基于动力特征分区的显式-精细混合积分法

大型动力系统中常因局部的高频振动及非线性等特性限制了系统的积分步长而导致整体计算量激增，针对此问题提出一种分区域异步长显式-精细混合积分方法。在特性复杂的局部区域采取显式积分法，根据精度和稳定性要求取较小的时间步长求解；在其余常规区域则应用精细积分方法，采取可以跨越显式积分区周期的大积分步长求解。对于精细积分区域边界荷载，提出一种基于离散FFT变换的线性项与主频谐波项的组合表示方法，并给出了此种荷载形式下的精细积分计算格式。数值算例结果表明该法能够明显提高计算效率，在显式积分区域和精细积分区域都有很高的精度。     

与荷载同步变化的时间步自动调整方法

为了提高计算效率,针对结构动力时程分析中由时间步长引起的误差,建立了时间步长与相对误差之间的关系式,实现了满足目标误差限的时间步自动调整,丰富了时间自适应理论。通过与解析解的对比,验证了该方法在提高计算效率方面的有效性。在局部,荷载变化越快,对应的自适应时间步长越小;荷载变化越慢,对应的自适应时间步长越大。该方法可以有效解决在冲击荷载、振动荷载、爆炸荷载或地震荷载的动力数值计算中,因时间步长的设置不当导致计算结果发散甚至计算中断的问题。     

基于EBE策略实现结构动力响应的并行计算

基于EBE(Element by Element)策略的并行算法不用形成总体刚度矩阵,而且无需进行三维模型的区域分解,从而提高并行计算的速度和效率,是实现结构动力响应快速分析的有效途径。采用Newmark法,结合EBE并行算法和Jacobi预处理技术实现结构动力方程的并行计算。在此基础上,利用虚拟激励方法实现结构随机振动的并行计算。最后在网络集群环境下,综合运用多种编程语言和分析工具,应用该并行算法对三维零件的冲击响应以及随机振动进行仿真计算,并与Ansys、精细时程积分法的相比较。结果表明,该并行算法的计算误差小,并行效率较高,适用于工程计算。     

工程结构非线性动力响应数值分析中零能量模态控制对响应的影响

在工程结构非线性动力响应数值分析中,通常采用显式积分格式。这样可避免大量的刚度矩阵求逆叠代运算。但显式积分有条件稳定的,从而时间步长△t的取值受到限制,这样必导致进行大量的小时间步长循环计算。为了减少计算量,通常采用高斯积分一类的数值积分。单点高斯积分的采用可引起hourglass模态。控制hourglass模态是结构非线性动力响应数值分析中必须解决的问题之一。本文以八节点六面体实体单元单点高斯积分为例详细分析了hourglass模态产生的机理,并在此基础上讨论了hourglass模态的控制措施及具体应用。通过数值算例分析发现hourglass模态控制的采用对正常动力响应模态造成一定的影响。     

任意随机激励下结构随机振动分析的一种数值方法

应用复化Cotes数值积分方法改进精细积分方法,建立一种新的高效的精细积分方法：C-PTSIM,并基于有限元理论讨论了此方法在任意随机激励下线性结构随机动力响应的应用。采用复化Cotes积分方法计算结构动力响应状态方程一般解的积分项,推导出随机激励下结构动力响应的显式表达式,利用一阶矩和二阶矩运算规律计算结构响应的均值和方差。C-PTSIM方法避免了精细积分过程中系数矩阵求逆问题,有效改善了精细积分在时间步长内载荷线性化假设带来的误差,在不改变时间步长时采用高次数复化积分时获得与更精细步长时同样精度的结果,表明该方法对时间步长的弱敏感性,并能节省大量的计算时间。基于此方法给出结构随机振动响应分析算例,并与其他方法对比,说明了该方法的高效率和高精度。     

结构动力方程的一种自适应步长增维精细积分法EI北大核心CSCD

增维精细积分法是一种求解结构动力方程的高精度逐步积分算法,其步长的选取会对计算精度产生极大的影响,在实际应用中存在难以确定合适步长的问题。为满足实际工程中对计算精度和效率的要求,提出了一种计算误差的估计方法,并以估计误差和迭代收敛速度为基准,建立了一种自适应步长增维精细积分法。针对三种结构动力方程的算例结果表明,在计算各类线性及非线性振动问题时,该方法均可以在保证计算精度的前提下快速有效地控制算法的计算步长,并且仅需较少的额外计算消耗,显著提高了增维精细积分法的计算效率,使该方法在求解结构动力方程时更具计算优势和实用价值。     

