This thesis discusses an application of the Dynamic Relaxation (DR) method to metal forming problems. The DR method is a numerical iteration method in which a Finite Element or Finite Difference dynamic computer program is adopted by adding an artificial damping term to the equation of motion. Then the equation of motion is integrated with respect to time. With a properly chosen damping constant, both acceleration and velocity approach zero and the system converges to the equilibrium state that is the static solution to the external applied load. In this thesis the DR method is used in conjunction with a dynamic Finite Element Method (FEM) program using direct integration without global stiffness matrix. Because of the fact that the global stiffness matrix is not constructed in the calculation, the CPU time, as well as storage used to update and to factorize the global stiffness matrix, is saved. The method studied in this thesis is suitable to large deformation and large strain solid mechanics problems of elastic or elastic-plastic material with any forms of hardening feature. The theory of DR is described and example problems such as simple upsetting and ring compression are discussed. Also high velocity compression of a cylinder is simulated, the simulation demonstrates that both static and dynamic problems can be attacked by a unified program.
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