柔性结构弹塑性碰撞动态子结构方法的研究
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摘要
现代工业所要求的高速、高精度、高性能柔性结构系统的应用已经越来越普及,柔性系统间发生的弹塑性碰撞所造成的结构损伤和系统性能的劣化日益受到工程界的关注。柔性结构弹塑性碰撞动力学分析是一个涉及材料动态特性、碰撞接触变形、碰撞瞬态波传播、碰撞接触与分离状态频繁切换等强非线性问题,理论分析十分困难。因此,发展准确、高效的数值分析方法显得十分重要。本文结合有限元理论和固定界面模态综合方法,提出了柔性结构弹塑性碰撞动态子结构方法和柔性结构弹粘塑性碰撞动态子结构方法,对柔性杆和柔性梁的弹塑性和弹粘塑性碰撞问题进行了数值分析,并通过三维非线性有限元方法和实验方法,对提出的动态子结构法进行了验证。主要研究工作如下：
(1)针对柔性结构的弹塑性碰撞问题,忽略材料应变率效应,采用弹塑性有限元理论和固定界面模态综合方法,推导了模态坐标下的弹塑性碰撞动力学控制方程,理论证明了主模态的存在性和模态截断的收敛性,建立了柔性结构弹塑性碰撞动态子结构方法的基本理论,简称为"DSPI方法’
(2)运用DSPI方法研究了刚性质量纵向碰撞弹塑性悬臂直杆问题,采用粘结接触模型处理刚性质量与杆的碰撞约束,讨论了方法的数值收敛性。计算了碰撞弹塑性波的传播、弹塑性杆的碰撞动态响应和二次碰撞现象,计算结果与三维非线性动力有限元的计算结果相吻合。
(3)运用DSPI方法研究了钝圆柱头质量横向碰撞简支直梁问题,采用修正的单轴压缩局部接触模型处理钝圆柱头质量与简支梁的碰撞约束,讨论了方法的数值收敛性。计算了碰撞弹塑性波传播、波弥散效应、弹塑性梁的碰撞动态响应和碰撞过程中的多次的接触分离现象,计算结果与三维非线性动力有限元的计算结果相吻合,并与实验结果相符合。
(4)针对柔性结构的弹粘塑性碰撞问题,考虑材料应变率效应,采用弹粘塑性有限元理论和固定界面模态综合方法,推导了模态坐标下的弹粘塑性碰撞动力学控制方程,理论证明了主模态的存在性和模态截断的收敛性,建立了柔性结构弹粘塑性碰撞动态子结构方法的基本理论,简称为‘'DSVI方法”
(5)运用DSVI方法研究了刚性质量纵向碰撞线性强化弹粘塑性杆和钝圆柱头质量横向碰撞理想弹粘塑性直梁问题,讨论了方法的数值收敛性,计算了碰撞弹粘塑性波传播和碰撞弹粘塑性动态响应,计算结果与三维非线性动力有限元的计算结果相吻合。
以上的研究表明,DSPI方法和DSVI方法可以分别作为柔性结构弹塑性和弹粘塑性碰撞行为分析的有效的数值计算手段,为进一步将动态子结构方法运用于复杂柔性结构系统的弹塑性和弹粘塑性碰撞动力学行为研究打下了一定的基础。
In modern industry field, complicated flexible mechanical systems with high speed, high precision and high performance have been applied widely. The problems of structure failure and worsening of working capability resulted from elastic-plastic impacts between colliding bodies have increasingly attracted the concern of scientists. Since elastic-plastic impact dynamics is a strongly nonlinear problem which is related to material dynamic properties, the transient wave propagation, the contact deformation, the repeated switch of contact-separation state and etc, it is hard to solve this problem by analytical methodology. Hence, to develop an accurate and efficient numerical method becomes more important and necessary. In this thesis, a dynamic substructure method for elastic-plastic impact and a dynamic substructure method for elastic-viscoplastic impact of flexible structure are developed through incorporating elastic-plastic finite element theory with fixed-interface modal synthesis method. By the application of the present method, the elastic-plastic impact problem and elastic-viscoplastic impact problem of the flexible systems constituted of flexible rods or beams are analyzed numerically. The feasibility of the dynamic substructure method is validated by comparing the computation results with those obtained by three-dimensional dynamic finite element method (FEM) and experiment method. The main researches of this thesis are shown as follows:
(1) A complete foundation theory of dynamic substructure method for elastic-plastic impact problem of flexible structure is developed. Neglecting strain-rate effect, the governing equations expressed by modal coordinate are derived by using of the elastic-plastic finite element theory and fixed-interface modal synthesis technique. The existence of normal modes and the convergence of mode truncation are proved theoretically. The solving procedure for the nonlinear governing equations is given. This procedure is referred to as 'DSPI method'.
