Numerical Method Research For Beams Collision And Its Visualization Realization

Collision problems frequently encountered in engineering，it alwaysattracts the attention of scholars at home and abroad. Collision problem isactually a complex problem which has theoretical solutions for simpleimpacts between bars, but most of solutions can be obtained only byusing some effective numerical models and associated algorithms.Among them the Finite Element Method has played a very important role.Firstly a restitution coefficient e is introduced to obtain thetheoretical solution for two-circle spring-mass system collision in thispaper. Then describing the numerical handling method according to thebasic concept of dynamic contact theory, and applying the method tosolve the collision between spring-mass system, on the one hand thenumerical method is proved to be correct compared with the thoreticalsolution gotten by the classical impact thoery, and on the other hand thereasonable value of restitution coefficient is suggested for thespring-mass system collision by using the classical impact thoery.Numerical expressions of the transverse collision and oblique collisionbetween two beams are deduced with the general conditions. It isdescribed how to handle the node load first, and then the element loadwhich can be transformed to the node load by linear interpolation method.Using Fortran to compile the finite element calculation program andcombining with Visual Basic6.0, a dynamic analysis finite elementsoftware with a good pre-post processing system is developed for beamcollision by using a mixed programming technique. The proposedtechnique can overcome respective defects of two kind of compilerlanguages. Combination of Fortran powerful computing function and thevisualization interface of VB is realized. Parameters input are achieved inpre-processing, and in post-processing time history curves such as the displacement curve and velocity curve can be drawed, and the beamcollision also can be showed vividly.Adopting dynamic theory and using Newmark-β method, thedynamic response for all kinds of collisions between beams are computedby a self-developed program. The numerical solution and analyticalsolution is close for the central collision. For the transverse collision itshows that there are several times impacts during the process of collision.And the time step is stricter for the transverse collision compared with thecentral collision because of a shorter time needed for wave propagation.By examining with many examples, the self-developed finite elementdynamic response program is correct in numerical method handling, andthe calculation results are dependable.