A novel plate element based on absolute nodal coordinate formulation with collocation strategy

In this paper, a novel multi-node plate element with absolute node coordinate formulation (ANCF) is proposed. The nodes of the element are collocated to coincide with the in-plane integral quadrature points, which are used to calculate the elastic and inertia functions. The unevenly distributed nodes of the element are the zero points of the second-order derivative of Legendre polynomial and the boundary ends of the element. The tensor product of the two-direction univariate Lagrange interpolation is used to define the displacement field. To alleviate the locking problem, the gradient deficient setup and the second-order gradient of the thickness direction are used as the nodal coordinates. The standard continuum mechanic formulation is used to deduce the elastic forces. The proposed plate element based on the ANCF with collocated nodes is denoted as ANCF_\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\_$$\end{document}C element. The performance of the ANCF_\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\_$$\end{document}C element is verified by static, eigenfrequency and dynamic examples. The results show that the ANCF_\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\_$$\end{document}C element is more accurate and computationally efficient.