Isogeometric multi-patch shell analysis using the Geometry + Simulation Modules

TL;DR

This paper introduces new software modules within the G+Smo framework that enable advanced isogeometric multi-patch shell analysis, including patch coupling, error estimation, and wrinkling modeling, enhancing versatility and future extensibility.

Contribution

The paper presents a software implementation of isogeometric Kirchhoff-Love shells with new modules for patch coupling, error estimation, and wrinkling analysis, supporting multi-patch shell modeling.

Findings

Provides patch coupling via penalty methods and unstructured splines.

Includes goal-oriented error estimators for shell analysis.

Features advanced algorithms for wrinkling in hyperelastic membranes.

Abstract

Isogeometric Analysis (IGA) bridges Computer-Aided Design (CAD) and Finite Element Analysis (FEA) by employing splines as a common basis for geometry and analysis. One of the advantages of IGA is in the realm of thin shell analysis: due to the arbitrary continuity of the spline basis, Kirchhoff-Love shells can be modeled without the need to introduce unknowns for the mid-plane rotations, leading to a reduction in the number of unknowns. In this paper, we provide the background of an implementation of Isogeometric Kirchhoff--Love shells within the Geometry + Simulation Modules (G+Smo). This paper accompanies multiple previous publications and elaborates on the design of the software used in these papers, rather than the novelty of the methods presented therein. The presented implementation provides patch coupling via penalty methods and unstructured splines, goal-oriented error estimators, several algorithms for structural analysis and advanced algorithms for the modeling of wrinkling in hyperelastic membranes. These methods are all contained in three new modules in G+Smo: a module for Kirchhoff-Love shells, a module for structural analysis, and a module for unstructured spline constructions. As motivated in this paper, the modules are implemented to be compatible with future developments. For example, by providing base implementations of material laws, by using black-box functions for the structural analysis module, or by providing a standardized approach for the implementation of unstructured spline constructions. Overall, this paper demonstrates that the new modules contribute to a versatile ecosystem for the modeling of multi-patch shell problems through fast off-the-shelf solvers with a simple interface, designed to be extended in future research.