efficient node-to-surface contact algorithm

In this paper, a simple and efficient contact algorithm is presented for the evaluation of density distribution in three-dimensional dynamic modeling of powder compaction processes. The contact node-to-surface algorithm is employed to impose the contact constraints in large deformation frictional contact, and the contact frictional slip is modified by the Coulomb friction law to simulate the frictional behavior between the rigid punch and the work-piece. The 3D nonlinear contact friction algorithm is employed together with a double-surface cap plasticity model within the framework of large finite element deformation in order to predict the non-uniform relative density distribution during the dynamic simulation of powder die-pressing. The accuracy and robustness of contact algorithm is verified by the impact analysis of two elastic rods, which is compared with the analytical solution. Finally, the performance of computational schemes is illustrated in dynamic modeling of a set of powder components.     

Finite element simulation of compressible particle-laden gas flows

A macroscopic two-fluid model of compressible particle-laden gas flows is considered. The governing equations are discretized by a high-resolution finite element method based on algebraic flux correction. A multidimensional limiter of TVD type is employed to constrain the local characteristic variables for the continuous gas phase and conservative fluxes for a suspension of solid particles. Special emphasis is laid on the efficient computation of steady state solutions at arbitrary Mach numbers. To avoid stability restrictions and convergence problems, the characteristic boundary conditions are imposed weakly and treated in a fully implicit manner. A two-way coupling via the interphase drag force is implemented using operator splitting. The Douglas-Rachford scheme is found to provide a robust treatment of the interphase exchange terms within the framework of a fractional-step solution strategy. Two-dimensional simulation results are presented for a moving shock wave and for a steady nozzle flow.     

Application of the string method to compute minimum energy paths for a chain of bi-stable elements using the finite element method and molecular dynamics

Activated processes are frequently found in solid state mechanics. The energy landscape of such processes show a non-convex behaviour, and therefore the computation of energy barriers between two stable minima is of importance. Such barriers are revealed by computing minimum energy paths. The string method is a simple and efficient algorithm to move curves over an energy landscape and to identify minimum energy paths. A hierarchical two-scale model recently introduced to the literature (molecular dynamics coupled with the finite element method) is used in this paper to investigate the string method in a model phase transition in a copper single crystal. To do so, bi-stable elements are constructed and the energetic behaviour of a two-elements chain is investigated. We identify successfully the minimum energy path between two local stable minima of the chain and demonstrate thereby the performance of the string method applied to a complex multiscale model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于最佳超收敛阶EEP法的一维有限元自适应求解

基于新近提出的具有最佳超收敛阶的单元能量投影（EEP）超收敛算法,提出用具有最佳超收敛阶的EEP超收敛解对有限元解进行误差估计,用均差法进行网格划分,用拟有限元解进行多次遍历而不反复求解有限元真解,形成一套新型的一维有限元自适应求解策略．该法理论上简明清晰,算法上高效可靠,对于大多数问题,一步自适应迭代便可给出按最大模度量逐点满足误差限的有限元解答．以二阶椭圆型常微分方程模型问题为例,介绍了该法的基本思想、实施策略及具体算法,并给出具有代表性的数值算例,以展示该法的优良性能和效果．     

Blast Damage Simulation With the Discontinuous Galerkin Finite Element Method of Bond⁃Based Peridynamics北大核心CSCD

近场动力学是一种积分型非局部的连续介质力学理论,已广泛应用于固体材料和结构的非连续变形与破坏分析中,其数值求解方法主要采用无网格粒子类的显式动力学方法.近年来,弱形式近场动力学方程的非连续Galerkin有限元法得到发展,该方法不仅可以描述考察体的非局部作用效应和非连续变形特性,还可以充分利用有限单元法高效求解的特点,并继承了有限元法能直接施加局部边界条件的优点,可有效避免近场动力学的表面效应问题.该文阐述了键型近场动力学的非连续Galerkin有限元法的基本原理,导出了计算列式,给出了具体算法流程和细节,计算模拟了脆性玻璃板动态开裂分叉问题,并对爆炸冲击荷载作用下混凝土板的毁伤过程进行了计算分析.研究结果表明,该方法能够再现爆炸冲击荷载作用下结构的复杂破裂模式和毁伤破坏过程,且具有较高的计算效率,是模拟结构爆炸冲击毁伤效应的一种有效方法.     

Formulation and evaluation of a finite element model for the linear analysis of stiffened composite cylindrical panels

A finite element model for linear static and free vibration analysis of composite cylindrical panels with composite stiffeners is presented. The proposed model is based on a cylindrical shell finite element, which uses a first-roder shear deformation theory. The stiffeners are curved beam elements based on Timoshenko and Saint-Venant assumptions for bending and torsion respectively. The two elements are developed in a cylindrical coordinate system and their stiffness matrices result from a hybrid-mixed formulation where the element assumed stress field is such that exact equilibrium equations are satisfied. The elements are free of membrane and shear locking with correct satisfaction of rigid body motions. Several examples dealing with stiffened isotropic and laminated plates and shells with eccentric as well as concentric stiffeners are analyzed showing the validity of the models.     

