After space discretization employing traditional dynamic isogeometric analysis of structures (composite type) with/without dissimilar materials, the issues that persist include either using numerically non-dissipative time integration algorithms that induces the high frequency participation (oscillations) in solution, or using dissipative algorithms that can dampen the high frequency participation but simultaneously induce significant loss of total energy of the system. To circumvent this dilemma, we instead develop a novel approach via a proper orthogonal decomposition (POD) based dynamic isogeometric methodology/framework that eliminates (significantly reduces) high-frequency oscillations whilst conserving the physics (e.g., total energy) for dynamic analysis of (composite or hybrid) structures comprising of dissimilar materials. This proposed framework and contributions therein are comprised of three phases, namely, (1) it successfully filters the high-frequency part via first simulating the original IGA semi-discretized structure with dissimilar materials for a few time steps using numerically dissipative type integration schemes, and then obtain the reduced IGA system via POD. (2) We then simulate the reduced IGA system (high-frequency oscillations being eliminated) with instead a numerically non-dissipative algorithm to conserve the underlying physics. As consequence, we successfully preserve the physics (energy) associated with the low frequency modes whilst eliminating/reducing the high-frequency oscillations. (3) Three illustrative examples, with/without dissimilar materials demonstrate the advantages of IGA for applications to structures with dissimilar materials over FEM, in particular, in modeling complex geometries and providing more accurate dynamic solutions with less number of degrees of freedom. Furthermore, we show the effectiveness and efficiency of the proposed approach in further advancing the dynamic isogeometric analyses for both linear, and material and/or geometrically nonlinear cases.
|Original language||English (US)|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|State||Published - Feb 1 2020|
Bibliographical noteFunding Information:
The authors would like to thank the Luxembourg National Research Fund for Intuitive modeling and SIMulation platform (IntuiSIM) ( PoC17/12253887 ), National Key R&D Program of China ( 2017YFB1002704 ), National Science Foundation of China ( 11472101 ), National Science Foundation of China ( 81772025 ), and the Foundation for Innovative Research Groups of the National Natural Science Foundation of China ( 51621004 ) support to this work.
© 2019 Elsevier B.V.
Copyright 2019 Elsevier B.V., All rights reserved.
- Dynamic isogeometric analysis (IGA)
- Numerically dissipative and non-dissipative time integration algorithms
- Physics conserved whist high-frequency oscillation eliminated
- Proper orthogonal decomposition (POD)