A numerical method is presented to incorporate plastic mechanics theory with component mode synthesis technique for the analysis of elastic-plastic dynamic responses of flexible structure subjected impulsive load. To do this, the nonlinearity induced by plastic deformation is treated and approximated as an internal excited load, which is placed on the right-hand side of the incremental governing equations. This technique is so-called pseudo-force method. And then, the governing equations of plastic dynamic problems in modal coordinate are derived from fixed-interface component mode synthesis technique, the solving method of these equations is also introduced. By using the proposed method, the modal transformation matrix of system is calculated only once, and is used throughout the entire analysis. This will be an improvement of computational efficiency. A simply supported beam suffered harmonic load and impact event are studied, respectively. The simulation results show that the proposed method has a higher computational efficiency and accuracy by comparing with the full model finite element method.
QIAN Pengbo
,
QIAN Linfang
,
YIN Xiaochun
. Analysis of Elastic-plastic Transient Response Based on Reduced Model[J]. Journal of Mechanical Engineering, 2018
, 54(5)
: 113
-120
.
DOI: 10.3901/JME.2018.05.113
[1] TONGE A L,RAMESH K. Multi-scale defect interactions in high-rate failure of brittle materials,Part Ⅱ:Application to design of protection materials[J]. Journal of the Mechanics and Physics of Solids,2016,86:237-258.
[2] CORIGLIANO A,DOSSI M,MARIANI S. Model order reduction and domain decomposition strategies for the solution of the dynamic elastic-plastic structural problem[J]. Computer Methods in Applied Mechanics and Engineering,2015,290:127-155.
[3] FLODÉN O,PERSSON K,SANDBERG G. Reduction methods for the dynamic analysis of substructure models of lightweight building structures[J]. Computers & Structures,2014,138:49-61.
[4] HURTY W C. Dynamic analysis of structural systems using component modes[J]. AIAA journal,1965,3(4):678-685.
[5] KLERK D D,RIXEN D,VOORMEEREN S. General framework for dynamic substructuring:history, review and classification of techniques[J]. AIAA Journal,2008,46(5):1169-1181.
[6] 郑兆昌. 非线性系统动力分析的模态综合技术[J]. 应用数学和力学,1983,4(4):563-572. ZHENG Zhaochang. Dynamic analysis of nonlinear systems by modal synthesis techniques[J]. Applied Mathematics and Mechanics,1983,4(4):563-572.
[7] ALAMDARI M M,LI J,SAMALI B,et al. Nonlinear joint model updating in assembled structures[J]. Journal of Engineering Mechanics,2014,140(7):04014042.
[8] 郑兆昌,谭明一. 非线性系统动态响应的数值计算方法[J]. 应用数学和力学,1985(1):93-101. ZHENG Zhaochang,TAN Mingyi. Numerical method in dynamic response of nonlinear systems[J]. Applied Mathematics and Mechanics,1985(1):93-101.
[9] WU S C,HAUG E J. A Substructure technique for dynamics of flexible mechanical systems with contact-impact[J]. Journal of Mechanical Design,1990,112(3):390-398.
[10] SHEN Yunian,YIN Xiaochun. Dynamic substructure analysis of stress waves generated by impacts on non-uniform rod structures[J]. Mechanism and Machine Theory,2014,74:154-172.
[11] CHEN P,LIU Jinyang,HONG Jiazhen. Contact-impact formulation for multi-body systems using component mode synthesis[J]. Acta Mechanica Sinica,2013,29(3):437-442.
[12] 骞朋波,尹晓春,沈煜年,等. 碰撞激发弹塑性波传播的动态子结构方法[J]. 力学学报,2012,44(1):184-188. QIAN Pengbo,YIN Xiaochun,SHEN Yunian,et al. Dynamic substructure method for propagation of elastic-plastic wave induced by impact[J]. Chinese Journal of Theoretical and Applied Mechanics,2012,44(1):184-188.
[13] 孔德平,骞朋波,沈煜年,等. 碰撞激发弹粘塑性波传播的动态子结构方法[J]. 机械工程学报,2013,49(1):95-101. KONG Deping,QIAN Pengbo,SHEN Yunian,et al. Dynamic substructure technique for elastic-viscoplastic wave propagation excited by impact[J]. Journal of Mechanical Engineering,2013,49(1):95-101.
[14] KUETHER R J,DEANER B J,HOLLKAMP J J,et al. Evaluation of geometrically nonlinear reduced-order models with nonlinear normal modes[J]. AIAA Journal,2015,53(11):3273-3285.
[15] 王勖成. 有限单元法[M]. 北京:清华大学出版社,2003. WANG Xucheng. Finite element method[M]. Beijing:Tsinghua University Press,2003.
[16] MOLNAR A J,VASCHI K M,GAY C W. Application of normal mode theory and pseudo-force methods to solve problems with nonlinearities[J]. Journal of Pressure Vessel Technology,1976,98:151-156.
[17] KAMMER D C,TRILLER M J. Selection of component modes for Craig-Bampton substructure representations[J]. Journal of Vibration and Acoustics,1996,118(2):264-270.
[18] BOND J,KHRAISHI T. Transient non-linear simulation with component mode synthesis[J]. International Journal of Mechanics and Materials in Design,2009,5(4):365-380.
[19] 王文亮. Hurty-Craig约束模态综合法的动力原理和它的一种变体[J]. 复旦学报,1982,21(2):121-130. WANG Wenliang. Dynamic principle of Hurty-Craig's modal synthesis method and its variety[J]. Journal of Fudan University,1982,21(2):121-130.
[20] 杨钧,尹晓春,刘中华,等. 刚性质量对自由梁的弹粘塑性次撞击[J]. 机械工程学报,2012,48(1):72-77. YANG Jun,YIN Xiaochun,LIU Zhonghua,et al. elastic viscoplastic sub-impacts of free-free beam struck by rigid mass[J]. Journal of Mechanical Engineering,2012,48(1):72-77.