An efficient formulation based on the Lagrangian method for contact–impact analysis of flexible multi-body system

In this paper,an efficien formulation based on the Lagrangian method is presented to investigate the contact–impact problems of f exible multi-body systems.Generally,the penalty method and the Hertz contact law are the most commonly used methods in engineering applications.However,these methods are highly dependent on various non-physical parameters,which have great effects on the simulation results.Moreover,a tremendous number of degrees of freedom in the contact–impact problems will influenc thenumericalefficien ysignificantl.Withtheconsideration of these two problems,a formulation combining the component mode synthesis method and the Lagrangian method is presented to investigate the contact–impact problems in fl xible multi-body system numerically.Meanwhile,the finit element meshing laws of the contact bodies will be studied preliminarily.A numerical example with experimental verificatio will certify the reliability of the presented formulationincontact–impactanalysis.Furthermore,aseries of numerical investigations explain how great the influenc of the finit element meshing has on the simulation results.Finally the limitations of the element size in different regions are summarized to satisfy both the accuracy and efficien y.

Sensitivity analyses of random cave groups on karst tunnel stability based on water–rock interaction using a novel contact dynamic method

This paper concentrates on the sensitivity and dynamic simulation of randomly distributed karst cave groups on tunnel stability and connectivity extended ratio based on water–rock interaction using a novel contact dynamic method(CDM).The concept of karst cave group connectivity extended ratio during tunneling and water inrush is proposed.The effects of cave shape and spatial distribution on Qiyueshan tunnel are investigated.Tunnel deformation and damage index,and connectivity extended ratio with uniform random karst cave groups are evaluated.The results demonstrate that the connectivity extended ratio is verified as a crucial judgment in predicting the safe distance and assessing the stability of the tunnel with the karst cave group.CDM model captures the fracture propagation and contact behavior of rock mass,surface flow,as well as the bidirectional water–rock interaction during the water inrush of Qiyueshan tunnel with multiple caves.A larger cave radius and smaller minimum distance between the cave and tunnel increase the deformation and damage index of the surrounding rock.When the cave radius and cave area ratio increase,the failure pattern shifts from overall to local failure.These findings potentially have broad applications in various surface and subsurface scenarios involving water–rock interactions.