A New Triangular Hybrid Displacement Function Element for Static and Free Vibration Analyses of Mindlin-Reissner Plate

• Main Authors: Jun-Bin Huang, Song Cen, Yan Shang, Chen-Feng Li
• Format: Article
• Language: English
• Published: Marcílio Alves
• Series: Latin American Journal of Solids and Structures
• Subjects: Finite element method; Mindlin-Reissner plate element; hybrid displacement function element method; modified principle of complementary energy; static and free vibration analyses
• Online Access: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252017000500765&lng=en&tlng=en

Abstract A new 3-node triangular hybrid displacement function Mindlin-Reissner plate element is developed. Firstly, the modified variational functional of complementary energy for Mindlin-Reissner plate, which is eventually expressed by a so-called displacement function F, is proposed. Secondly, the locking-free formulae of Timoshenko’s beam theory are chosen as the deflection, rotation, and shear strain along each element boundary. Thirdly, seven fundamental analytical solutions of the displacement function F are selected as the trial functions for the assumed resultant fields, so that the assumed resultant fields satisfy all governing equations in advance. Finally, the element stiffness matrix of the new element, denoted by HDF-P3-7β, is derived from the modified principle of complementary energy. Together with the diagonal inertia matrix of the 3-node triangular isoparametric element, the proposed element is also successfully generalized to the free vibration problems. Numerical results show that the proposed element exhibits overall remarkable performance in all benchmark problems, especially in the free vibration analyses.