### Detail description of design tools

The Finite Element based optimisation loop employed at CoDeT Engineering for Variable Stiffness structures is shown below. For a Steered Fibre laminate, there are multiple sets of material stiffness properties (ABD matrices): One for every node in the Finite Element Model of the component, since the fibre orientations change throughout the component. The performance is dependent on all of these nodal stiffness properties. Traditionally, the design variables are chosen to be the laminate definition (fibre angles at each node for VS design). Optimisation then becomes costly because the Laminate Analysis and Structural Analysis need to be performed in each iteration and direct fibre angle optimisation is normally a non-convex (thus computationally expensive) problem. The advanced method employed at CoDeT splits up the process into two main stages: Stiffness optimisation performed by **ALDO** and fibre angle (CS / blended laminates) or fibre path (VS laminates) retrieval performed by **OLGA** and **THEO.** This reduces computational costs and provides maximum elastic tailoring potential for any structure geometry and loading. A description of the package functionality for CS, blended and VS laminate design is given below.

**ALDO** (__A__dvanced __L__aminate __D__esign __O__ptimization) is used for CS, blended and VS laminate design. It works with a Finite Element based optimization technique that obtains the best stiffness distribution for a given laminated structure. The stiffness distribution is expressed in terms of the extensional, coupling, and bending matrices (ABD matrices) of Classical Laminate Theory (CLT), and can be defined as constant values within a pre-defined region (CS or blended laminates) or vary at each mesh node within a region (VS laminates). The elements of the stiffness matrices are not wholly independent, but linked through mathematical relationships (Lamination Parameters) to ensure that their final values can be constructed using a realistic multi-layered laminate. This technique removes the orientation angles of the orthotropic plies as design variables, which is often a complicating factor in discrete stacking sequence design, and generates a simpler gradient-based optimization problem, resulting in faster convergence and fewer finite element analyses. Presently the solution can consider material and multi-mode vibration/buckling failure estimations and also utilizes basic fibre-steering constraints to ensure manufacturable designs for gradual stiffness variation.

**OLGA** (__O__ptimization of __L__aminates using __G__enetic __A__lgorithms) is used for CS and blended laminate design. It uses genetic algorithm (GA) concepts to find laminates that match a stiffness distribution (given by **ALDO**). The discrete choices of materials and fibre orientation angles for each layer of the laminate(s) are coded into genetic strings and subjected to computational operation based on evolutionary processes until the best design is found. A GA usually needs many analysis runs, which would become extremely costly when Finite Element analyses are used. However, the goal in CoDeT’s approach is merely to match a given set of laminate stiffnesses, which requires only relatively fast Laminate Analyses. Ply continuity rules can be formulated for blended laminate design to prevent entirely discontinuous laminates from region to region. Structures that contain unblended laminates are also a suitable starting point for **OLGA**, which transforms a part that is difficult to manufacture into a blended design with similar stiffness characteristics to the original stiffness distribution. Customized laminate rules, such as discrete angle constraints and typical laminate restrictions, are easily incorporated into the solution process.

**THEO**** **(__The__ta __O__ptimisation) will become a commercialised package based on previously developed and verified academic methods for Variable Stiffness optimisation. **THEO **applies two substeps to find the optimal VS design.

Firstly, **OLGA** can be used to create initial laminate designs for **THEO** on each node, purely based on matching the stiffness that **ALDO** gives on that node. **THEO** then performs global Gradient Based rapid converging optimisation of the fibre angle on each node in each ply for maximum performance, whilst taking into account manufacturing constraints such as allowable fibre steering radius.

Secondly the optimal tow paths are determined using a streamline analogy method, which ensures that the spacing of tow paths creates a smooth thickness variation and limits excessive local thickness build-up in the part. The result is a Steered Fibre laminate, ready to be programmed for Automated Fibre Placement machines.