After the review of the basic theory of the inverse method, a new modified arc-length search method is proposed to find better initial solution. The methods to deal with the vertical walls are also discussed and presented. Then, a generalized multi-step inverse FEM method is proposed. It solves two key obstacles: the first one is to determine the initial solution of the intermediate three-dimensional configurations and the other is to control the movement of nodes so they could only slide on constraint surfaces during the search by Newton-Raphson iteration. The computer implementation of the generalized multi-step inverse FEM is also presented. By comparing to the simulation results using a commercial software system, the effectiveness of the new method is validated. / Currently, there are a number of commercial FEM software systems available in the market. These software systems are based on an incremental FEM process that models the sheet metal stamping process in small incremental steps. Even though the incremental FEM is accurate, it is not suitable for the initial conceptual design for its needing of detailed design parameters and enormous calculation times. As a result, another type of FEM, called the inverse FEM method or one-step FEM method, has been proposed. While it is less accurate than that of the incremental method, this method requires much less computation and hence, has a great potential. However, it also faces a number of unsolved problems, which limits its application. This motivates the presented research. / From a physical point of view, the formability and the quality of a product are influenced by several factors. The design of the product in the initial stage and the motion of the press during the production stage are two of these crucial factors. This thesis focuses on the numerical simulation for these two factors using FEM. / Other than the product design, the punch motion (including punch speed and punch trajectory) of the stamping press also has significant effect on the formability and the quality of the product. In fact, this is one of the major reasons why hydraulic presses and/or servo presses are used for parts which demand high quality. In order to reveal the quantitative correlation between the punch motion and the part quality, the Cowper-Symonds strain rate constitutive model and the implicit dynamic incremental FEM are combined to conduct the research. The effects of the punch motion on the part quality, especially the plastic strain distribution and the potential springback, have been investigated for the deep drawing and the bending processes respectively. A qualitative relationship between the punch motion and the part quality is also derived. / The reaction force of the punch motion causes the dynamic deformation of the press during the stamping, which in turn influences the part quality as well. This dynamic information, in the form of the strain signal, is an important basis for the on-line monitoring of the part quality. By using the actual force as the input to the press, the incremental FEM is needed to predict the strain of the press. The result is validated by means of experiments and can be used to assist the on-line monitoring. / The sheet metal stamping process plays an important role in modern industry. With the ever-increasing demand for shape complexity, product quality and new materials, the traditional trial and error method for setting up a sheet metal stamping process is no longer efficient. As a result, the Finite Element Modeling (FEM) method has now been widely used. / Huang Ying. / "March 2006." / Adviser: Ruxu Du. / Source: Dissertation Abstracts International, Volume: 67-11, Section: B, page: 6694. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (p. 141-160). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.