Numerical modelling of thin anisotropic membrane under dynamic load

Abstract

This work aims to describe a mathematical model and a numerical method to simulate a thin anisotropic membrane moving and deforming in 3D space under a dynamic load of an arbitrary time and space profile. The anisotropic continuum medium model described in the article can be used to model a membrane made of composite material using its effective elastic parameters. The model and the method allow the consideration of problems when the quasi-static approximation is not valid and elastic waves caused by the impact should be calculated. The model and the method can be used for numerical study of different processes in thin composite layers, such as shock load, ultrasound propagation, non-destructive testing procedures and vibrations. The thin membrane is considered as a 2D object in 3D space, an approach that allows a reduction in the computational time compared with full 3D models, while still having an arbitrary material rheology and load profile.