THEORY AND NUMERICS OF THREE-DIMENSIONAL BEAMS WITH ELASTOPLASTIC MATERIAL BEHAVIOUR ∗

By Friedrich Gruttmann, R. Sauer, Werner Wagner. 2000

177 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/75c5a3c03d557d6553eb5386af6a973eee2a2c3c

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In Biomedical Engineering

In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Structural analysis of composite laminates using a mixed hybrid shell element (2006, methodology): “The second variation of the current orthogonal base system has been derived in [ 31 ]”
Isogeometric Reissner–Mindlin shell analysis with exactly calculated director vectors (2013, background): “Second variation of the current director vector The derivation of hI ·∆δdI conducted in [14] for nodal values hI and ∆δdI can be adapted straight-forward for the term h · ∆δdh.”
The interpolation of rotations and its application to finite element models of geometrically exact rods (2004, methodology): “This idea was previously employed by [14, 13] within the context of a different rod theory.”
Recent developments on refined theories for beams with applications (2015, methodology): “In Gruttmann et al. (2000) and Wagner and Gruttmann (2001), the unknown warping function has been approximated using an isoparametric concept.”
An isogeometric Reissner–Mindlin shell element based on Bézier dual basis functions: Overcoming locking and improved coarse mesh accuracy (2020, background): “The derivations of the variations of the directors and their derivatives follow standard approaches [4, 46, 5].”
A robust non‐linear mixed hybrid quadrilateral shell element (2005, background): “The second variation of the current director vector reads according to [30] hI ·ΔδdI = δwI ·MI ΔwI MI(hI) = 1 2 (dI ⊗ hI + hI ⊗ dI) + 12(tI ⊗ ωI + ωI ⊗ tI) + c101 tI = −c3 bI + (c6 + c2c9) (bI · ωI)ωI bI = dI × hI c2 = ωI − sinωI ω I”
Director‐based beam finite elements relying on the geometrically exact beam theory formulated in skew coordinates (2014, background): “[5], see also Chapter 9 in Belytschko et al.”