交叉立体桁架系巨型网格结构的超级元与子结构相结合计算法
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摘要
针对交叉立体桁架系巨型网格结构杆件、节点多、计算工作量大的特点,提出了超级有限元与子结构相结合的简化求解方法:采用三节点立体桁架超级元来处理主体结构中的立体桁架,用子结构法来处理大网格内的子结构。推导了超级元刚度矩阵及子结构参与协同承载时对整体结构的刚度贡献。经编程对比计算分析表明,该法计算精度高,误差基本保持在5%以内,计算工作量较完全有限元法明显降低,且可考虑子结构的参与协同承载,是分析巨型网格结构的一种比较优越的方法。
In this paper, a simplified analysis method of combining super finite elements and substructures is presented and studied for reticulated mega-structure in which the main-structure is lattice-intersected three-dimensional system. To reduce the calculation time, the main-structure is discretized using super element of three nodes and substructures of large grids. The super element stiffness matrix and the stiffness contribution of substructures to the whole structure are developed. It is shown that the calculating time of the present method is reduced significantly in comparison with complete finite element analysis and accurate results are obtained. The present method can also consider the load-bearing contribution of the sub-structures. It is a superior analysis method for the reticulated mega-structures.
In this paper, a simplified analysis method of combining super finite elements and substructures is presented and studied for reticulated mega-structure in which the main-structure is lattice-intersected three-dimensional system. To reduce the calculation time, the main-structure is discretized using super element of three nodes and substructures of large grids. The super element stiffness matrix and the stiffness contribution of substructures to the whole structure are developed. It is shown that the calculating time of the present method is reduced significantly in comparison with complete finite element analysis and accurate results are obtained. The present method can also consider the load-bearing contribution of the sub-structures. It is a superior analysis method for the reticulated mega-structures.
引文
[1]董石麟,姚谏.网壳结构的未来与发展[J].空间结构,1994,1(1):3-10.Dong Shilin,Yao Jian.The future and development of latticed shell structures[J].Spatial Structures,1994,1(1):3-10.(in Chinese)
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[4]贺拥军.巨型网格结构的动力特性、地震响应及结构简化计算方法研究[R].湖南大学,2003,4.He Yongjun.On dynamic and seismic responses and simplified analysis method of reticulated mega-structures[R].Hunan University,2003,4.(in Chinese)
[5]贺拥军,周绪红,董石麟.平板网架子结构圆柱面交叉立体桁架系巨型网格结构的研究[J].土木工程学报,2002,35(6):24-31.He Yongjun,Zhou Xuhong,Dong Shilin.On mega-structure braced with substructures of double layer grids[J].China Civil Engineering Journal,2002,35(6):24-31.(in Chinese)
[6]贺拥军,周绪红,董石麟.叉筒网壳子结构圆柱面交叉立体桁架系巨型网格结构的稳定性研究[J].建筑结构学报,2003,24(2):54-63.He Yongjun,Zhou Xuhong,Dong Shilin.On cylindrical lattice-intersected three-dimensional reticulated mega--structure with single layer lattice-intersected cylindrical shell substructure[J].Journal of Building Structures,2003,24(2):54-63.(in Chinese)
[7]贺拥军,董石麟.圆柱面组合杆系巨型网格结构的优化与适宜跨度分析[J].土木工程学报,2002,35(2):108-110.He Yongjun,Dong Shilin.Optimal analysis of cylindrical reticulated mega-structures[J].China Civil Engineering Journal,2002,35(2):108-110.(in Chinese)
[8]曹志远.复杂结构分析的超级元法[J].力学与实践,1992,14(4):10-14.Cao Zhiyuan.Super-element method for complex structural analysis[J].Mechanics and Practice.1992,14(4):10-14.(in Chinese)
[9]周汉斌,曹志远.超级有限元法在桁架组合结构中的应用[J].上海力学,1993,14(3):31-36.Zhou Hanbin,Cao Zhiyuan.A super finite element method and its application in analysis of composite structures with truss system[J].Shanghai Journal of Mechanics,1993,14(3):31-36.(in Chinese)
[10]杜国君,崔春阳.网壳结构分析的超级元法[J].燕山大学学报,2002,26(1):27-30.Du Guojun,Cui Chunyang.A super finite element method for analyzing shell type truss structures[J].Journal of Yanshan University,2002,26(1):27-30.(in Chinese)
[2]贺拥军,董石麟.巨型网格结构的形体分析与力学模型[A].第九届空间结构学术会议论文集[C].萧山:2000.81-86.He Yongjun,Dong Shilin.The forms and mechanical model of reticulated mega-structures[A].the Ninth Symposium of Spatial Structures[C].Xiaoshan,2000.81-86.(in Chinese)
[3]贺拥军.巨型网格结构的形体、静力及稳定性研究[D].浙江大学,2001,2.He Yongjun.On structural forms,static and stability of latticed mega-structures[D].Zhejiang University,2001,2.(in Chinese)
[4]贺拥军.巨型网格结构的动力特性、地震响应及结构简化计算方法研究[R].湖南大学,2003,4.He Yongjun.On dynamic and seismic responses and simplified analysis method of reticulated mega-structures[R].Hunan University,2003,4.(in Chinese)
[5]贺拥军,周绪红,董石麟.平板网架子结构圆柱面交叉立体桁架系巨型网格结构的研究[J].土木工程学报,2002,35(6):24-31.He Yongjun,Zhou Xuhong,Dong Shilin.On mega-structure braced with substructures of double layer grids[J].China Civil Engineering Journal,2002,35(6):24-31.(in Chinese)
[6]贺拥军,周绪红,董石麟.叉筒网壳子结构圆柱面交叉立体桁架系巨型网格结构的稳定性研究[J].建筑结构学报,2003,24(2):54-63.He Yongjun,Zhou Xuhong,Dong Shilin.On cylindrical lattice-intersected three-dimensional reticulated mega--structure with single layer lattice-intersected cylindrical shell substructure[J].Journal of Building Structures,2003,24(2):54-63.(in Chinese)
[7]贺拥军,董石麟.圆柱面组合杆系巨型网格结构的优化与适宜跨度分析[J].土木工程学报,2002,35(2):108-110.He Yongjun,Dong Shilin.Optimal analysis of cylindrical reticulated mega-structures[J].China Civil Engineering Journal,2002,35(2):108-110.(in Chinese)
[8]曹志远.复杂结构分析的超级元法[J].力学与实践,1992,14(4):10-14.Cao Zhiyuan.Super-element method for complex structural analysis[J].Mechanics and Practice.1992,14(4):10-14.(in Chinese)
[9]周汉斌,曹志远.超级有限元法在桁架组合结构中的应用[J].上海力学,1993,14(3):31-36.Zhou Hanbin,Cao Zhiyuan.A super finite element method and its application in analysis of composite structures with truss system[J].Shanghai Journal of Mechanics,1993,14(3):31-36.(in Chinese)
[10]杜国君,崔春阳.网壳结构分析的超级元法[J].燕山大学学报,2002,26(1):27-30.Du Guojun,Cui Chunyang.A super finite element method for analyzing shell type truss structures[J].Journal of Yanshan University,2002,26(1):27-30.(in Chinese)
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