The Inverse Axisymmetic Elastoplastic Boundary Element Method And Its Application

Research on the friction behavior during material forming process can provide important information for the process design and improve the forming precision. The cirque compression is always used in the investigation of friction mechanism, and it is effective to solve such axisymmetric problem by using the axisymmetric Boundary Element Method (BEM).The axisymmetric BEM is widely used in engineering fields and significant efforts have been paid to treat the miscellaneous fundamental solution and sensitivity integral in the application of this method. In the present study, the fundamental solution of the axisymmetric elastic and elastoplastic BEM was deduced and its explicit expression was given. The singular integral was dealt with by the way of an axisymmetic general solution and the pole coordinate transform. The sensitivity ellipse integral was also treated properly.The inverse problem has significant applications in engineering. But the solution is not stable and restricts its development. This dissertation introduced the calculation process of inverse BEM and made the theory modeling for the cirque compression. The linear equations were solved by the singular value decomposition. The distribution of contact friction force and the metal flow during cirque compressing were analyzed, the axis equilibrium equations were used as additional constraints to stabilize the solution in some extent. At last, the input contact pressure data were regularized by the least square way and satisfaction results with ±2% random error in the input were obtained. It is a new idea to investigate the friction mechanism using the inverse BEM. However, the ill-posed nature of inverse problems has brought the obstacle to obtain the accurate solutions. Further insight into the improvement of the stability of solutions as well as the friction phenomena should be performed in future.