Shell-to-Beam Numerical Homogenization of 3D Thin-Walled Perforated Beams.

Natalia Staszak,Tomasz Gajewski,Tomasz Garbowski

doi:10.3390/ma15051827

Natalia Staszak, Tomasz Gajewski + Show 1 more

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https://doi.org/10.3390/ma15051827

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Abstract

Determining the geometric characteristics of even complex cross-sections of steel beams is not a major challenge nowadays. The problem arises when openings of various shapes and sizes appear at more or less regular intervals along the length of the beam. Such alternations cause the beam to have different stiffnesses along its length. It has different bending and shear stiffnesses at the opening point and in the full section. In this paper, we present a very convenient and easy-to-implement method of determining the equivalent stiffness of a beam with any cross-section (open or closed) and with any system of holes along its length. The presented method uses the principles of the finite element method (FEM), but does not require any formal analysis, i.e., solving the system of equations. All that is needed is a global stiffness matrix of the representative volumetric element (RVE) of the 3D representation of a beam modeled with shell finite elements. The proposed shell-to-beam homogenization procedure is based on the strain energy equivalence, and allows for precise and quick determination of all equivalent stiffnesses of a beam (flexural and shear). The results of the numerical homogenization procedure were compared with the existing analytical solution and experimental results of various sections. It has been shown that the results obtained are comparable with the reference results.

Highlights

Load-bearing members of structures often require regular perforations/holes or uniquely placed openings
The calculations were made for the C and Z profile without holes and no corner-rounding, depending on the elongation depth and mesh seed size
The homogenization technique proposed has been adapted from the already existing technique based on elastic deformation energy equivalence

Summary

Introduction

Load-bearing members of structures often require regular perforations/holes or uniquely placed openings. Going towards more and more smart buildings, the number of wiring systems will increase in the coming years. Another reason for these features is to fix the mounting to the load bearing element, which was analyzed, for example, in [2]. The mounting holes may be localized in specific locations (pre-planned) or in periodic manner (enabling adjustment of the mounting location in situ). In the former type, the cross-section is weakened in a single location, while in the latter type the cross-section has variable and reduced stiffness along its length. If at the same time the load bearing capacity needs to be kept at a certain level, optimization techniques are often required [3–5]

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