Monolithic FE2 approach for the thermomechanical modeling of beam structures

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

Abstract

In the present contribution, the FE 2 scheme for beam elements is extended to thermomechanically coupled problems. Beam elements have the advantage of drastically reducing the number of degrees of freedom compared to solid elements. However, the major challenge in modeling structures with beam elements lies in developing sophisticated non‐linear beam material models. This drawback resides in the fact that these elements require effective cross‐sectional properties involving material and geometric properties. The FE 2 method, combined with a homogenization scheme based on the Hill‐Mandel condition, solves this problem. Within this scheme, homogenization of a representative volume element (RVE) on the mesoscopic scale provides effective cross‐sectional properties for the macroscopic scale. This homogenization procedure allows the consideration of non‐linear material formulations and cross‐sectional deformation within the analysis of a beam structure. The applicability of such a FE 2 scheme for purely mechanical problems was already shown. In the present contribution, an extension to thermomechanically coupled problems is provided. In the proposed setting, the macroscopic scale is represented by beam elements with displacement, rotation, and temperature degrees of freedom. Solid elements with displacements and temperature degrees of freedom describe the behavior of the RVE. Hence, the proposed extension solves both scales in a monolithic approach. The assumption of a steady state problem at both scales allows a focus on a consistent scale transition and a discussion about the choice of suitable boundary conditions under the assumption of beam kinematics.

Details

OriginalspracheEnglisch
Aufsatznummere202300259
FachzeitschriftProceedings in Applied Mathematics and Mechanics: PAMM
Jahrgang23
Ausgabenummer4
PublikationsstatusVeröffentlicht - Dez. 2023
Peer-Review-StatusJa

Externe IDs

Mendeley 8ebf43e7-b28d-3694-8cf3-1455a846ab62
unpaywall 10.1002/pamm.202300259

Schlagworte