工程结构非线性动力响应数值分析显式积分格式的研究

工程结构非线性动力响应数值分析中时间积分的处理是其难点之一,它关系到此类动力响应分析程序的运算效率及分析精度。本文详细介绍了有限元直接积分法中显式积分格式及其稳定性条件。通过分析可看出,对于求解强冲击载荷作用下的非线性结构动力响应及波传播等问题,显式算法是一种好的选择。文中给出了各种类型单元稳定性条件下临界时间步长△tcrit的计算公式,并以数值算例给出了实现的步骤。     

一种工程实用的数值积分方法

在实际工程结构动力反应分析中,往往由于结构型式十分复杂,常用的两种直接积分方法,即显式积分方法和隐式积分方法,在使用中都存在着一定的局限性,如何将这两种积分方法合理有效地结合起来,是一个十分有意义的研究课题。针对实际工程问题中整体结构计算时间步长的选择往往受局部区域的材料特性、尺寸大小等因素影响的这一现象,提出了一种对结构局部区域进行隐式积分、对其余区域进行显式积分的工程实用的显隐式数值积分方法,这种积分格式相对于显式积分格式而言,能显著提高整体结构的计算速度。最后采用三个数值计算实例对这一方法进行验证。     

网络机群下多项式预处理EBE-PCG并行算法设计与实现

针对单机上实现困难，计算费用高昂的大规模结构动力学问题，本文采用将总体运算分解到单元上进行的EBE计算策略和基于区域分裂的SBS存储和任务分配策略，设计了粗粒度EBE－PCG并行算法，并在网络机群环境下得以实现。在PCG迭代法中分别采用Jacobi预处理矩阵和多项式预处理矩阵，比较它们的迭代求解效率。悬臂梁受冲击载荷与吉普车车架振动响应分析问题的数值算例，证明了该算法不但能够显著地提高问题的求解规模，适合大规模结构分析计算；而且还能获得良好的并行效率，是一种适合网络机群并行环境的有效的粗粒度并行算法。     

基于Bathe隐式算法的结构动力学显式算法

提出了一种新的计算时具有结构动力特性相关性的无条件稳定的结构动力学时间积分算法。该算法不仅位移与速度均具有显式表达的特点,而且具有了Bathe复合时间积分方案的优点。该新算法的数值特征与Bathe隐式复合积分算法的数值特性相同,但新算法不需要任何时间步长内的子步细分,相对于新提出的算法而言,时间步长内的子步细分成了Bathe隐式复合积分算法的缺点。为了进一步了解所提出的新方法的谱特性,对新算法的稳定性和精度进行了全面的分析,包括数值耗散和色散。此外,当采用提出的算法计算多自由度系统时,给出了两个积分参数的推导过程和表达式。通过计算线性和非线性问题并与采用现有算法的结果比较,验证了新算法的正确性和有效性。     

一种结构动力方程的并行直接积分方法

本文提出了一种求解大型结构动力方程的新的并行直接积分方法。该方法在L.Brusa和L.Nigro提出的一步(one-step)直接积分方法的基础上,引进并行运算步骤。并行运算步骤是通过将动力积分方程子结构化,同时进行组集和凝聚实现的。该方法在西安交通大学ELXSI-6400并行机上程序实现,计算结果表明能有效地求解大型结构有限元动力方程的并行直接积分方法。     

A time‐staggered partitioned coupling algorithm for transient heat conduction

We present a time‐staggered partitioned coupling algorithm for transient heat conduction finite element simulations. This algorithm divides a large structural mesh into a number of smaller subdomains, solves the individual subdomains separately and couples the solutions to obtain the response to the original problem. The proposed algorithm is a mixed multi‐timestep algorithm and enables arbitrary time integration schemes and meshes to be coupled with different timesteps in the various subdomains. In this procedure, the solution of each partition is separately evaluated over a system timestep after which the interfacial conditions are enforced making this a staggered algorithm that facilitates parallel computation. We present examples showing the feasibility of the coupling algorithm and discuss the merits in terms of convergence and stability. Copyright © 2009 John Wiley & Sons, Ltd.     

有限元并行计算中网格自动区域划分的研究

本文针对集群系统下大规模并行有限元分析,设计了简单实用的网格自动区域划分算法,以使并行计算时减少由于负载不均衡所引起的效率下降,并应用于“汽车碰撞模拟”项目中的车架模型的分割。重点讨论并改进了贪婪算法和ANP算法,并比较了两种算法各自的特点及其适用性。通过数值算例证明,对于不同类型的有限元网格都得到了满意的结果,本文的算法具有广泛的适用性。且对该算法稍加改进,则可应用于各类动态并行计算问题所提出的动态负载均衡要求。     

Parallel computing of high‐speed compressible flows using a node‐based finite‐element method

