Bending and Free Vibration Analysis of Thin Plates

Linear bending and free vibration analysis of a thin plate using 16 degree of freedom Bogner-Fox-Schmit plate finite elements.

Linear bending and free vibration analysis of a thin plate is performed. The problem is solved using Bogner-Fox-Schmit [1] plate finite elements containing four nodes and sixteen degrees of freedom. Mass and stiffness matrices are computed using the computationally-efficient method described in Ref. [2]. Additional information regarding the BFS element and code structure was gathered from Refs. [3-4].

Bending: A thin plate is subjected to either uniform or non-uniform static pressure loading. Clamped and simply supported boundary conditions can be applied. Displacement results are checked using analytical formulas and Ref. [1].

Free vibration: The natural frequencies and mode shapes of a thin plate are computed by solving the eigenvalue problem. Clamped and simply supported boundary conditions can be applied. Simply supported natural frequencies are checked using analytical formulas.

References:

[1] Bogner, F.K, Fox, R.L, and Schmit, L.A., "The Generation of Inter-Element-Compatible Stiffness and Mass Matrices by the Use of Interpolation Formulas," Report AFFDL-TR-66-80, 1966, pp. 395-443.

[2] Bismarck-Nasr, M.N., "On The Sixteen Degree of Freedeom Rectangular Plate Element" Computers & Structures, 1991, Vol. 40, No. 4, pp. 1059-1060.

[3] Friedmann, P.P., Lesieutre, G., and Huang, D., "Finite Element Method and Model Reduction," Structural Dynamics: Theory and Applications to Mechanical and Aerospace Engineering, 1st ed., Cambridge University Press, 2023, pp. 214-220.

[4] Ferreira, A.J.M., "Analysis of Mindlin Plates", MATLAB Codes for Finite Element Analysis, 1st ed., Springer, 2009, pp. 165-191.