Computer Methods in Applied Mechanics and Engineering· 2026Q1
A computational model for short-range van der Waals interactions between beams and shells
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- Q1SCImago
- 2026year
Short summary
A new computational model accurately and efficiently captures short-range van der Waals forces between beams and shells by analytically pre-integrating over beam cross-sections and using a surrogate plate approximation.
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Key points
- A coarse-grained model is developed for potential-based interactions (van der Waals attraction, steric repulsion) between beams and shells.
- A 6D integral is reduced to a 5D analytical pre-integration over the beam's cross-section and a 1D numerical integration along the beam's axis.
- The model uses isogeometric finite elements and a continuation method to solve the nonlinear weak form of quasi-static equilibrium.
- Error estimates and convergence analysis are provided, demonstrating excellent accuracy and efficiency for small separations.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Computer Methods in Applied Mechanics and Engineering, 2026 · DOI ↗
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Field: Mechanics of Materials
Mechanics of MaterialsEngineering