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On a stress resultant geometrically exact shell model. VI: Conserving algorithms for nonlinear dynamics. (English) Zbl 0760.73045

[For the parts I to IV see: Comput. Methods Appl. Mech. Eng. 81, No. 1, 91-126 (1990; Zbl 0746.73016); part V, ibid. 96, No. 2, 133-171 (1992).]
In the former parts of the present work, the formulation and finite element implementation of a nonlinear stress resultant shell model are considered in detail. This paper is concerned with the extension of these results to incorporate completely general nonlinear dynamic response. Of special interest here is the dynamics of very flexible shells undergoing large overall motion which conserves the total linear and angular momentum and, for the Hamiltonian case, the total energy. A main goal of this paper is the design of nonlinear time-stepping algorithms, and the construction of finite element interpolations, which preserve exactly these fundamental constants of motion.

MSC:

74K15 Membranes
74H45 Vibrations in dynamical problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
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