 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 13427 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8178
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| In English (Mech. Solids): | | 5249 |
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| << Previous article | Volume 60, Issue 6 / 2025 | Next article >> |
| A. Belounar, F. Boussem, and L. Belounar, "Higher Order Strain-Based Quadrilateral Membrane Finite Element for Static and Free vibration Analysis," Mech. Solids. 60 (6), 4656-4672 (2025) |
| Year |
2025 |
Volume |
60 |
Number |
6 |
Pages |
4656-4672 |
| DOI |
10.1134/S0025654425601727 |
| Title |
Higher Order Strain-Based Quadrilateral Membrane Finite Element for Static and Free vibration Analysis |
| Author(s) |
A. Belounar (Department of Civil Engineering, University Center of Tipaza, Tipaza, Algeria; NMISSI Laboratory, Faculty of Science and Technology, Biskra University, Biskra, Algeria, belounarab@yahoo.fr)
F. Boussem (NMISSI Laboratory, Faculty of Science and Technology, Biskra University, Biskra, Algeria;Department of Hydrocarbons and Renewable Energies, Adrar University, Adrar, Algeria, fboussem@gmail.com)
L. Belounar (NMISSI Laboratory, Faculty of Science and Technology, Biskra University, Biskra, Algeria, belounarl@yahoo.com) |
| Abstract |
This paper presents a new membrane finite element with in-plane rotational degrees of freedom and an additional internal node formulated using the assumed strain formulation. Designed for
static and free vibration analyses, the proposed element is a quadrilateral with five nodes, which contains two translational and one in-plane rotational degrees of freedom at each corner node and only
two in-plane translations for the central node. To improve computational efficiency, the static condensation concept is applied to remove the degrees of freedom of the central node, reducing system
complexity without affecting accuracy or stability. A series of extensive static tests, including well-known reference problems such as cantilever beams with different shapes, and thick cylinders subjected to internal pressure, demonstrated the element’s superior performance on both regular and distorted meshes. In addition, the present element showed good agreement in free vibration studies of a
cantilever wall, a cantilever beam, a variable-section cantilever beam, and a wall with openings.
Results indicate that the proposed element achieves an accuracy comparable to higher-order elements,
making it an effective and reliable choice for modeling thin-walled structures with significant in-plane behavior. |
| Keywords |
Membrane finite element, static condensation, internal node, strain-based approach, drilling rotational degrees of freedom |
| Received |
12 April 2025 | Revised |
31 July 2025 | Accepted |
03 August 2025 |
| Link to Fulltext |
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