The current generation of proprietary software codes have been in existance in organ- isations such as BAE Systems since the early 1970’s, maturing to meet the specific sizing needs of the companies and their design processes (Duysinux and Fluery (1993), ap C. Harris (1997b)). Within BAE Systems the ECLIPSE code was developed to provide engineers with a material distribution within an aircraft configuration that min- imised the mass of the structure whilst meeting structural design criteria. These criteria included strength, stability, generalised deflection and aeroelasticity phenomena such as flutter.
The principle behind ECLIPSE was to use the results of a FE analysis of the structure to calculate the cross-sectional properties of elements in the model necessary to just meet the design criteria. The implication is that in doing so the mass of the structure will be minimised. The FE model would then be updated with these properties and reanalysed to allow for internal redistribution of loads. The process would then be repeated until the structural mass converged to a similar value between iterations, typically less than a 5% change, or until other stopping criteria were met. Strength and panel stability criteria were met using stress ratio methods (SRM) and sequential linear programming (SLP) for metallics and laminates respectively (as described in Section3.2). The panel stability method was a decomposition approach, with panel geometry based on a manually defined scale factor of finite element width for a given set of elements representing a panel. This assumed that the element sizes within a panel were roughly uniform. Optimality criterion methods using an element strain-energy formulation, discussed previously in Section3.4, were used to size metallics and laminates for stiffness related criteria (Thompson(1999), Thompson et al. (1999)).
Figure 3.9 shows a top-level overview of the ECLIPSE sizing process. A FE model would be analysed using NASTRAN and the resulting element stresses used to size the model for strength and stability criteria. The initial model would then be sized to meet stiffness criteria using the strain energy approach. The FE models obtained from these two sizings were then combined using a proprietary set of criteria to produce a structure that aimed to meet both sets of constraints. The sized model would then be reanalysed and the process repeated until convergence or other specified stopping criteria were met.
Chapter 3 Structural Sizing - Technology Review 44
ECLIPSE has been used to size the EAP aircraft and Eurofighter Typhoon and Gripen wings. Other similar, proprietary, codes include: STARS (Bartholomew and Wellen (1990)); ASTROS (Neill et al.(1990),Canfield and Venkayya(1990)) and LAGRANGE (Schuhmacher et al. (2004)). These capabilities are summarised in Appendix A.
RESIZE FOR STRENGTH AND STABILITY CRITERIA NO YES RESIZE FOR STIFFNESS CRITERIA NUMBER OF ITERATIONS MET? POST-PROCESS SIZED MODEL START STOP
Figure 3.9: Air vehicle design process used for Eurofighter Typhoon
Commercial alternatives to proprietary capability are increasingly available both as stand-alone applications and as part of wider suites of packages. DOT (Vanderplaats (1999a)) and BIGDOT (Vanderplaats (2002)) are two such optimisers used within FE analysis codes such as NASTRAN and GENESIS. These optimisers are used for struc- tural problems with low numbers of variables (O(100)) and very high numbers respec- tively (O(100k)). Within DOT it is possible to use the Method of Feasible Directions (MFD), Sequential Linear Programming (SLP) and Sequential Quadratic Programming (SQP) methods. BIGDOT uses an exterior penalty function method to create a repre- sentation of the objective and constraint functions for nonlinear problems. The mini- mum of this function is then found using a conjugate direction method (Vanderplaats (2002)). DOT is available as part of the GENESIS (Inc (2004)) structural optimisation toolkit, the NASTRAN SOL200 solution sequence (Moore (1994)) and Phoenix Integra- tion’s ‘ModelCenter’ problem solving environment. BIGDOT is used by GENESIS and NASTRAN v2005.
Altair Engineering’s ‘Optistruct’ code is used within the automotive and aerospace com- munities, with a number of examples of its application on structural optimisation of vehicle components. It implements the SIMP layout optimisation method for strength, stability, and stiffness related criteria discussed previously in Section 3.3. It has been used by Airbus to size the wing leading-edge ribs on the A380 aircraft (Krog et al. (2004)).
An example of a COTS decomposition type optimiser is found in Hypersizer/Pro. Hyper- sizer is derived from the NASA ST-SIZE code and is used to analyse stiffened panels for failure criteria including strength and stiffness (Collier Research Corporation (2003)). It contains a number of empirical analyses for stringer stiffened panels with different stringer types, honeycomb stiffened panels and laminated composite panels. Hyper- sizer/Pro includes the ability to generate free-body diagrams from a FE model using the element stresses. These free-body diagrams can include consideration of the effect of panel curvature on failure criteria and pressure bending effects. Sizing then takes place for each free body panel, and it is possible to subsequently re-combine these in the FE model for later re-analysis in the FE package. The sizing process uses a design
space discretised by assigning variables a fixed number of levels. The effect is that it is not possible to find a true optimum in a given sizing, but rather the value of the closest design point. The suppliers argue that one of the main benefits of this method is that it can search a design space described by discrete and continuous variables (Col- lier Research Corporation (1997)). However, since the analysis functions are accessible through a COM interface it should is possible to use different optimisation methods when necessary. Hypersizer has been integrated into a structural sizing process within the ModelCenter PSE (Cerro et al. (2002)).