TY - JOUR
T1 - Homogenisation of periodic lattices with lumped and distributed mass
T2 - Beam models, continualisation and stabilisation
AU - Askes, Harm
AU - Lombardo, Mariateresa
AU - Nguyen, Duc C.D.
N1 - Publisher Copyright:
© 2024 The Author(s)
PY - 2024/10/1
Y1 - 2024/10/1
N2 - Periodic lattice models of beams are homogenised to obtain equivalent continuum models. Various modelling aspects for the discrete model are discussed, such as the selection of a beam theory and the assumption of mass distribution. Straightforward continualisation by means of Taylor series leads, upon truncation, to a hierarchical series of models of increasing accuracy: the lowest order of these belong to the category of couple stress theories, whereas in the higher-order models the equations of motion are extended with strain gradients and acceleration gradients of the displacement and rotational degrees of freedom. Some of the resulting models are affected by instabilities. These instabilities can be eliminated by alternative approaches to continualisation based on Padé approximations, as will be demonstrated. Throughout, a systematic comparison between lumped mass and distributed mass is made.
AB - Periodic lattice models of beams are homogenised to obtain equivalent continuum models. Various modelling aspects for the discrete model are discussed, such as the selection of a beam theory and the assumption of mass distribution. Straightforward continualisation by means of Taylor series leads, upon truncation, to a hierarchical series of models of increasing accuracy: the lowest order of these belong to the category of couple stress theories, whereas in the higher-order models the equations of motion are extended with strain gradients and acceleration gradients of the displacement and rotational degrees of freedom. Some of the resulting models are affected by instabilities. These instabilities can be eliminated by alternative approaches to continualisation based on Padé approximations, as will be demonstrated. Throughout, a systematic comparison between lumped mass and distributed mass is made.
KW - UT-Hybrid-D
KW - Generalised continuum
KW - Homogenisation
KW - Micropolar theory
KW - Periodic lattice
KW - Continualisation
UR - http://www.scopus.com/inward/record.url?scp=85199208596&partnerID=8YFLogxK
U2 - 10.1016/j.ijsolstr.2024.112988
DO - 10.1016/j.ijsolstr.2024.112988
M3 - Article
AN - SCOPUS:85199208596
SN - 0020-7683
VL - 302
JO - International journal of solids and structures
JF - International journal of solids and structures
M1 - 112988
ER -