可扩展冲击-接触并行计算及其在汽车碰撞模拟中的应用
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摘要
大型复杂结构系统的冲击接触，例如汽车碰撞，涉及大变形的几何非线性、弹塑性本构的材料非线性、多接触面的边界条件非线性，而且是高自由度系统的瞬态动力响应问题。此类问题的数值模拟通常要对数十万自由度系统进行数十万时间步的响应计算，对于计算机的存储量和计算时间都提出了很高的要求，在不具备超级计算机的条件下，通常很难获得满足工程需要的计算结果。为此本文研究了此类问题在微机机群环境下的可扩展并行算法，并改进了区域自动划分算法，并将这些算法应用到汽车碰撞的数值模拟，取得了比较满意的结果。本文主要内容包括如下几个部分：
首先，为了有效地进行大型复杂结构系统的冲击接触数值模拟，需要保证包含诸多复杂因素的计算模型充分协调。为此，文中从推导变分方程开始，给出了包括接触边界条件、壳单元内力计算在内的全部列式，并列出了识别接触界面的搜索算法，接触力计算以及动力响应计算的时间积分算法的有关公式等等。本文的计算格式不仅使上述各部分之间协调相容，并且通过不同算例表明，它具有较高的计算效率。
本文分别设计了内力计算、接触搜索和接触力的并行算法。内力计算部分和接触计算部分所基于的区域分裂都在单元级上完成，避免了以前冲击－接触并行计算时两部分之间的不相容性的问题。提出了一种修正的greedy算法以完成区域自动划分的任务，相对于传统的greedy算法，新算法使得分割子域具有更好的长宽比，且适用于不规则几何形状的有限元网格的区域划分。
最后，在微机机群环境下采用上述模型和提出的算法实现了汽车碰撞模拟的大规模并行计算。计算中采用了双重动态区域划分技术，但内力计算和接触计算区域划分均在单元级上完成，从而保持了计算模型的一致性。实际车架和整车碰撞模拟的结果通过与试验结果的比较证明是合理的，关键结果曲线趋势吻合，数值接近。微机机群并行计算比单台微机计算能显著减少计算时间，并具有良好的可扩展性。在八结点机群环境下，并行加速比可达到5.5，对于150000自由度的整车碰撞问题，计算160000个时间步，计算时间仅为7.26小时。从而说明在机群环境下，通过并行计算，可以胜任汽车碰撞工程问题的数值模拟。
Contact-impact of large-scale complex structural system, such as car crash, is involved with geometric nonlinearity caused by large deformation, material nonlinearity due to elastoplastic constitutive relation, and boundary nonlinearity related to multiple contact surfaces; furthermore it is transient response of a system with large number of DOF. For the numerical simulation of such problem, in general, it is required to carry out the response computation of several hundred thousands time steps for a system with several hundred thousands DOF, which raises very high demand for the memory of computer and the computing speed. It was very difficult to obtain the satisfactory results required by the engineering practice without supercomputers. In order to improve such situation, it is dealt with the scalable parallel algorithm for the simulation of such problem on a PC cluster in this dissertation; an improved automatic domain-decomposition algorithm is presented as well. The presented algorithms are applied to the simulation of practical car crash problem, and some satisfactory results have been obtained.
The dissertation consists of several parts as follows:
At first, it is required to ensure the computational model containing many complex factors fully compatible, in order to carry out the numerical simulation of the impact response of such large-scale complex structural efficiently. Therefore it is started with the derivation of variational equation, full formulations including contact boundary conditions, internal forces of shell element are given, and the algorithms for contact-surfaces searching, contact-force computation, and even time integration for the response computation are listed as well. The computational model formulated is fully compatible, and numerical examples have shown rather high efficiency.
Based on domain decomposition method, parallel algorithms for internal force computation, contact searching and contact force determination are developed, in which the domain decomposition approach on element level is adopted for both internal and contact force computation, and in this way the incompatibility of two parts of parallel computation encountered in literature has been avoided. The numerical examples have shown that the parallel algorithm presented for contact-impact simulation on a PC cluster exhibits good parallel efficiency and scalability. A new Modified Greedy Algorithm is presented in this paper which can obtain better length to width ratio through considering the information of nodes
coordinate. The numerical examples have shown that the algorithm presented gives satisfactory results for several different meshes
Finally, the large-scale parallel computation of car crash simulation is carried out on a PC cluster using the presented numerical model and algorithms. Dual dynamic domain decomposition technique is integrated into parallel algorithm, and the domain decomposition both for internal force computation and contact force computation is accomplished on element level, in order to keep the consistency of computational model. The simulation results of practical car case- and car-crash, in comparison with the corresponding experimental results, show that the numerical simulation is reasonable, the variation tendence of response curves and some key values of the numerical and experimental results at some key points have shown good agreement. In comparison with the computation on single PC, the parallel computing on PC cluster can reduce computing time significantly, and has good scalability. On a PC cluster with 8 nodes, the speedup can approximately reach 5.5, and for the whole car crash simulation of 150000 DOFs and 160000 time steps takes the computing time of 7.26 hours. In this way, the parallel computing on PC cluster consisted of 8 nodes can be applied to the numerical simulation of practical car crashworthiness.