An efficient parallel computing method for high‐speed compressible flows is presented. The numerical analysis of flows with shocks requires very fine computational grids and grid generation requires a great deal of time. In the proposed method, all computational procedures, from the mesh generation to the solution of a system of equations, can be performed seamlessly in parallel in terms of nodes. Local finite‐element mesh is generated robustly around each node, even for severe boundary shapes such as cracks. The algorithm and the data structure of finite‐element calculation are based on nodes, and parallel computing is realized by dividing a system of equations by the row of the global coefficient matrix. The inter‐processor communication is minimized by renumbering the nodal identification number using ParMETIS. The numerical scheme for high‐speed compressible flows is based on the two‐step Taylor–Galerkin method. The proposed method is implemented on distributed memory systems, such as an Alpha PC cluster, and a parallel supercomputer, Hitachi SR8000. The performance of the method is illustrated by the computation of supersonic flows over a forward facing step. The numerical examples show that crisp shocks are effectively computed on multiprocessors at high efficiency. Copyright © 2003 John Wiley & Sons, Ltd.     

Implementation of mixed time integration techniques on a vectorized computer with shared memory

The implementation of subcycling in an explicit finite element program executed on a concurrent computer with shared memory is described. The effects of vectorization and parallelization on the speed-up and efficiency achieved with subcycling is discussed. Numerical studies are presented to illustrate the effects of the number of processors, the size of element blocks and problem size. Finally, an efficient allocation algorithm which minimizes the effects of processor idleness is presented.     

A robust and efficient substepping scheme for the explicit numerical integration of a rate‐dependent crystal plasticity model

This paper describes the development of efficient and robust numerical integration schemes for rate‐dependent crystal plasticity models. A forward Euler integration algorithm is first formulated. An integration algorithm based on the modified Euler method with an adaptive substepping scheme is then proposed, where the substepping is mainly controlled by the local error of the stress predictions within the time step. Both integration algorithms are implemented in a stand‐alone code with the Taylor aggregate assumption and in an explicit finite element code. The robustness, accuracy and efficiency of the substepping scheme are extensively evaluated for large time steps, extremely low strain‐rate sensitivity, high deformation rates and strain‐path changes using the stand‐alone code. The results show that the substepping scheme is robust and in some cases one order of magnitude faster than the forward Euler algorithm. The use of mass scaling to reduce computation time in crystal plasticity finite element simulations for quasi‐static problems is also discussed. Finally, simulation of Taylor bar impact test is carried out to show the applicability and robustness of the proposed integration algorithm for the modelling of dynamic problems with contact. Copyright © 2014 John Wiley & Sons, Ltd.     

An implicit multi-time step integration method for structural dynamics problems

A multi-time step integration algorithm is developed based on the trapezoidal rule time integration method for finite element equations of motion. This algorithm uses nodal groups to partition the mesh into subdomains that are updated with different time steps. A␣stability analysis of the method shows that the scheme retains the unconditionally stable behavior of the trapezoidal rule and conserves the same pseudo energy as the parent algorithm. Several numerical examples are used to verify the stability of the method and to investigate the accuracy of the scheme.     

Parallel computation for acoustic radiation in a subsonic nonuniform flow with a coupled FEM/BEM formulation

This paper presents a parallel implementation of the coupled finite element method/boundary element method formulation for sound radiation in a subsonic nonuniform flow. The parallelization is based on a cost analysis of the sequential algorithm and is implemented on a heterogeneous computer system using the Parallel Virtual Machine software. A dynamically distributed parallel computation scheme (DDPCS) is developed to improve efficiency and reliability. Our test cases demonstrate that it is possible to get high parallel efficiency and reliability on a virtual parallel machine, although greater heterogeneity decreases efficiency.     

A parallel Galerkin boundary element method for surface radiation and mixed heat transfer calculations in complex 3‐D geometries

This paper presents a parallel Galerkin boundary element method for the solution of surface radiation exchange problems and its coupling with the finite element method for mixed mode heat transfer computations in general 3‐D geometries. The computational algorithm for surface radiation calculations is enhanced with the implementation of ideas used for 3‐D computer graphics applications and with data structure management involving creating and updating various element lists optimized for numerical performance. The algorithm for detecting the internal third party blockages of thermal rays is presented, which involves a four‐step procedure, i.e. the primary clip, secondary clip and adaptive integration with checking. Case studies of surface radiation and mixed heat transfer in both simple and complex 3‐D geometric configurations are presented. It is found that a majority of computational time is spent on the detection of foreign element blockages and parallel computing is ideally suited for surface radiation calculations. Results show that the decrease of the CPU time approaches asymptotically to an inverse rule for parallel computing of surface radiation exchanges. For large‐scale computations involving complex 3‐D geometries, an iterative procedure is a preferred approach for the coupling of the Galerkin boundary and finite elements for mixed mode heat transfer calculations. Copyright © 2004 John Wiley & Sons, Ltd.