Simultaneous analysis of curved Kirchhoff beams and Kirchhoff--Love shells embedded in bulk domains
arXiv:2602.14566 · doi:10.1016/j.compstruc.2026.108289
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 -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.
arXiv commentArticle has been submitted to Computers & Structures
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