C1 Triangular Isogeometric Analysis of the von Karman Equations

TL;DR

This paper demonstrates that rational triangular Bezier splines within an isogeometric analysis framework can efficiently and accurately solve high-order PDEs like the von Karman equations, achieving optimal convergence rates.

Contribution

It introduces a novel approach using rational triangular Bezier splines for direct solution of fourth order PDEs without mixed formulations.

Findings

High accuracy in benchmark problems

Optimal convergence rates in multiple norms

Efficient solution of high-order PDEs

Abstract

In this paper, we report the use of rational Triangular Bezier Splines (rTBS) to numerically solve the von Karman equations, a system of fourth order PDEs. $C^{1}$ smoothness of the mesh, generated by triangular Bezier elements, enables us to directly solve the von Karman systems of equations without using mixed formulation. Numerical results of benchmark problems show high accuracy and optimal convergence rate in L1, H1 and H2 norm for quadratic and cubic triangular Bezier elements. Results of this study show that triangular isogeometric analysis can efficiently and accurately solve systems of high order PDEs. Keywords: Rational triangular Bezier splines; Isogeometric analysis; Von Karman; Optimal convergence rate; High order PDEs; Smooth mesh; Triangular elements.