TY - JOUR
T1 - Variational asymptotic homogenization of beam-like square lattice structures
AU - Barchiesi, Emilio
AU - Khakalo, Sergei
N1 - Funding Information:
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Academy of Finland through the project Adaptive isogeometric methods for thin-walled structures (grant numbers 270007 and 304122) and the Magnus Ehrnrooth Foundation. Access and licences for the commercial FE software Abaqus were provided by CSC–IT Center for Science (www.csc.fi).
Funding Information:
The authors thank Dr Placidi and Dr Niiranen for insightful discussions and comments. The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Academy of Finland through the project Adaptive isogeometric methods for thin-walled structures (grant numbers 270007 and 304122) and the Magnus Ehrnrooth Foundation. Access and licences for the commercial FE software Abaqus were provided by CSC?IT Center for Science (www.csc.fi).
Publisher Copyright:
© The Author(s) 2019.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
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
SN - 1081-2865
VL - 24
SP - 3295
EP - 3318
JO - Mathematics and Mechanics of Solids
JF - Mathematics and Mechanics of Solids
IS - 10
ER -