Hierarchy of beam models for lattice core sandwich structures

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2020-11
Major/Subject
Mcode
Degree programme
Language
en
Pages
Series
International Journal of Solids and Structures
Abstract
A discrete-to-continuum transformation to model 2-D discrete lattices as energetically equivalent 1-D continuum beams is developed. The study is initiated in a classical setting but results in a non-classical two-scale micropolar beam model via a novel link within a unit cell between the second-order macrorotation-gradient and the micropolar antisymmetric shear deformation. The shear deformable micropolar beam is reduced to a couple-stress and two classical lattice beam models by successive approximations. The stiffness parameters for all models are given by the micropolar constitutive matrix. The four models are compared by studying stretching- and bending-dominated lattice core sandwich beams under various loads and boundary conditions. A classical 4th-order Timoshenko beam is an apt first choice for stretching-dominated beams, whereas the 6th-order micropolar model works for bending-dominated beams as well. The 6th-order couple-stress beam is often too stiff near point loads and boundaries. It is shown that the 1-D micropolar model leads to the exact 2-D lattice response in the absence of boundary effects even when the length of the 1-D beam (macrostructure) equals that of the 2-D unit cell (microstructure), that is, when L=l.
Description
| openaire: EC/H2020/745770/EU//SANDFECH
Keywords
lattice material, constitutive modelng, sandwich beam, micropolar, couple-stress
Other note
Citation
Karttunen , A T & Reddy , J N 2020 , ' Hierarchy of beam models for lattice core sandwich structures ' , International Journal of Solids and Structures , vol. 204-205 , pp. 172-186 . https://doi.org/10.1016/j.ijsolstr.2020.08.020