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A viscoelastic higher-order beam finite element. (English) Zbl 0893.73064
Whiteman, J. R. (ed.), The mathematics of finite elements and applications. Highlights 1996. Proceedings of the 9th conference, MAFELAP 1996, Uxbridge, GB, June 25–28, 1996, Chichester: Wiley. 333-345 (1997).
First, we present a brief review of the history integral form of the Maxwell solid to provide background for the differential constitutive law. Then we derive a new differential constitutive law for the Maxwell solid which describes large strain viscoelastic deformations of rubber. This differential constitutive law is then combined with the higher-order beam theory and finite element formulation providing viscoelastic theory for thick beams. The additional strain variables required in the constitutive law are replaced with element nodal variables that are conjugate to the elastic nodal variables. This results in only minor modifications to the elastic finite element code. Finally, several numerical examples are presented demonstrating the viscoelastic, thick-beam response under quasi-static loading.
For the entire collection see [Zbl 0867.00027].

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74D10 Nonlinear constitutive equations for materials with memory
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