A modular and efficient approach to computational modeling and sensitivity analysis of robot and human motion dynamics

In this paper a new class library for the computation of the forward multi-body-system (MBS) dynamics of robots and biomechanical models of human motion is presented. By the developed modular modeling approach the library can be flexibly extended by specific modeling elements like joints with specific geometry or different muscle models and thus can be applied efficiently for a number of dynamic simulation and optimization problems. The library not only provides several methods for solving the forward dynamics problem (like articulated body or composite rigid body algorithms) which can transparently be exchanged. Moreover, the numerical solution of optimal control problems, like in the forward dynamics optimization of human motion, is significantly facilitated by the computation of the sensitivity matrix with respect to the control variables. Examples are given to demonstrate the efficiency of the approach. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reduced multiscale computation on adapted grid for the convection-diffusion Robin problem

We propose a reduced multiscale finite element method for a convection-diffusion problem with a Robin boundary condition. The small perturbed parameter would cause boundary layer oscillations, so we apply several adapted grids to recover this defect. For a Robin boundary relating to derivatives, special interpolating strategies are presented for effective approximation in the FEM and MsFEM schemes, respectively. In the multiscale computation, the multiscale basis functions can capture the local boundary layer oscillation, and with the help of the reduced mapping matrix we may acquire better accuracy and stability with a less computational cost. Numerical experiments are provided to show the convergence and efficiency.     

离散系统运动方程的Galerkin有限元EEP法自适应求解

对于结构动力分析中的离散系统运动方程,现有算法的计算精度和效率均依赖于时间步长的选取,这是时间域问题求解的难点.基于EEP(element energy projection)超收敛计算的自适应有限元法,以EEP超收敛解代替未知真解,估计常规有限元解的误差,并自动细分网格,目前已对诸类以空间坐标为自变量的边值问题取得成功.对离散系统运动方程建立弱型Galerkin有限元解,引入基于EEP法的自适应求解策略,在时间域上自动划分网格,最终得到所求时域内任一时刻均满足给定误差限的动位移解,进而建立了一种时间域上的新型自适应求解算法.     

A Lagrange multiplier/fictitious domain method for the numerical simulation of incompressible viscous flow around moving rigid bodies: (I) case where the rigid body motions are known a priori

We describe in this Note a method for the numerical simulation of incompressible viscous flow around moving rigid bodies; we suppose the rigid body motions a priori known. The computational technique takes advantage of a time discretization by operator splitting à la Marchuk-Yanenko and of a finite element space discretization on a fixed mesh, to combine a Lagrange multiplier/fictitious domain treatment of the rigid body motions with an L²-projection technique, to force the incompressibility condition. The results of numerical experiments concerning flow around moving disks at Reynolds number of the order of 100 are presented.     

Modelling and computation of acrylic bone cement injection and curing within the framework of vertebroplasty

This contribution deals with the simulation based investigation of processes related to the surgical treatment of vertebroplasty. In this regard, a simulation framework has been developed, which includes the generation of microstructural computer models of cancellous bone structures, the simulation of bone cement injection by computational fluid dynamics (CFD) methods and finite element (FE) simulations of bone cement curing processes. The modelling and computation strategy is illustrated and different material modelling approaches for the representation of acrylic bone cements as a non-linear fluid and a non-linear viscoelastic solid with curing dependent properties are outlined. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Energy harvesting through arterial wall deformation: A FEM approach to fluid–structure interactions and magneto-hydrodynamics

Engineers are confronted with the energy demand of active medical implants in patients with increasing life expectancy. Scavenging energy from the patient’s body is envisioned as an alternative to conventional power sources. Joining in this effort towards human-powered implants, we propose an innovative concept that combines the deformation of an artery resulting from the arterial pressure pulse with a transduction mechanism based on magneto-hydrodynamics. To overcome certain limitations of a preliminary analytical study on this topic, we demonstrate here a more accurate model of our generator by implementing a three-dimensional multiphysics finite element method (FEM) simulation combining solid mechanics, fluid mechanics, electric and magnetic fields as well as the corresponding couplings. This simulation is used to optimize the generator with respect to several design parameters. A first validation is obtained by comparing the results of the FEM simulation with those of the analytical approach adopted in our previous study. With an expected overall conversion efficiency of 20% and an average output power of 30 μW, our generator outperforms previous devices based on arterial wall deformation by more than two orders of magnitude. Most importantly, our generator provides sufficient power to supply a cardiac pacemaker.     

Transient Finite Element Simulation of the Temperature Field during Cryogenic Turning of Metastable Austenitic Steel AISI 347

The process chain in manufacturing often consists of many steps. As part of current researches the possibility of combining two process steps, turning and hardening, is investigated to optimize the manufacturing time and to decrease the energy consumption of the process. For metastable austenitic steels, deformation induced hardening during turning can be used to achieve surface hardening [1] and thus to increase the wear resistance [2] as well as the fatigue strength [3], by applying high passive forces onto the workpiece. This enables an austenite-martensite phase transformation, for which it is necessary to maintain low process temperatures, typically below room temperature. Thus, cryogenic coolants are applied [4]. For a better understanding of the influence of cutting parameters on the process temperatures and thus martensite formation, knowledge of the exact temperature distribution in the workpiece and in the contact zone between workpiece and tool is essential. Since the experimental determination of the temperature field is hardly possible, an inverse determination of the process temperatures via transient finite element simulation is performed. The present finite element approach only takes thermal loads into account. The simulations are performed in the finite element program FEAP (Finite Element Analysis Program) with an Eulerian mesh, which requires special consideration of the rigid body rotation of the workpiece. In order to prevent unphysical oscillations in the solution, introduced by the convective time derivative, a streamline upwind / Petrov–Galerkin stabilization scheme is utilized. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)