A computational model for short-range van der Waals interactions between beams and shells

TL;DR

This paper introduces a computational model that efficiently simulates short-range van der Waals and steric interactions between beams and shells using a hybrid analytical and numerical approach, with applications in structural analysis.

Contribution

It presents a novel hybrid analytical-numerical method for modeling beam-shell interactions with van der Waals forces, including error estimates and convergence analysis.

Findings

The method achieves a good balance between accuracy and efficiency.

Numerical examples demonstrate the model's effectiveness.

Error estimates and convergence are rigorously analyzed.

Abstract

We consider potential-based interactions between beams (or fibers) and shells (or membranes) using a coarse-grained approach with focus on van der Waals attraction and steric repulsion. The involved 6D integral over volumes of a beam and a shell is split into a 5D analytical pre-integration over the beam's cross section and a surrogate plate tangential to the closest point on the shell, and the remaining 1D numerical integration along the beam's axis. This general inverse-power interaction potential is added to the potential energies of the Bernoulli-Euler beam and the Kirchhoff-Love shell. The total potential energy is spatially discretized using isogeometric finite elements, and the nonlinear weak form of quasi-static equilibrium is solved using the continuation method. We provide error estimates and convergence analysis, together with two intriguing numerical examples. The developed approach provides excellent balance between accuracy and efficiency for small separations.