(2) The'DSPI method'method is applied to investigate a flexible uniform elastic-plastic bar longitudinally struck by a rigid block. To treat contact constrains between the rigid block and the bar, an adhesive contact model is adapted. The numerical convergence of the method is discussed systematically. The propagation of transient waves, the impact responses and the second impact phenomenon are calculated. The DSPI numerical solutions agree with the FEM solutions excellently.
(3) The' DSPI method' is adopted to study an impact problem of a simply supported uniform beam transversely struck by a round-nosed rigid mass.A modified uniaxial compression contact model is used to treat the contact constrains, and the numerical convergence of the method is discussed systematically. The dynamic characteristics such as propagation of transient waves, dispersion of flexural waves, dynamic responses of the elastic-plastic beam and the phenomenon of multiple contacts and separations are all simulated. The DSPI numerical solutions agree with the FEM solutions and experiment datas excellently.
(4) A complete foundation theory of dynamic substructure method for elastic-viscoplastic impact problem of flexible structure is developed. For an elastic-viscoplastic impact problem, the strain-rate effect of material is taken into account. The governing equations expressed by modal coordinates are derived by using of the elastic-viscoplastic finite element theory and the fixed-interface modal synthesis technique. The existence of normal modes and the convergence of mode truncation are proved theoretically. This method is referred to as the'DSVI method'
(5) By the application of the'DSVI method', a linear harding elastic-viscoplastic rod longitudinally struck by a rigid block and an ideal elastic-viscoplastic beam transversely struck by a round-nosed rigid mass are investigated. Systematical discussions on the numerical convergence are done. The elastic-viscoplastic waves and elastic-viscoplastic transient responses are calculated. The DSVI solutions agree with the FEM solutions excellently.
The above investigations show that DSPI method and DSVI method are an effective numerical tools to analyze elastic-plastic impact and elastic-viscoplastic impact of flexible structure, respectively. The investigations in this thesis establish a foundation for applying the DSPI method and the DSVI method to calculate the elastic-plastic impact responses and elastic-viscoplastic impact responses of more complicated structure system.
(1)针对柔性结构的弹塑性碰撞问题,忽略材料应变率效应,采用弹塑性有限元理论和固定界面模态综合方法,推导了模态坐标下的弹塑性碰撞动力学控制方程,理论证明了主模态的存在性和模态截断的收敛性,建立了柔性结构弹塑性碰撞动态子结构方法的基本理论,简称为"DSPI方法’
(2)运用DSPI方法研究了刚性质量纵向碰撞弹塑性悬臂直杆问题,采用粘结接触模型处理刚性质量与杆的碰撞约束,讨论了方法的数值收敛性。计算了碰撞弹塑性波的传播、弹塑性杆的碰撞动态响应和二次碰撞现象,计算结果与三维非线性动力有限元的计算结果相吻合。
(3)运用DSPI方法研究了钝圆柱头质量横向碰撞简支直梁问题,采用修正的单轴压缩局部接触模型处理钝圆柱头质量与简支梁的碰撞约束,讨论了方法的数值收敛性。计算了碰撞弹塑性波传播、波弥散效应、弹塑性梁的碰撞动态响应和碰撞过程中的多次的接触分离现象,计算结果与三维非线性动力有限元的计算结果相吻合,并与实验结果相符合。
(4)针对柔性结构的弹粘塑性碰撞问题,考虑材料应变率效应,采用弹粘塑性有限元理论和固定界面模态综合方法,推导了模态坐标下的弹粘塑性碰撞动力学控制方程,理论证明了主模态的存在性和模态截断的收敛性,建立了柔性结构弹粘塑性碰撞动态子结构方法的基本理论,简称为‘'DSVI方法”
(5)运用DSVI方法研究了刚性质量纵向碰撞线性强化弹粘塑性杆和钝圆柱头质量横向碰撞理想弹粘塑性直梁问题,讨论了方法的数值收敛性,计算了碰撞弹粘塑性波传播和碰撞弹粘塑性动态响应,计算结果与三维非线性动力有限元的计算结果相吻合。
以上的研究表明,DSPI方法和DSVI方法可以分别作为柔性结构弹塑性和弹粘塑性碰撞行为分析的有效的数值计算手段,为进一步将动态子结构方法运用于复杂柔性结构系统的弹塑性和弹粘塑性碰撞动力学行为研究打下了一定的基础。
In modern industry field, complicated flexible mechanical systems with high speed, high precision and high performance have been applied widely. The problems of structure failure and worsening of working capability resulted from elastic-plastic impacts between colliding bodies have increasingly attracted the concern of scientists. Since elastic-plastic impact dynamics is a strongly nonlinear problem which is related to material dynamic properties, the transient wave propagation, the contact deformation, the repeated switch of contact-separation state and etc, it is hard to solve this problem by analytical methodology. Hence, to develop an