Details

Autor(en) / Beteiligte

• Fries, Thomas-Peter
• Kaiser, Michael Wolfgang

Titel

On the simultaneous solution of structural membranes on all level sets within a bulk domain

Ist Teil von

• Computer methods in applied mechanics and engineering, 2023-10, Vol.415, p.116223, Article 116223

Ort / Verlag

Elsevier B.V

Erscheinungsjahr

2023

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• A mechanical model and numerical method for structural membranes implied by all isosurfaces of a level-set function in a three-dimensional bulk domain are proposed. The mechanical model covers large displacements in the context of the finite strain theory and is formulated based on the tangential differential calculus. Alongside curved two-dimensional membranes embedded in three dimensions, also the simpler case of curved ropes (cables) in two-dimensional bulk domains is covered. The implicit geometries (shapes) are implied by the level sets and the boundaries of the structures are given by the intersection of the level sets with the boundary of the bulk domain. For the numerical analysis, the bulk domain is discretized using a background mesh composed by (higher-order) elements with the dimensionality of the embedding space. The elements are by no means aligned to the level sets, i.e., the geometries of the structures, which resembles a fictitious domain method, most importantly the Trace FEM. The proposed numerical method is a hybrid of the classical FEM and fictitious domain methods which may be labelled as “Bulk Trace FEM”. Numerical studies confirm higher-order convergence rates and the potential for new material models with continuously embedded sub-structures in bulk domains. •Curved structures are implied by all level sets over a bulk domain.•Mechanical model for all implied structural ropes and membranes considered at once.•New finite strain theory for the simultaneous analysis of a set of curved structures.•The Bulk Trace FEM for the numerical solution of the mechanical model is proposed.•Numerical results confirm optimal convergence rates.