- Higher-order beam elements based on the absolute nodal coordinate formulation for three-dimensional elasticity

$Relative errors obtained in the numerical calculation of the flapwise displacement in the Princeton beam experiment with an angle of α=30∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =30^{\circ }$$\end{document} and a force of F3pb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_3^{\text {pb}}$$\end{document}. For the calculation of the relative error, the result obtained with the largest number of elements depicted in Table 6 was used as a reference value for the respective elements. Hence, since only relative errors are shown, it should be noted that the results of element 3333c converge against an incorrect value$

Relative errors obtained in the numerical calculation of the flapwise displacement in the Princeton beam experiment with an angle of α=30∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =30^{\circ }$$\end{document} and a force of F3pb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_3^{\text {pb}}$$\end{document}. For the calculation of the relative error, the result obtained with the largest number of elements depicted in Table 6 was used as a reference value for the respective elements. Hence, since only relative errors are shown, it should be noted that the results of element 3333c converge against an incorrect value

Go to figure page

Reference

Higher-order beam elements based on the absolute nodal coordinate formulation for three-dimensional elasticity - Scientific Figure on ResearchGate. Available from: https://www.researchgate.net/figure/Relative-errors-obtained-in-the-numerical-calculation-of-the-flapwise-displacement-in-the_fig2_311957858 [accessed 26 Apr 2025]

Caption

Relative errors obtained in the numerical calculation of the flapwise displacement in the Princeton beam experiment with an angle of α=30∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =30^{\circ }$$\end{document} and a force of F3pb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_3^{\text {pb}}$$\end{document}. For the calculation of the relative error, the result obtained with the largest number of elements depicted in Table 6 was used as a reference value for the respective elements. Hence, since only relative errors are shown, it should be noted that the results of element 3333c converge against an incorrect value

Embed code

<a href="https://www.researchgate.net/figure/Relative-errors-obtained-in-the-numerical-calculation-of-the-flapwise-displacement-in-the_fig2_311957858"><img src="https://www.researchgate.net/publication/311957858/figure/fig2/AS:941803696046115@1601554907952/Relative-errors-obtained-in-the-numerical-calculation-of-the-flapwise-displacement-in-the.gif" alt="Relative errors obtained in the numerical calculation of the flapwise displacement in the Princeton beam experiment with an angle of α=30∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =30^{\circ }$$\end{document} and a force of F3pb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_3^{\text {pb}}$$\end{document}. For the calculation of the relative error, the result obtained with the largest number of elements depicted in Table 6 was used as a reference value for the respective elements. Hence, since only relative errors are shown, it should be noted that the results of element 3333c converge against an incorrect value"/></a>