journal article·2024-02-28Open access

Influence of Applied Loads on Free Vibrations of Functionally Graded Material Plate–Shell Panels

José Simões Moita, Victor Franco Correia, Cristóvão Mota Soares

Applied Sciences· Volume 14· Issue 5

Abstract

An analysis of the influence of applied loads on free vibrations of plate and shell panels made of functionally graded materials is analyzed in the present work. Formulations for the static analysis considering geometrically nonlinear behavior, as well as linear buckling and free vibrations analyses are considered. A calculation of the through-thickness stress distribution is also performed. The finite element model is based on a higher order shear deformation theory using a non-conforming flat triangular plate/shell element with three nodes, and eight degrees of freedom per node is used in the numerical implementation. The results obtained with this numerical model are presented, discussed, and compared with alternative solutions published by other authors in some benchmark applications.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Composite Structure Analysis and Optimization · Vibration and Dynamic Analysis · Structural Load-Bearing Analysis

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

ENIDH—Escola Superior Náutica Infante D. Henrique, Av. Eng. Bonneville Franco, 2770-058 Paço de Arcos, Portugal

Funding

FCT, Fundação para a Ciência e Tecnologia, through IDMEC, under LAETA

References (25)

Show source-provided references
1. Nonlinear analysis of functionally graded plates and shallow shells10.1016/S0020-7683(01)00048-8 ↗
2. Reddy, J.N., and Arciniega, R.A. (2006). Analysis and Design of Plated Structures: Dynamics, Woodhead Publishing.
3. Large deformation analysis of functionally graded shells10.1016/j.ijsolstr.2006.08.035 ↗
4. Geometrically nonlinear analysis of functionally graded material (FGM) plates and shells using a four-node quasi-conforming shell element10.1177/0021998307086211 ↗
5. Geometrically nonlinear analysis of functionally graded shells10.1016/j.ijmecsci.2008.12.004 ↗
6. Isogeometric analysis of functionally graded plates using higher-order shear deformation theory10.1016/j.compositesb.2013.02.045 ↗
7. A simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded plates10.1016/j.compstruct.2012.08.025 ↗
8. Natarajan, S., Ferreira, A.J.M., Bordas, S., Carrera, E., Cinefra, M., and Zenkour, A.M. (2014). Analysis of Functionally Graded Material Plates Using Triangular Elements with Cell-Based Smoothed Discrete Shear Gap Method. Math. Probl. Eng., 247932.10.1155/2014/247932 ↗
9. Geometrically nonlinear analysis of functionally graded plates using isogeometric analysis10.1108/EC-09-2013-0220 ↗
10. Material and Geometric Nonlinear Analysis of Functionally Graded Plate-Shell Type Structures10.1007/s10443-016-9473-8 ↗
11. Higher-order finite element models for the static linear and nonlinear behaviour of functionally graded material plate-shell structures10.1016/j.compstruct.2019.01.046 ↗
12. Displacement-based and stress-based analytical approaches for nonlinear bending analysis of functionally graded porous plates resting on elastic substrate10.1007/s00707-022-03196-5 ↗
13. Pham, V.V., Nguyen, V.C., Hadji, L., Mohamed-Ouejdi, B., and Ömer, C. (2023). A comprehensive analysis of in-plane functionally graded plates using improved first-order mixed finite element model. Mech. Based Des. Struct. Mach.10.1080/15397734.2023.2245876 ↗
14. Multiple cracking in functionally graded ceramic/metal coatings10.1016/0020-7683(94)00267-Z ↗
15. Zienkiewicz, O.C. (1977). The Finite Element Method, McGraw-Hill.
16. A simple and effective element for analysis of general shell structures10.1016/0045-7949(81)90029-8 ↗
17. Bathe, K.J. (1982). Finite Element Procedures in Engineering Analysis, Prentice-Hall Inc.
18. Analysis of active-passive plate structures using a simple and efficient finite element model10.1080/15376494.2010.496062 ↗
19. A fast incremental/iterative solution procedure that handles snap-through
20. Crisfield, M.A. (1991). Non-Linear Finite Element Analysis of Solid and Structures, Volume 1: Essentials, John Wiley & Sons.
21. Analysis of functionally graded plates by an efficient finite element method with node-based strain smoothing10.1016/j.tws.2012.01.013 ↗
22. Post-buckling analysis of functionally graded rectangular plates10.1016/j.compstruct.2005.08.026 ↗
23. A mesh-free method for analysis of the thermal and mechanical buckling of functionally graded cylindrical shell panels10.1007/s00466-009-0446-8 ↗
24. Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation10.1016/j.jsv.2008.03.056 ↗
25. Free vibration analysis of functionally graded shells by a higher-order shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations10.1016/j.euromechsol.2012.05.005 ↗