Research On Dynamic Substructure Method For Elastic-Plastic Impact Of Flexible Structures

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.