Corotational Hinge-based Thin Plates/Shells

TL;DR

This paper introduces six novel corotational hinge-based models for thin plates and shells, improving simulation accuracy, efficiency, and stability for both flat and curved geometries in graphics and engineering.

Contribution

It develops six new curvature-based models derived from three curvature operators within a corotational framework, enhancing simulation capabilities for thin structures.

Findings

Models demonstrate high accuracy in benchmarks

Efficient and stable with large time steps

Applicable to both flat and curved geometries

Abstract

We present six thin plate/shell models, derived from three distinct types of curvature operators formulated within the corotational frame, for simulating both rest-flat and rest-curved triangular meshes. Each curvature operator derives a curvature expression corresponding to both a plate model and a shell model. The corotational edge-based hinge model uses an edge-based stencil to compute directional curvature, while the corotational FVM hinge model utilizes a triangle-centered stencil, applying the finite volume method (FVM) to superposition directional curvatures across edges, yielding a generalized curvature. The corotational smoothed hinge model also employs a triangle-centered stencil but transforms directional curvatures into a generalized curvature based on a quadratic surface fit. All models assume small strain and small curvature, leading to constant bending energy Hessians, which benefit implicit integrators. Through quantitative benchmarks and qualitative elastodynamic simulations with large time steps, we demonstrate the accuracy, efficiency, and stability of these models. Our contributions enhance the thin plate/shell library for use in both computer graphics and engineering applications.