Abstract
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.
Original language | English |
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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 |
Funding
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.
Keywords
- variational asymptotic homogenization
- beam-like square lattice structures
- Timoshenko beam
- multiscale description
- Piola’s ansatz