Dynamic Condensation for Efficient Band-Structure Calculations of 2D Periodic Structures

Efficient band-structure calculations are essential for understanding the mechanical behaviors of periodic materials, with significant implications in material design and phononic engineering. This paper introduces the application of the improved reduced system (IRS) technique to expedite elastic band-structure calculations. The IRS, a dynamic condensation method, partitions the unit cell degrees of freedom (DOFs) into primary and secondary sets. A strategic selection of primary DOFs retains a subset of interior DOFs alongside all exterior DOFs while truncating the remaining interior DOFs. The integration of IRS with the Craig–Bampton method for additional reduction and the imposition of Bloch boundary conditions yields a notable decrease in computational overhead. Additionally, for structures with a high number of interior DOFs, a substructuring scheme can be implemented to further enhance efficiency. This approach offers a compelling combination of accuracy and expedited computation, making it applicable across diverse periodic materials.