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Generalized midpoint finite element dynamic analysis of elastoplastic systems. (English) Zbl 0769.73076

Summary: The application of a four-parameter generalized midpoint integration method to small-displacement elastoplastic dynamic problems is considered. The integration of the governing relations over a time step is formulated as a nonlinear algebraic problem (finite-step problem) by making use of generalized variables finite element modelling. Uniqueness and an extremum characterization of the solution of the finite-step problem are discussed. Sufficient conditions for convergence of various iterative algorithms, including Newton-Raphson, are given. The \(B\)- stability of the proposed procedure is assessed.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
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