Influence functions and goal-oriented error estimation for finite element analysis of shell structures. (English) Zbl 1122.74507

Grätsch, Thomas; Bathe, Klaus-Jürgen

Int. J. Numer. Methods Eng. 63, No. 5, 709-736 (2005).

Summary: We first present a consistent procedure to establish influence functions for the finite element analysis of shell structures, where the influence function can be for any linear quantity of engineering interest. We then design some goal-oriented error measures that take into account the cancellation effect of errors over the domain to overcome the issue of over-estimation. These error measures include the error due to the approximation in the geometry of the shell structure. In the calculation of the influence functions we also consider the asymptotic behaviour of shells as the thickness approaches zero. Although our procedures are general and can be applied to any shell formulation, we focus on MITC finite element shell discretizations. In our numerical results, influence functions are shown for some shell test problems, and the proposed goal-oriented error estimation procedure shows good effectivity indices.

MSC:

74S05	Finite element methods applied to problems in solid mechanics
74K25	Shells

Keywords:

shell structures; influence functions; goal-oriented error estimation; MITC shell elements

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