Abstract
A bilinear 4-node element, widely used in finite-element numerical analysis, yields poor solutions in some cases of large elastoplastic deformation. The locking phenomenon and hourglass modes are observed when applying the exact and reduced integration techniques, respectively, for the displacement-based method. Even though the mixed method can overcome these shortcomings, the cpu time increases rapidly for a large-scale problem, because the pressure field is added to the matrix formulation and the exact integration technique becomes indispensable. On the other hand, several improved methods, such as the selective reduced integration technique, the so-called B approach and the hourglass stiffness stabilization method, have been proposed to overcome these difficulties. We here give the finite-element formulation of rate types in large deformation fields for these improvement techniques for a bilinear 4-node element and discuss the differences among these methods using the numerical simulations.
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