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On drilling degrees of freedom. (English) Zbl 0691.73015

The authors have investigated variational principles employing independent rotation fields. In the two-dimensional case these lead to membrane elements with ‘drilling degrees of freedom’ of practical use in shell analysis. It is argued that formulations employing ‘conventional’ displacement, rotations, and stress interpolations are doomed to failure. Identifying the difficulties, the authors propose a modified variational principle possessing the same Euler-Lagrange equations as Reinner’s, but with improved stability properties in the context of discrete approximations. Convenient interpolations are rendered convergent by the modified principle. Several other formulations are proposed and shown to be convergent for displacement/rotation interpolations of all orders.
Reviewer: P.Narain

MSC:

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