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A formulation of membrane finite elements with true drilling rotation: The compatible triangular element

Djamel Boutagouga (Department of Civil Engineering, Laboratoire des Mines, University of Tebessa, Tebessa, Algeria)

Engineering Computations

ISSN: 0264-4401

Article publication date: 7 August 2019

Issue publication date: 16 January 2020



This paper aims to describe the formulation of a displacement-based triangular membrane finite element with true drilling rotational degree of freedom (DOF).


The presented formulation incorporates the true drilling rotation provided by continuum mechanics into the displacement field by way of using the polynomial interpolation. Unlike the linked interpolation, that uses a geometric transformation between displacement and vertex rotations, in this work, the interpolation of the displacement field in terms of nodal drilling rotations is obtained following an unusual approach that does not imply any presumed geometric transformation.


New relationship linking the mid-side normal displacement to corner node drilling rotations is derived. The resulting new element with true drilling rotation is compatible and does not include any problem-dependent parameter that may influence the results. The spurious zero-energy mode is stabilized in a careful way that preserves the true drilling rotational degrees of freedom (DOFs).


Several works dealing with membrane elements with vertex rotational DOFs have been published with improved convergence rate, however, owing to the need for incorporating rotations in the finite element meshes involving solids, shells and beam elements, having finite elements with true drilling rotational DOFs is more appreciated.



Boutagouga, D. (2020), "A formulation of membrane finite elements with true drilling rotation: The compatible triangular element", Engineering Computations, Vol. 37 No. 1, pp. 203-236.



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