Simultaneous analysis of curved Kirchhoff beams and Kirchhoff--Love shells embedded in bulk domains

2026-02-16

AI Summary

This work proposes an efficient and high-accuracy volumetric approach for the simultaneous modeling and analysis of multiple curved beams and Kirchhoff–Love shell structures implicitly defined by level-set functions. Building upon Kirchhoff–Love theory, the method embeds diverse thin structures within a unified bulk computational domain using level-set representations and introduces a hybrid high-order Bulk Trace Finite Element Method (Bulk Trace FEM). This formulation circumvents the need for high-order continuity in the displacement field by employing only standard C⁰-continuous Lagrange elements. Numerical experiments demonstrate the method’s high-order convergence and accuracy, and provide reproducible benchmark cases that lay the groundwork for multiphysics simulations involving complex thin-walled structures.

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Abstract

A set of curved beams and shells is geometrically implied by level sets of a scalar function over some bulk domain. The mechanical model for each structure is based on the Kirchhoff--Love theory, that is, small displacements without shear deformations are considered. These models for individual geometries are extended to bulk models, simultaneously modeling the whole set of beams/shells on all level sets. A major focus is on the numerical analysis of such models. A mixed-hybrid and higher-order accurate Bulk Trace FEM is proposed that enables the use of standard $C^0$-continuous Lagrange elements with dimensionality of the bulk domain. That is, the higher-order continuity requirements of displacement-based formulations in context of the Kirchhoff--Love theory are successfully alleviated. Several numerical tests confirm the accuracy and higher-order convergence of the proposed methodology, also qualifying as benchmark test cases in future studies.

Problem

• Kirchhoff beams
• Kirchhoff–Love shells
• level sets
• numerical analysis
• higher-order continuity

Innovation

• Bulk Trace FEM
• Kirchhoff–Love shells
• level set method
• mixed-hybrid formulation
• higher-order accuracy