accurate and efficient numerical method becomes more important and necessary. In this thesis, a dynamic substructure method for elastic-plastic impact and a dynamic substructure method for elastic-viscoplastic impact of flexible structure are developed through incorporating elastic-plastic finite element theory with fixed-interface modal synthesis method. By the application of the present method, the elastic-plastic impact problem and elastic-viscoplastic impact problem of the flexible systems constituted of flexible rods or beams are analyzed numerically. The feasibility of the dynamic substructure method is validated by comparing the computation results with those obtained by three-dimensional dynamic finite element method (FEM) and experiment method. The main researches of this thesis are shown as follows:
(1) A complete foundation theory of dynamic substructure method for elastic-plastic impact problem of flexible structure is developed. Neglecting strain-rate effect, the governing equations expressed by modal coordinate are derived by using of the elastic-plastic finite element theory and fixed-interface modal synthesis technique. The existence of normal modes and the convergence of mode truncation are proved theoretically. The solving procedure for the nonlinear governing equations is given. This procedure is referred to as 'DSPI method'.
(2) The'DSPI method'method is applied to investigate a flexible uniform elastic-plastic bar longitudinally struck by a rigid block. To treat contact constrains between the rigid block and the bar, an adhesive contact model is adapted. The numerical convergence of the method is discussed systematically. The propagation of transient waves, the impact responses and the second impact phenomenon are calculated. The DSPI numerical solutions agree with the FEM solutions excellently.
(3) The' DSPI method' is adopted to study an impact problem of a simply supported uniform beam transversely struck by a round-nosed rigid mass.A modified uniaxial compression contact model is used to treat the contact constrains, and the numerical convergence of the method is discussed systematically. The dynamic characteristics such as propagation of transient waves, dispersion of flexural waves, dynamic responses of the elastic-plastic beam and the phenomenon of multiple contacts and separations are all simulated. The DSPI numerical solutions agree with the FEM solutions and experiment datas excellently.
(4) A complete foundation theory of dynamic substructure method for elastic-viscoplastic impact problem of flexible structure is developed. For an elastic-viscoplastic impact problem, the strain-rate effect of material is taken into account. The governing equations expressed by modal coordinates are derived by using of the elastic-viscoplastic finite element theory and the fixed-interface modal synthesis technique. The existence of normal modes and the convergence of mode truncation are proved theoretically. This method is referred to as the'DSVI method'
(5) By the application of the'DSVI method', a linear harding elastic-viscoplastic rod longitudinally struck by a rigid block and an ideal elastic-viscoplastic beam transversely struck by a round-nosed rigid mass are investigated. Systematical discussions on the numerical convergence are done. The elastic-viscoplastic waves and elastic-viscoplastic transient responses are calculated. The DSVI solutions agree with the FEM solutions excellently.
The above investigations show that DSPI method and DSVI method are an effective numerical tools to analyze elastic-plastic impact and elastic-viscoplastic impact of flexible structure, respectively. The investigations in this thesis establish a foundation for applying the DSPI method and the DSVI method to calculate the elastic-plastic impact responses and elastic-viscoplastic impact responses of more complicated structure system.
引文
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