Orthotropic rotation-free thin shell elements

TL;DR

This paper introduces an efficient method for simulating orthotropic behavior in thin shell finite elements by transforming shape function derivatives, enabling accurate modeling of orthotropic materials with minimal computational overhead.

Contribution

A novel transformation approach for shape functions in rotation-free thin shell elements that efficiently incorporates orthotropic material behavior within existing finite element frameworks.

Findings

Accurately models wrinkling in orthotropic sheets with coarse meshes

Demonstrates minimal additional computational effort compared to isotropic models

Validates approach using standard shell deformation benchmarks

Abstract

A method to simulate orthotropic behaviour in thin shell finite elements is proposed. The approach is based on the transformation of shape function derivatives, resulting in a new orthogonal basis aligned to a specified preferred direction for all elements. This transformation is carried out solely in the undeformed state leaving minimal additional impact on the computational effort expended to simulate orthotropic materials compared to isotropic, resulting in a straightforward and highly efficient implementation. This method is implemented for rotation-free triangular shells using the finite element framework built on the Kirchhoff--Love theory employing subdivision surfaces. The accuracy of this approach is demonstrated using the deformation of a pinched hemispherical shell (with a 18{\deg} hole) standard benchmark. To showcase the efficiency of this implementation, the wrinkling of orthotropic sheets under shear displacement is analyzed. It is found that orthotropic subdivision shells are able to capture the wrinkling behavior of sheets accurately for coarse meshes without the use of an additional wrinkling model.