Wan Cheng

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering


Professor Mateusz P. Sklad


The contents of this thesis reflect a general effort in the endeavour of exploring and developing the effective FEM tools for metal forming analysis. There are three major parts in this work. In chapter 2, an unique mathematical derivation of large deformation equations is presented on the basis of a direct linearization of the "future" virtual work equation without using any pseudo stress tensor and corresponding conjugate strain tensor. A major advantage of this derivation is that a clear physical understanding is carried through the whole mathematical process. Therefore distinctive perception on key fundamentals such as: equilibrium equation, strain measure, constitutive relation, stress rotation and residual force evaluation are presented and discussed on a consistent and integrated basis. The code developed in this part of work forms an independent module for 2D bulk forming analysis, while the methodology is carried through the rest of thesis. A particular effort is described in Chapter 3, which addressed the problem and techniques used in dealing with the frictional contact boundary condition which is common in metal forming processes. A typical ring compression problem is used to show the problem and solution. The algorithm and code developed there is a part of the 2D package. Chapter 4 presents a full description of a 3D degenerated shell element formulation based on the consistent large deformation formulation presented in Chapter 2. Various aspects of techniques used in shell elements to prevent elements from locking have been reviewed. A special penalty method is devised to enforce the Kirchhoff constraint which has been missing in the degenerated shell element discretization. The method has successfully prevented 3-node and 4-node elements from shear locking in analysing the typical cup drawing process. At the end of the thesis, a summary of the thesis is presented. Conclusions and recommendations for further work are provided.

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