基于传统串行计算平台的有限元分析面临精度不足、耗时巨大的问题成为目前高层钢筋混凝土框架结构非线性动力时程分析面临的瓶颈，利用GPU强大的并行计算能力，开发了一种结构非线性有限元静力、动力分析的高精度和高效率分析平台HSNAS(GPU)。针对静力问题提出了适用于GPU计算，且能有效解决结构负刚度问题的位移增量迭代算法，开发了相应的GPU线性方程组并行求解器；针对动力问题，开发了GPU基于Newmark时间积分算法的动力分析软件平台，结合纤维模型单元技术，引入扭转、剪切变形以及材料非线性。算例模型表明，HSNAS(GPU)平台在满足精度条件下能有效地提高结构非线性静、动力分析的计算效率。
Abstract
The traditional serial computation platform has some disadvantages such as low accuracy and dramatically high time consuming, which hindered the development of structural nonlinear dynamics analysis. In order to achieve a higher computing accuracy and save calculation time in the process of nonlinear dynamic analysis of reinforced concrete (RC) frames, a simulation platform HSNAS(GPU) based on graphics processing unit (GPU) was developed. For static analysis, a GPU-based incremental displacement algorithm was introduced to deal with negative stiffness problems, and parallel Preconditioned Conjugate Gradients (PCG) solver was developed. For dynamic analysis, the GPU-based Newmark-beta algorithm was presented. The fiber beam model was improved by considering the effects of shear and torsion. In addition, the constitutive models of steel and concrete were developed. The results of numerical examples illustrate that the developed platform HSNAS(GPU) could improve the efficiency of nonlinear static and dynamic analysis beside satisfying the accuracy.
关键词
钢筋混凝土结构 /
非线性有限元 /
模拟平台 /
GPU /
纤维模型
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Key words
reinforced concrete structure /
nonlinear finite element analysis /
simulation platform /
GPU /
fiber model
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参考文献
[1] 李云贵. 工程结构设计中的高性能计算[J]. 建筑结构学报, 2010, 31(6): 89-95.
LI Yun-gui. High-performance computing in structural design [J]. Journal of Building Structures, 2010, 31(6): 89-95.
[2] 李红豫, 滕军, 李祚华. 基于CPU-GPU异构平台的高层结构地震响应分析方法研究[J]. 振动与冲击, 2014, 33(13)：86-91.
LI Hong-yu, TENG Jun, LI Zuo-hua. Analysis method for seismic response of high-rise structure based on CPU-GPU heterogeneous platform [J]. Journal of Vibration and Shock, 2014, 33(13): 86-91.
[3] Spacone E, Fillippou F C, Taucer F F. Fiber beam-column model for nonlinear analysis of RC frames: Part I. Formulation [J]. Earthquake Engineering & Structure Dynamics, 1996, 25: 711-725.
[4] Petrangeli M, Pinto P E, Ciampi V. Fiber Element for Cyclic Bending and Shear of RC Structures. I: Theory [J]. Journal of Engineering Mechanics, 1999, 125(9): 994-1001.
[5] 殷有泉. 非线性有限元基础[M]. 北京：北京大学出版社，2007.
[6] 丁峻宏, 宋雅丽, 王惠, 等. 大规模柴油机动力学抗冲击并行仿真计算[J]. 振动与冲击, 2014, 33(2)：163-167.
DING Jun-hong, SONG Ya-li, WANG Hui, et al. Parallel computing for large scale anti-shock dynamic simulation of diesel engine [J]. Journal of Vibration and Shock. 2014, 33(2): 163-167.
[7] nVidai Corporation. CUDA C Programming Guide [EB/OL]. http://docs.nvidia.com/cuda/pdf/CUDA_C_Programming_Guide.pdf. July 2013.
[8] Crisfield M A. An arc-length method including line searches and accelerations [J]. International Journal of Numerical Methods in Engineering, 1983, 19(9): 1269-1289.
[9] 杜修力, 曹惠, 金浏. 力-变位关系全过程模拟的有限元位移控制新方法[J]. 工程力学, 2012, 29(1): 1-6.
DU Xiu-li, CAO Hui, JIN Liu. A new finite element displacement control method of the whole process simulation of force-displacement relation [J]. Engineering Mechanics, 2012, 29(1): 1-6.
[10] 克拉夫 R, 彭津 J. 结构动力学(第二版)[M]. 王光远, 等,译校. 北京：高等教育出版社，2006.
[11] Menegotto M, Pinto P E, Slender R C. Compressed members in biaxial bending [J]. Journal of Structural Division, ASCE, 1977, 103(3): 587-605.
[12] Kent D C, Park R. Flexural Members with Confined Concrete [J]. Journal of the Structural Division, ASCE, 1971, 97(7): 1969-1990.
[13] Blakely R W G, Park R. Prestressed concrete sections with cyclic flexure [J]. Journal of the Structural Division, ASCE, 1973, 99(8): 1717-1742．
[14] Yassin M H M. Nonlinear analysis of prestressed concrete structures under monotonic and cycling loads [D]. University of California, Berkeley, 1994.
[15] Benzi M, Tuma M. A comparative study of sparse approximate inverse preconditioners [J]. Applied Numerical Mathematics, 1999, 30(2): 305-340.
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