A four-node rectangular plate finite element using Airy functions with transverse shear

• Published in: International journal of structural integrity Vol. 14; no. 6; pp. 891 - 904
• Main Author: Abderrahmani, Sifeddine
• Format: Journal Article
• Language: English
• Published: Bingley Emerald Publishing Limited 14.11.2023; Emerald Group Publishing Limited
• Subjects: Airy function; Approximation; Construction; Equilibrium conditions; Exact solutions; Finite element method; Harmonic functions; Interpolation; Kinematics; Kirchhoff theory; Load; Mathematical models; Numerical models; Polynomials; Rectangular plates; Robustness (mathematics); Stiffness matrix; Thin plates; Transverse shear; Analytic integration; Rectangular finite element; Airy function; Strain formulation; Thin plate bending
• ISSN: 1757-9864; 1757-9872
• DOI: 10.1108/IJSI-07-2023-0063

PurposeAmong different types of engineering structures, plates play a significant role. Their analysis necessitates numerical modeling with finite elements, such as triangular, quadrangular or sector plate elements, owing to the intricate geometrical shapes and applied loads. The scope of this study is the development of a new rectangular finite element for thin plate bending based on the strain approach using Airy's function. It is called a rectangular plate finite element using Airy function (RPFEUAF) and has four nodes. Each node had three degrees of freedom: one transverse displacement (w) and two normal rotations (x, y).Design/methodology/approachEquilibrium conditions are used to generate the interpolation functions for the fields of strain, displacements and stresses. The evolution of the Airy function solutions yielded the selection of these polynomial bi-harmonic functions. The variational principle and the analytical integration approach are used to evaluate the basic stiffness matrix.FindingsThe numerical findings for thin plates quickly approach the Kirchhoff solution. The results obtained are compared to the analytical solution based on Kirchhoff theory.Originality/valueThe efficiency of the strain based approach using Airy's function is confirmed, and the robustness of the presented element RPFEUAF is demonstrated. Because of this, the current element is more reliable, better suited for computations and especially intriguing for modeling this kind of structure.