What is it about?
The work on membrane elements with rotational DOF has faded in the last decades due to the fact that till nowadays, these elements cannot be used in real engineering problems and in commercial software because they do not deal with the true drilling rotational DOF. It has been more than 30 years since the successful work by Allman, and researchers still using membrane and shell elements with an incorrect rotational DOF "which has no physical interpretation" in engineering applications. This paper aims to form membrane and shell elements with compatible rotational DOFs of the other type of structural elements. Having the true drilling rotation as nodal DOF is the key for allowing a shell finite element to compatibly connect with other kinds of elements with rotational degrees of freedom. The objective of this research work is the development of a membrane element with true drilling rotation. We presented a completely new formulation to incorporate the drilling rotation into the displacement field interpolation.
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Why is it important?
The obtained element incorporates true drilling rotation (the correctness of the rotational DOF is proven mathematically in the paper). Thus, it can be correctly coupled with other engineering elements with rotational DOFs. I believe that the present formulation, which can be applied to triangular and quadrilateral elements, will replace Allman's concept to be the theoretical support for the development of several triangular and quadrangular membrane and shell elements. The main finding of the present work is the kinematic relation linking the mid-side lateral displacement to corner node drilling rotations.
Perspectives
It is found in this work that the kinematic relation linking the mid-side lateral displacement to corner node drilling rotations is dependent on the quality of the constraint adopted to remove singularity of the transformation matrix in Eq. 31. In this work, the kinematic relations in Eq. 55 are obtained by applying the inter-element compatibility condition. Other conditions can be investigated, and other relations can be established between the mid-side lateral displacements and corner node true drilling rotations if other constraints are adopted, such as equilibrium or energy conditions. In addition, investigating other constraints could yield in elements with better convergence rate using true drilling rotational DOFs.
Dr Djamel Boutagouga
Larbi Tébessi University - Tbessa
Read the Original
This page is a summary of: A formulation of membrane finite elements with true drilling rotation, Engineering Computations, July 2019, Emerald,
DOI: 10.1108/ec-12-2018-0572.
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