Perpustakaan Digital ITB

Fibre-reinforced polymer (FRP) laminates combine high specific stiffness with a strongly heterogeneous microstructure, so that their macroscopic structural response is governed by plylevel and fibre–matrix interactions that classical homogenized plate models cannot resolve directly. Two-scale finite element (FE²) framework recovers this physics but, in its conventional nested form, requires a solver-within-a-solver and is computationally and operationally expensive. The Direct FE² method removes the nested solver by embedding microscale representative volume elements (RVEs) into a single concurrent finite element job, linking the macroscale integration points to the RVE boundaries through linear multi-point constraints (MPCs) and energy-consistent volume scaling. This thesis develops and verifies a Direct FE² framework in which a Mindlin–Reissner (first-order shear deformation) macroscale shell, discretized with four-node S4 elements, is coupled to homogenized 3D solid RVEs placed at every in-plane and through-thickness Gauss point. The principal contribution is a multi-ply capability so each ply can carry its own RVE part and fibre orientation, multiple RVEs are stacked through the thickness at their physical Gauss-point heights, and a distinct RVE part may be assigned per through-thickness Gauss point. The kinematic coupling is realized entirely through Abaqus Equation constraints generated by a Python script, with the only constitutive subroutine being a minimal UMAT that supplies the 5/6 transverse-shear correction and a per- RVE energy weight ???????? . The framework is verified against the single-element reaction benchmarks and against an analytical Navier plate solution for a pressure-loaded simplysupported plate.