Shell Finite Elements with Arbitrary Fields Along the Thickness by using RMVT
Erasmo CARRERA, Daniele SCANO
Abstract. Enhanced two-dimensional finite elements based on the Reissner Mixed Variational Theorem are introduced in this paper. In this formulation, the three displacements and the three out-of-plane stresses constitute the unknowns of the mechanical problem. The development is carried out within the Carrera Unified Formulation, which permits the selection of the desired theory. The proposed approach allows for the independent selection of models for each of the six generalized variables, employing both Taylor and Lagrange expansions. Lagrange-based functions are used for the finite element discretization. Validation of the method is performed for the bending of a laminated composite shell by comparison with literature results and highly refined benchmark solutions. The findings indicate that optimal results can be achieved through careful selection of the employed model.
Keywords
Shell Models, Composite Structures, Refined Kinematic, RMVT, Refined Stress Analysis, Lagrange Polynomials
Published online 11/8/2026, 4 pages
Copyright © 2026 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA
Citation: Erasmo CARRERA, Daniele SCANO, Shell Finite Elements with Arbitrary Fields Along the Thickness by using RMVT, Materials Research Proceedings, Vol. 73, pp 290-293, 2026
DOI: https://doi.org/10.21741/9781644904459-56
The article was published as article 56 of the book Mechanics of Advanced Materials and Structures
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
References
[1] E. Carrera, M. Cinefra, M. Petrolo, E. Zappino, Finite Element Analysis of Structures Through Unified Formulation, Wiley, Amsterdam, 2014. https://doi.org/ 10.1002/9781118536643
[2] E. Carrera, Theories and Finite Elements for Multilayered Plates and Shells: A Unified compact formulation with numerical assessment and benchmarking, Arch. Comput. Methods Eng. 10 (2003) 215–296. https://doi.org/10.1007/BF02736224
[3] E. Carrera, D. Scano, Composite shell finite elements with arbitrary displacement fields along the thickness, Mech. Adv. Mater. Struct. 32 (2025) 1–21. https://doi.org/10.1007/s00419-022-02210-5
[4] K.J. Bathe, Finite Element Procedure, Prentice hall, Upper Saddle River, New Jersey, USA, 1996.
[5] J.G. Ren, Exact solutions for laminated cylindrical shells in cylindrical bending, Compos. Sci. Technol. 29 (1987) 169–187. https://doi.org/10.1016/0266-3538(87)90069-8
