Numerical formulations based on the Isogeometric Boundary Element Method for the mechanical analysis of three-dimensional reinforced nonhomogeneous solids - Rodrigues Neto, Antonio (2023)
The main objective of this doctoral thesis is the development of numerical formulations based on the Isogeometric Boundary Element Method (IGABEM) for the three-dimensional mechanical analysis of reinforced and nonhomogeneous structural systems. BEM's lack of domain mesh is advantageous in both contexts: the integration with IGA frameworks and the representation of reinforcements embedded into 3D bodies. This study takes advantage of those by working in reinforced IGABEM formulations. The sub-region technique applied to the 3D IGABEM allows for representing non-homogeneous bodies. The 1DBEM/IGABEM coupling formulation is extended to 3D domains, with the modelling of crossings between fibres and IGABEM boundaries via the connection element. That approach does not require remeshing in the NURBS surfaces and makes possible to represent reinforcements crossing crack surfaces modelled by either the Dual IGABEM or at interfaces. Nonlinear formulations are presented via elastoplastic reinforcements and bond-slip. Such formulations allow to accurately model the pull-out phenomenon in 3D numerical models. Besides, this study works with the cohesive crack approach to represent nonlinear fractures at the 3D body, via different cohesive laws. With that, nonlinearities can be represented in both matrix or reinforcements. This study also works with time-dependent behaviour of reinforced bodies by both the viscoelasticity at matrix or reinforcements and the viscous response of cohesive interfaces to different loading rates. Numerical applications show the accuracy of the proposed formulations to represent various mechanical behaviours, using both numerical or experimental results as reference. The IGABEM models to lead to accurate results with good performance with fewer degrees of freedom necessary when comparing against pure FEM or Lagrangian BEM models. The convergence of the proposed formulations is also studied. In this context, adaptive refinement strategies are proposed, making possible to use CAD geometrical models as basis for the mechanical analysis. Such models are refined via knot insertion, having the adaptive refinement guided by a posteriori error estimator. Innovative error estimators are proposed for both the IGABEM and its reinforced version. The last approach is able to identify the refinement required at the most critical fibre's regions, minimising the mechanical fields oscillations usually observed. The developed adaptive strategies present excellent convergence rates, which show better results when compared against global uniform refinement in several complex numerical applications.