Three Dimensional Multipole Bem For Elasto-Plastic Contact With Friction And Rolling Simulation Of Four-High Mill

In the rolling field, the simulation of rolling on four high mill that includes the sheet,working roll and back roll, is the frontal subject on the rolling theory, which is put asidebecause the operation scale is too large. Based on traditional three-dimensional BoundaryElement Method (BEM), combining with Multipole Expansion Method and GeneralizedMinimal Residual Method, 3-D fast Multipole-BEM is given out in this paper. Then 3-Dfast Multipole-BEM for elastic and elasto-plastic frictional contact with multi-bodies isdeveloped. The above method is highly efficient and the demanding of its computingmemory is very low, which makes the BEM simulation of four high roll is possible. Withthe help of parallel solution based on network platform, cold-roll process of 2030four-high mill is simulated. The flakiness ratio is up to 1850. In the paper, the quantitativedescription of deformation and displacement in the deformed area are given out. Thepressure distributions between the working roll and back roll and the deflection andbruising displacement are admeasured too. The paper includes five chapters. Chapter 1 is introduction, in which the developmenthistory, present state and perspectives of BEM are introduced. The numerical methodachievements in the simulation of rolling are simply retrospected. The advantages anddisadvantages of rolling simulation by BEM are retraced too. In chapter 2, MultipoleExpansion Method and Generalized Minimal Residual Method are introduced. Throughthe appropriate decomposition of traditional basic solution and combing with MultipoleExpansion Method and Generalized Minimal Residual Method, 3-D fast Multipole-BEMfor elastic problems is developed from traditional BEM. The numerical experiments showthat with the same precision, Multipole BEM is with high computing speed and lowermemory demanding for large-scale problems. When the DOF is less than 1700, thecomputing efficiency is lower than tradition BEM but the memory demanding is very low.A point-to-surface contact model is given out in chapter 3, which can avoid the error in thecomputing of large gliding contact problems when node-pairs contact model is adopted.The decision criterion of contact and penetration is admeasured too. AdoptingMathematical Programming Method accelerates the convergent ratio of friction iterationprocess. The computing efficiency and precision of are discussed through a computingmodel, which is under the condition of different load. Based on the former chapters, inchapter 4, the non-linear properties of the material (elasto-plastic properties) are IIconsidered. To be suitable for the Multipole Expansion Method, the plastic basic solutionsare decomposed into a new format. 3-D fast Multipole-BEM for elasto-plastic frictionalcontact with multi-bodies is developed. To the slit-elements, according to its aspect ratio,different integral methods are adopted. In chapter 5, incremental loading mode is adoptedbecause the simulation of four-high roll contains elastic frictional contact andelasto-plastic frictional contact, which makes the amount of computing very heavy. Thenparallel solution based on network platform is introduced, the computing time is shortenby controlling the step of load. The successful computing of 2030 four-high roll showsthat fast Multipole-BEM is efficient and reliable, and gives out the load and deformationinformation of the roll and the workpiece, which contributes a lot to the engineering.