基于杆系离散单元法的单层网壳结构屈曲行为研究
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摘要
离散单元法因适合处理大位移、非线性和非连续等问题而逐渐被应用于结构工程中,但采用离散单元法进行结构屈曲全过程分析还有待研究。为此,基于杆系离散单元法的基本理论和计算方法,提出离散元力控制法及离散元位移控制法,研究上述方法在结构弹性屈曲全过程分析中的特点及适用性,同时给出离散元位移控制法(力控制法不需要单独处理)对不同荷载工况的处理方法及离散元法在进行结构弹性屈曲分析时的计算流程。采用Fortran语言自编程序,对典型算例进行弹性屈曲全过程分析,与传统方法相比,该方法无需组集刚度矩阵,对几何非线性问题不需特殊处理即可模拟结构的屈曲行为,更具优越性,并通过结果对比,验证了离散单元法在单层网壳结构弹性失稳全过程分析中的有效性。
Discrete element method(DEM) has been gradually applied in structural engineering due to its capabilities of dealing with large displacement, nonlinearity and discontinuity issues. However, using the DEM for structural buckling process analysis remains to be studied. Therefore, the discrete element force control method and displacement control method were proposed on the basis of the member discrete element method in this study, and the characteristics and applicability of the above methods for whole process structural elastic buckling analysis were investigated. Meanwhile, treatment scheme for the displacement control method under different load conditions(no need for separate treatment for the force control method herein) as well as the calculational procedure of the DEM for structural elastic buckling analysis were proposed in this study. Finally, buckling process analyses of several typical examples were carried out using the program complied by Fortran language. Compared with other conventional numerical methods, the DEM which can simulate the buckling behavior of the structure without assembling the stiffness matrix and special treatments, is more advantage for handling geometric nonlinearity issue. Additionally, the effectivity of the DEM in the whole elastic buckling process analysis of single-layer reticulated shells was verified through the comparison between buckling behaviors obtained using DEM and those of the published studies.
Discrete element method(DEM) has been gradually applied in structural engineering due to its capabilities of dealing with large displacement, nonlinearity and discontinuity issues. However, using the DEM for structural buckling process analysis remains to be studied. Therefore, the discrete element force control method and displacement control method were proposed on the basis of the member discrete element method in this study, and the characteristics and applicability of the above methods for whole process structural elastic buckling analysis were investigated. Meanwhile, treatment scheme for the displacement control method under different load conditions(no need for separate treatment for the force control method herein) as well as the calculational procedure of the DEM for structural elastic buckling analysis were proposed in this study. Finally, buckling process analyses of several typical examples were carried out using the program complied by Fortran language. Compared with other conventional numerical methods, the DEM which can simulate the buckling behavior of the structure without assembling the stiffness matrix and special treatments, is more advantage for handling geometric nonlinearity issue. Additionally, the effectivity of the DEM in the whole elastic buckling process analysis of single-layer reticulated shells was verified through the comparison between buckling behaviors obtained using DEM and those of the published studies.
引文
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[9] YE Jihong, QI Nian. Progressive collapse simulation based on DEM for single-layer reticulated domes [J]. Journal of Constructional Steel Research, 2017, 128: 721-731.
[10] 叶继红, 齐念. 基于离散元法与有限元法耦合模型的网壳结构倒塌过程分析[J]. 建筑结构学报,2017,38(1):52- 61.(YE Jihong, QI Nian. Analysis of collapse process of reticulated shell based on coupling model of discrete element method and finite element method[J]. Journal of Architectural Structure, 2017, 38(1):52- 61. (in Chinese))
[11] IVO Caliò, MASSIMO Marletta, BARTOLOMEO Pantò. A new discrete element model for the evaluation of the seismic behaviour of unreinforced masonry buildings[J]. Engineering Structures, 2012,40: 327-338.
