| As typically encountered in practical applications, sheet metal forming processes of general geometry involve a highly-nonlinear response which requires careful consideration in their finite element modeling. To this end, the fully-nonlinear analysis of the coupled membrane/bending behavior of arbitrary-curved shells based on a simple quadrilateral mixed model is chosen for predicting the deformation behavior of sheet metals to assist in the design of die shapes and selection of sheet metal materials.; In the formulation, an updated Lagrange approach is adopted, and the governing equations are derived based on a consistent linearization of an incremental two-field variational principle of the Hellinger/Reissner type, utilizing independent assumptions for displacement and strain fields. Emphasis is placed on devising effective solution procedures to deal with finite rotations in space, large stretches, and generalized rat-type models for inelastic response. For the purpose of updating the spatial stress field of the element, an "objective" generalized midpoint integration rule is utilized, making use of the concept of polar decomposition of the deformation gradient, and in keeping with the underlying mixed method.; A number of numerical studies are investigated to determine the efficiency and convergence characteristics of different solution algorithms for obtaining nonlinear response of structures subjected to large deformations.; Finally, the effectiveness of the model developed is demonstrated through a number of numerical simulations for a variety of inelastic nonlinear test problems, as well as sheet metal forming problems, involving in-plane and out-of-plane stretching. Also, an interactive graphics package, which is extremely useful for finite element data preparation, as well as the interpretation of results, was developed to display the effectiveness of finite elements in sheet metal forming problems. |
