Bridging multi-scale approach to consider the effects of local deformations in the analysis of thin-walled members

Abstract

Thin-walled members that have one dimension relatively large in comparison to the cross-sectional dimensions are usually modelled by using beam-type one-dimensional finite elements. Beam-type elements, however, are based on the assumption of rigid cross-section, thus they only allow considerations associated with the beam axis behaviour such as flexural-, torsional-or lateral-buckling and cannot consider the effects of local deformations such as flange local buckling or distortional buckling. In order to capture the local effects of this type shell-type finite element models can be used. Based on the Bridging multi-scale approach, this study proposes a numerical technique that is able to split the global analysis, which is performed by using simple beamtype elements, from the local analysis which is based on more sophisticated shell-type elements. As a result, the proposed multi-scale method allows the usage of shell elements in a local region to incorporate the local deformation effects on the overall behaviour of thin-walled members without necessitating a shell-type model for the whole member. Comparisons with full shell-type analysis are provided in order to illustrate the efficiency of the method developed herein.

Multi-scale modelling for bending analysis of heterogeneous plates by coupling BEM and FEM

“…Observe that if the RVE stiffness is reduced, the material integrity of the local point of the macro-continuum is also reduced, requiring therefore a non-linear formulation for the macrocontinuum. In most of the works about multi-scale analysis the Finite Element Method (FEM) is used to model both the macro and micro continuums ( [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]), although some few formulations adopting the Boundary Element Method (BEM) to model one or even both scales have been proposed (see [29,30]). …”

Multi-scale overlapping domain decomposition to consider local effects in the analysis of pipes

“…In order to capture ovalization in pipe elbows, efficient beam type formulations were developed in (Bathe & Almeida, 1982;Militello & Huespe, 1988). Recently, R. E. Erkmen (2013) developed an analysis procedure based on the Bridging multi-scale method of Liu et al (2006), in order to incorporate local deformation effects in the analysis of thin-walled members. This approach allows employment of two kinematic models within the numerical analysis, and while simple beam-type elements are used for the analysis of the overall structure, more sophisticated shell-type elements are employed for the local fine-scale analysis in a relatively narrow span of the member.…”

“…This approach allows employment of two kinematic models within the numerical analysis, and while simple beam-type elements are used for the analysis of the overall structure, more sophisticated shell-type elements are employed for the local fine-scale analysis in a relatively narrow span of the member. In the present study, we extend the procedure developed in R. E. Erkmen (2013) for the elasto-plastic analysis of pipes. Comparisons with full shell-and beam-type models are provided in order to illustrate the efficiency of the proposed analysis.…”

Multi-Scale Overlapping Domain Decomposition to Consider Elasto-Plastic Local Buckling Effects in the Analysis of Pipes

“…This approach allows employment of two kinematic models within the numerical analysis, and while simple beam-type elements are used for the analysis of the overall structure, more sophisticated shell-type elements are employed for the local fine-scale analysis in a relatively narrow span of the member. In the present study, we extend the procedure developed in Erkmen [38] for the elasto-plastic analysis of pipes. Comparisons with full shell-and beam-type models are provided in order to illustrate the efficiency of the proposed analysis.…”

“…In order to capture ovalization in pipe elbows, efficient beam type formulations were developed in [34][35][36]. Recently, Erkmen [38] developed an analysis procedure based on the Bridging multi-scale method of Liu et al [25][26][27][28], in order to incorporate local deformation effects in the analysis of thin-walled members. This approach allows employment of two kinematic models within the numerical analysis, and while simple beam-type elements are used for the analysis of the overall structure, more sophisticated shell-type elements are employed for the local fine-scale analysis in a relatively narrow span of the member.…”