Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 3295-3318 |
| Journal | Mathematics and Mechanics of Solids |
| Volume | 24 |
| Issue number | 10 |
| DOIs | |
| Publication status | Published - 1 Oct 2019 |
| MoE publication type | A1 Journal article-refereed |
Fingerprint
Keywords
- variational asymptotic homogenization
- beam-like square lattice structures
- Timoshenko beam
- multiscale description
- Piola’s ansatz
Cite this
}
Variational asymptotic homogenization of beam-like square lattice structures. / Barchiesi, Emilio (Corresponding Author); Khakalo, Sergei.
In: Mathematics and Mechanics of Solids, Vol. 24, No. 10, 01.10.2019, p. 3295-3318.Research output: Contribution to journal › Article › Scientific › peer-review
TY - JOUR
T1 - Variational asymptotic homogenization of beam-like square lattice structures
AU - Barchiesi, Emilio
AU - Khakalo, Sergei
PY - 2019/10/1
Y1 - 2019/10/1
N2 - By means of variational asymptotic homogenization, using Piola’s meso-macro ansatz, we derive the linear Timoshenko beam as the macro-scale limit of a meso-scale beam-like periodic planar square lattice structure. By considering benchmarks in statics and dynamics, meso-to-macro convergence is numerically analyzed. At the finest micro-scale, a 2D assembly of elastic, geometrically linear, isotropic and homogeneous Cauchy continua in plane strain with different material parameters is considered. Using this description, we calibrate the meso-scale model using standard methodology and, by exploiting the meso-to-macro homogenization scaling laws, we recover bending and shear Timoshenko beam moduli. It turns out that the Timoshenko beam found in this way and the finest-scale description based on the Cauchy continuum are in excellent agreement.
AB - By means of variational asymptotic homogenization, using Piola’s meso-macro ansatz, we derive the linear Timoshenko beam as the macro-scale limit of a meso-scale beam-like periodic planar square lattice structure. By considering benchmarks in statics and dynamics, meso-to-macro convergence is numerically analyzed. At the finest micro-scale, a 2D assembly of elastic, geometrically linear, isotropic and homogeneous Cauchy continua in plane strain with different material parameters is considered. Using this description, we calibrate the meso-scale model using standard methodology and, by exploiting the meso-to-macro homogenization scaling laws, we recover bending and shear Timoshenko beam moduli. It turns out that the Timoshenko beam found in this way and the finest-scale description based on the Cauchy continuum are in excellent agreement.
KW - variational asymptotic homogenization
KW - beam-like square lattice structures
KW - Timoshenko beam
KW - multiscale description
KW - Piola’s ansatz
UR - http://www.scopus.com/inward/record.url?scp=85065244907&partnerID=8YFLogxK
U2 - 10.1177/1081286519843155
DO - 10.1177/1081286519843155
M3 - Article
VL - 24
SP - 3295
EP - 3318
JO - Mathematics and Mechanics of Solids
JF - Mathematics and Mechanics of Solids
SN - 1081-2865
IS - 10
ER -