首先，为了有效地进行大型复杂结构系统的冲击接触数值模拟，需要保证包含诸多复杂因素的计算模型充分协调。为此，文中从推导变分方程开始，给出了包括接触边界条件、壳单元内力计算在内的全部列式，并列出了识别接触界面的搜索算法，接触力计算以及动力响应计算的时间积分算法的有关公式等等。本文的计算格式不仅使上述各部分之间协调相容，并且通过不同算例表明，它具有较高的计算效率。
本文分别设计了内力计算、接触搜索和接触力的并行算法。内力计算部分和接触计算部分所基于的区域分裂都在单元级上完成，避免了以前冲击－接触并行计算时两部分之间的不相容性的问题。提出了一种修正的greedy算法以完成区域自动划分的任务，相对于传统的greedy算法，新算法使得分割子域具有更好的长宽比，且适用于不规则几何形状的有限元网格的区域划分。
最后，在微机机群环境下采用上述模型和提出的算法实现了汽车碰撞模拟的大规模并行计算。计算中采用了双重动态区域划分技术，但内力计算和接触计算区域划分均在单元级上完成，从而保持了计算模型的一致性。实际车架和整车碰撞模拟的结果通过与试验结果的比较证明是合理的，关键结果曲线趋势吻合，数值接近。微机机群并行计算比单台微机计算能显著减少计算时间，并具有良好的可扩展性。在八结点机群环境下，并行加速比可达到5.5，对于150000自由度的整车碰撞问题，计算160000个时间步，计算时间仅为7.26小时。从而说明在机群环境下，通过并行计算，可以胜任汽车碰撞工程问题的数值模拟。
Contact-impact of large-scale complex structural system, such as car crash, is involved with geometric nonlinearity caused by large deformation, material nonlinearity due to elastoplastic constitutive relation, and boundary nonlinearity related to multiple contact surfaces; furthermore it is transient response of a system with large number of DOF. For the numerical simulation of such problem, in general, it is required to carry out the response computation of several hundred thousands time steps for a system with several hundred thousands DOF, which raises very high demand for the memory of computer and the computing speed. It was very difficult to obtain the satisfactory results required by the engineering practice without supercomputers. In order to improve such situation, it is dealt with the scalable parallel algorithm for the simulation of such problem on a PC cluster in this dissertation; an improved automatic domain-decomposition algorithm is presented as well. The presented algorithms are applied to the simulation of practical car crash problem, and some satisfactory results have been obtained.
The dissertation consists of several parts as follows:
At first, it is required to ensure the computational model containing many complex factors fully compatible, in order to carry out the numerical simulation of the impact response of such large-scale complex structural efficiently. Therefore it is started with the derivation of variational equation, full formulations including contact boundary conditions, internal forces of shell element are given, and the algorithms for contact-surfaces searching, contact-force computation, and even time integration for the response computation are listed as well. The computational model formulated is fully compatible, and numerical examples have shown rather high efficiency.
Based on domain decomposition method, parallel algorithms for internal force computation, contact searching and contact force determination are developed, in which the domain decomposition approach on element level is adopted for both internal and contact force computation, and in this way the incompatibility of two parts of parallel computation encountered in literature has been avoided. The numerical examples have shown that the parallel algorithm presented for contact-impact simulation on a PC cluster exhibits good parallel efficiency and scalability. A new Modified Greedy Algorithm is presented in this paper which can obtain better length to width ratio through considering the information of nodes
coordinate. The numerical examples have shown that the algorithm presented gives satisfactory results for several different meshes
Finally, the large-scale parallel computation of car crash simulation is carried out on a PC cluster using the presented numerical model and algorithms. Dual dynamic domain decomposition technique is integrated into parallel algorithm, and the domain decomposition both for internal force computation and contact force computation is accomplished on element level, in order to keep the consistency of computational model. The simulation results of practical car case- and car-crash, in comparison with the corresponding experimental results, show that the numerical simulation is reasonable, the variation tendence of response curves and some key values of the numerical and experimental results at some key points have shown good agreement. In comparison with the computation on single PC, the parallel computing on PC cluster can reduce computing time significantly, and has good scalability. On a PC cluster with 8 nodes, the speedup can approximately reach 5.5, and for the whole car crash simulation of 150000 DOFs and 160000 time steps takes the computing time of 7.26 hours. In this way, the parallel computing on PC cluster consisted of 8 nodes can be applied to the numerical simulation of practical car crashworthiness.
引文
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