A Novel Multilayer 3D Hexahedral Finite Element for Static and Free Vibration Analysis of Isotropic and Functionally Graded Structures

Randa Bourenane; Belkacem Amieur; Sifeddine Abderrahmani; Abdulrahman M. AL-Nadhari

A Novel Multilayer 3D Hexahedral Finite Element for Static and Free Vibration Analysis of Isotropic and Functionally Graded Structures

Authors

Randa Bourenane Department of Civil Engineering, Laboratory of Applied Civil Engineering (LGCA), University of Echahid Cheikh Larbi Tebessi https://orcid.org/0009-0006-5416-8425
Belkacem Amieur Reliability of Materials and Structures Laboratory, TAHRI Mohamed University of Bechar https://orcid.org/0000-0002-9032-5380
Sifeddine Abderrahmani Department of Civil Engineering, Laboratory of Applied Civil Engineering (LGCA), University of Echahid Cheikh Larbi Tebessi https://orcid.org/0000-0003-2578-8343
Abdulrahman M. AL-Nadhari LARGHYDE Laboratory, Department of Civil Engineering and Hydraulics, Faculty of Sciences and Technology, University of Biskra https://orcid.org/0009-0002-6611-1857

Abstract

This study introduces, for the first time, a high-order three-dimensional quadrature element for the coupled membrane and bending analysis of plate and beam structures under static and free vibration conditions. The formulation combines high-order polynomial interpolation with quadrature-based numerical integration to accurately represent three-dimensional stress and displacement fields. Unlike conventional two-dimensional approaches, the proposed model accounts for through-thickness deformation, making it suitable for both thin and thick structures. Consistent formulations are developed for in-plane and out-of-plane behaviors, with natural coupling achieved within a unified 3D framework. Numerical examples demonstrate the accuracy, efficiency, and robustness of the element in handling complex boundary conditions and higher vibration modes for isotropic and functionally graded materials. The results show rapid convergence, strong agreement with reference solutions, and reliable prediction of natural frequencies. This work provides an effective tool for high-fidelity structural analysis using three-dimensional finite elements.

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Published

28-04-2026

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Articles in Press

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Original Article

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