New Two 20-Node High-Order Finite Elements Based on the SFR Concept for Analyzing 3D Elasticity Problems

Document Type : Research Paper


1 Laboratoire de G´enie Energ´etique et Mat´eriaux (LGEM), University of Biskra, Biskra, Algeria

2 Laboratoire de G´enie Energ´etique et Mat´eriaux (LGEM), University of Biskra, Biskra, Algeria---- University of Batna 2, Faculty of Technology, Department of Mechanics, Batna, Algeria

3 Laboratoire de G´enie M´ecanique (LGM), University of Biskra, Biskra, Algeria



This paper proposes conforming and nonconforming 20-node hexahedral finite elements. The elements’ formulation stems from the so-called Space Fiber Rotation (SFR) concept, allowing a spatial rotation of three-dimensional virtual fiber within the elements. Adding rotational degrees of freedom results in six degrees of freedom per node (three rotations and three translations) which enhances the approximation of the classical displacement field. The incompatible modes approach has been adopted in the nonconforming element formulation in order to avoid numerical deficiencies associated with the Poisson’s ratio locking phenomenon. The accuracy of the proposed elements is examined through a series of three-dimensions linear elastic benchmarks including beam, plates, and shell structures. The proposed elements were shown to give better results than the standard 20-node hexahedron especially when mesh distortion is applied.  This confirms that the two proposed elements are less sensitive to mesh distortion. The elements also show good performance when compared with analytical and numerical solutions from the literature.


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