Resolving high frequency issues via proper orthogonal decomposition based dynamic isogeometric analysis for structures with dissimilar materials

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.