[12] 王泳嘉,邢纪波. 散单元法及其在岩土工程中的应用[M]. 沈阳:东北工学院出版社,1991:12-34.(WANG Yongjia, XING Jibo. Scatter element method and its application in geotechnical engineering [M]. Shenyang: Northeast China Institute of Technology Press, 1991:12-34. (in Chinese))
[13] 田伟,赵阳,董石麟. 考虑杆件失稳的网壳结构稳定分析方法[J]. 工程力学,2012,29(10):149-156.(TIAN Wei, ZHAO Yang, DONG Shilin. Stability analysis method for reticulated shells considering the instability of members [J]. Engineering Mechanics, 2012, 29(10): 149-156. (in Chinese))
[2] RIKS E. An increment approach to the solution of snapping and buckling problems[J]. International Journal of Solids Structures, 1979, 15(5): 529-551.
[3] CRISFIELD M A. An arc-length method including line searches and accelerations[J]. International Journal of Numerical Methods in Engineering, 1983, 19(2): 1269-1289.
[4] CUNDALL P A. A computer model for simulating progressive large-scale movements in block rock mechanics[C]// Proceedings of the International Symposium on Rock Fracture. Nancy, France: Springer-Verlag,1971:1-8.
[5] 齐念,叶继红. 基于离散元法的杆系结构几何非线性大变形分析[J]. 东南大学学报,2013, 43(5):917-922.(QI Nian, YE Jihong. geometrical nonlinear large deformation analysis of rod structure based on discrete element method[J]. Journal of Southeast University, 2013, 43(5): 917-922. (in Chinese))
[6] QI N, YE J H. Nonlinear dynamic analysis of space frame structures by discrete element method[J]. Applied Mechanics and Materials, 2014, 638/639/640: 1716-1719.
[7] 许玲玲,叶继红,薛素铎. 大质量法在基于离散元法多点激励分析中的应用和误差修正[J]. 土木工程学报,2016,49(增刊1):32-36.(XU Lingling, YE Jihong, XUE Suduo. Application of large mass method in multi-point excitation analysis based on discrete element method and error correction[J]. China Civil Engineering Journal, 2016, 49(Suppl.1): 32-36. (in Chinese))
[8] 齐念. DEM/FEM耦合计算方法研究及其在网壳倒塌破坏模拟中的应用[D]. 南京:东南大学,2016: 11-20.(QI Nian. Research on DEM/FEM coupling calculation method and its application in collapse simulation of reticulated shell [D]. Nanjing: Southeast University, 2016: 11-20. (in Chinese))
[9] YE Jihong, QI Nian. Progressive collapse simulation based on DEM for single-layer reticulated domes [J]. Journal of Constructional Steel Research, 2017, 128: 721-731.
[10] 叶继红, 齐念. 基于离散元法与有限元法耦合模型的网壳结构倒塌过程分析[J]. 建筑结构学报,2017,38(1):52- 61.(YE Jihong, QI Nian. Analysis of collapse process of reticulated shell based on coupling model of discrete element method and finite element method[J]. Journal of Architectural Structure, 2017, 38(1):52- 61. (in Chinese))
[11] IVO Caliò, MASSIMO Marletta, BARTOLOMEO Pantò. A new discrete element model for the evaluation of the seismic behaviour of unreinforced masonry buildings[J]. Engineering Structures, 2012,40: 327-338.
[12] 王泳嘉,邢纪波. 散单元法及其在岩土工程中的应用[M]. 沈阳:东北工学院出版社,1991:12-34.(WANG Yongjia, XING Jibo. Scatter element method and its application in geotechnical engineering [M]. Shenyang: Northeast China Institute of Technology Press, 1991:12-34. (in Chinese))
[13] 田伟,赵阳,董石麟. 考虑杆件失稳的网壳结构稳定分析方法[J]. 工程力学,2012,29(10):149-156.(TIAN Wei, ZHAO Yang, DONG Shilin. Stability analysis method for reticulated shells considering the instability of members [J]. Engineering Mechanics, 2012, 29(10): 149-156. (in Chinese))