Application of hybrid Trefftz finite element method to non-linear problems of minimal surface

Abstract

This investigation provides a hybrid Trefftz finite element approach for analysing minimal surface problems. The approach is based on combining Trefftz finite element formulation with radial basis functions (RBF) and the analogue equation method (AEM). In this method, use of the analogue equation approach avoids the difficulty of treating the non-linear terms appearing in the soap bubble equation, making it possible to solve non-linear problems with the Trefftz method. Global RBF is used to approximate the inhomogeneous term induced from non-linear functions and other loading terms. Finally, some numerical experiments are implemented to verify the efficiency of this method. Show more