Specht Triangle Approximation of Large Bending Isometries

Abstract

We propose a Specht triangle discretization for a geometrically nonlinear Kirchhoff plate model with large bending isometry. A combination of an adaptive time-stepping gradient flow and a Newton’s method is employed to solve the ensuing nonlinear minimization problem. $\Gamma$−convergence of the Specht triangle discretization and the unconditional stability of the gradient flow algorithm are proved. We present several numerical examples to demonstrate that our approach significantly enhances both the computational efficiency and accuracy.