Design and optimisation of large structures, including the positioning of lower-level components, typically require extensive user involvement and sequential mechanical analysis/optimisation iterations. This paper presents an original method that enables adaptive positioning of lower-level models (such as components) within higher level-models (such as large structures), and that achieves a combined mechanical/optimisation problem for the design of structures with various hierarchical levels (such as the positioning of stiffeners within a wingbox). As the position of the lower-level model evolves, our proposed method does not require re-generating of the geometry, remeshing or modifying the stiffness matrix of the elements corresponding to the various hierarchical levels. Instead, we achieve the adaptive positioning via an original concept that we propose here: Floating Connector (FC) elements. In this paper, we validate the FC elements against reference purely-mechanical solutions, show that they can be combined with gradient-descent method and genetic algorithms, and that they can be applied to optimise the positioning of a stiffener runout taking into account a debonding manufacturing defect.

This paper presents a new polymorphic element modelling approach for multi-scale simulation, with an application to fracture in composite structures. We propose the concept of polymorphic elements; these are elements that exist as an evolving superposition of various states, each representing the relevant physics with the required level of fidelity. During a numerical simulation, polymorphic elements can change their formulation to more effectively represent the structural state or to improve computational efficiency. This change is achieved by transitioning progressively between states and by repartitioning each state on-the-fly as required at any given instant during the analysis. In this way, polymorphic elements offer the possibility to carry out a multiscale simulation without having to define a priori where the local model should be located. Polymorphic elements can be implemented as simple user-defined elements which can be readily integrated in a Finite Element code. Each individual user-defined polymorphic element contains all the relevant superposed states (and their coupling), as well as the ability to self-refine. We implemented a polymorphic element with continuum (plain strain) and structural (beam) states for the multiscale simulation of crack propagation. To verify the formulation, we applied it to the multiscale simulation of known mode I, mode II andmixed-mode I and II crack propagation scenarios, obtaining good accuracy and up to 70% reduction in computational time —the reduction in computational time can potentially be even more significant for large engineering structures where the local model is a small portion of the total. We further applied our polymorphic element formulation to the multiscale simulation of a more complex problem involving interaction between cracks (delamination migration), thereby demonstrating the potential impact of the proposed multiscale modelling approach for realistic engineering problems.