TY - JOUR

T1 - Indirect reduced-order modelling

T2 - Using nonlinear manifolds to conserve kinetic energy

AU - Nicolaidou, Evangelia

AU - Hill, Tom L

AU - Neild, Simon A

PY - 2020/10/21

Y1 - 2020/10/21

N2 - Nonlinear dynamic analysis of complex engineering structures modelled using commercial ﬁnite element (FE) software is computationally expensive. Indirect reduced-order modelling strategies alleviate this cost byconstructinglow-dimensionalmodelsusingastatic solution dataset from the FE model. The applicability of such methods is typically limited to structures in which (a) the main source of nonlinearity is the quasi-static coupling between transverse and inplane modes (i.e. membrane stretching); and (b) the amount of in-plane displacement is limited. We show that the second requirement arises from the fact that, in existing methods, in-plane kinetic energy is assumed to be negligible. For structures such as thin plates and slender beams with ﬁxed/pinned boundary conditions, this is often reasonable, but in structures with free boundary conditions (e.g. cantilever beams), this assumption is violated. Here, weexploittheconceptofnonlinearmanifoldstoshow how the in-plane kinetic energy can be accounted for in the reduced dynamics, without requiring any additional information from the FE model. This new insight enables indirect reduction methods to be applied to a far wider range of structures whilst maintainingaccuracytohigherdeﬂectionamplitudes. The accuracy of the proposed method is validated using an FE model of a cantilever beam.

AB - Nonlinear dynamic analysis of complex engineering structures modelled using commercial ﬁnite element (FE) software is computationally expensive. Indirect reduced-order modelling strategies alleviate this cost byconstructinglow-dimensionalmodelsusingastatic solution dataset from the FE model. The applicability of such methods is typically limited to structures in which (a) the main source of nonlinearity is the quasi-static coupling between transverse and inplane modes (i.e. membrane stretching); and (b) the amount of in-plane displacement is limited. We show that the second requirement arises from the fact that, in existing methods, in-plane kinetic energy is assumed to be negligible. For structures such as thin plates and slender beams with ﬁxed/pinned boundary conditions, this is often reasonable, but in structures with free boundary conditions (e.g. cantilever beams), this assumption is violated. Here, weexploittheconceptofnonlinearmanifoldstoshow how the in-plane kinetic energy can be accounted for in the reduced dynamics, without requiring any additional information from the FE model. This new insight enables indirect reduction methods to be applied to a far wider range of structures whilst maintainingaccuracytohigherdeﬂectionamplitudes. The accuracy of the proposed method is validated using an FE model of a cantilever beam.

M3 - Article (Academic Journal)

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 1364-5021

ER -