Optimization Assisted Structural Design of a New Military ... - AIAA ARC

AIAA 2004-4641

10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference 30 August - 1 September 2004, Albany, New York

OPTIMIZATION ASSISTED STRUCTURAL DESIGN OF A NEW MILITARY TRANSPORT AIRCRAFT Gerd Schuhmacher*, Martin Stettner‡, Rainer Zotemantel‡, Owen O’Leary ‡, Markus Wagner‡ EADS Military Aircraft, Munich, Germany

Abstract.

2 Optimization Assisted Design Process

Topology and Structural Optimization methods have been applied in order to support the develo pment of the A400M rear fuselage. This paper first gives an overview about the optimization assisted design process implemented at EADS Military Aircraft. The optimization models and the topology optimization results for A400M rear fuselage will be described afterwards. The topology optimization has been applied at a system level, in order to determine an optimum concept for the complete A400M rear fuselage. These results have then been refined for the internal support structure and further detailed for a single tail-plane frame.

The optimization-assisted design process applied at EADS Military Aircraft in Munich is depicted in Figure 1. It starts from the definition of the available design space describing the inner and outer boundaries of the space, within which material can be arranged. In case of an aircraft, this is usually defined by the outer loft driven by aerodynamic requirements and the inner loft determined by the space required for passengers, cargo load, systems and other functional requirements. The complete design space is meshed by appro priate finite solid-, shell- or other elements and loaded by the relevant design loads. The resulting FE-Model is the basis for the topology optimization, which is used to determine optimum load paths and qualitative topological hints for a minimum weight design. The results of the topology optimization have to be interpreted carefully and “translated” into a design concept, which is a sensible compromise between the theoretical optimum material distribution, manufacturing requirements as well as buckling- and other design constraints. The shape and sizing parameters of the resulting design concept can then be optimized by structural optimization methods. As a basis for this second optimization loop, a finite element model and an optimization model defining design variables and constraints (stress, buckling, aeroelastic efficiency etc.) must be generated, Reference1,3. The quantitative results (component dimensions) are then the basis for the subsequent detailed design- and verification process. Finally, the optimum structure can be manufactured.

The sizing of a fuselage requires consideration of the post-buckling behavior. The. paper explains the post-buckling analysis capabilities, which have been implemented in the optimization procedure LAGRANGE. The sizing optimization models applied with the ongoing A400M sizing optimization activities are briefly discussed. 1 Introduction Topology optimization methods and applications have experienced rapid development within the last few years. Several commercial codes offering topology optimization capabilities have been developed and mainly applied to structures in the mechanical engineering and automotive area. The tools have demo nstrated their power to determine optimum load paths and weight optimum designs for complex comp onents. The huge weight-saving potential and the relatively easy handling of the topology optimization tools have strongly supported their rapid dissemination. The number of applications in aerospace has been fairly limited up to now. However, positive experiences have been gained with the application of topology and stru ctural optimization methods in different aerospace projects at EADS Military Aircraft. The development of the A400M Rear Fuselage has been supported by optimization methods during the concept- and pre-design phase. The paper gives an overview about the optimization process and the results achieved within this project.

Final Part

Design Space (Loft)

Manufacturing Realised Part Topology Optimisation Load Paths Material Accumulation and Orientation Stiffness Distribution Structural Concept Clues

CAE Detailed Analysis and Verfication

CAD Detailing of Structural Optimisation Results

Structural Concept Interpretation of Topology Optimisation Structural Concept Structural Optimisation Dimension and Shape of Structural Members

Figure 1: Optimization Assisted Design Process

* ‡

.Manager, Department “Optimization and Special Analysis”, Team member, Department “Optimization and Special Analysis”

1 Institute ofrights Aeronautics Copyright © 2004 by the American Institute of AeronauticsAmerican and Astronautics, Inc. All reserved.

and Astronautics

3 Design Task for the Rear Fuselage of the A400M Military Transport Aircraft The Rear Fuselage of the A400M Military Transport Aircraft consists of outer shells, supported by stringers and frames (Figure 2). The aircraft can be loaded and unloaded with big vehicles as well as other cargo loads, via a ramp opening outwards and cargo door opening inwards (Figure 3). The ramp is hinged at its front end and the cargo door is hinged at its rear end, close to the pressure bulkhead (Figure 4). The complete structure has to be designed for minimum weight considering strength, fatigue, damage tolerance, buckling and post-buckling constraints. Furthermore, there is a requirement that the cargo door and ramp can also be opened and closed during flight, even under severe gust or maneuver loads. This requires keeping the relative deflections between cargo door and rear fuselage within relatively small limits, in order to avoid collisions and to ensure a proper opening and closing function. The same holds true for the ramp.

Figure 4: Cargo Door Opening Mechanism The Finite Element Model of the rear fuselage design is shown in Figure 5. The nodes of this model are loaded with several maneuver, gust and cargo loads. Pressure loads are applied at each skin node. The fuselage/vertical tail interface in section C (Figs. 5 and19) is subject to significant concentrated loads introducing bending and torsion into the rear fuselage. Open and closed conditions for ramp and cargo door are analysed, where restrictions on the gap between door/ramp and fuselage in the open condition are considered. In total, 41 load cases have been considered with the topology optimization process. Section C Section B Section A

Figure 2: A400M Rear Fuselage Design

Cargo Door Interface Ramp / Cargo Door Ramp Longerons Floor

Figure 5: A400M Rear Fuselage FE Model

4 Topology Optimization 4.1 Design Space and Optimization Model The space within which material can be arranged to carry loads and to fulfill functional requirements is the topology optimization design space. In the case of the A400M Rear Fuselage, this is the space between outer and inner loft (Figure 6). The outer loft is mainly determined by aerodynamic considerations whilst the inner loft is driven by cargo load and system requirements.

Figure 3: A400M Military Transport Aircraft

2 American Institute of Aeronautics and Astronautics

Frames removed

Design Space modelled by Solids

+ Floor & Longerons removed

Figure 7: Topology Optimization Analysis Model

Cargo Door Space Limitation

4.2 Solid (3D) Topology Optimization Results

Cargo Load Space Limitation

In a first study, the entire design space was filled with 3D solid elements. Initial optimizations concentrated on single load cases in order to study the principal load paths. Some features of these “single load” topologies re-appeared in runs with combined loads, facilitating interpretation of at least some areas of material accumulation, Fig. 8. Note that in the following figures outer skin, door, and ramp have been omitted to provide better visibility. Red areas indicate maximum density and blue areas very low density.

Baseline-Frames

Figure 6: A400M Rear Fuselage Design Space The design space was meshed with solid elements. The density of each element represents one design variable of the SIMP (Solid Isotropic Microstructure with Penalty) topology optimization process. This set of design variables is used to obtain hints for the optimum inner support structure (frames, floor-support, longerons, etc.) of the rear fuselage.

Pressure Torsion

Skin elements had to be retained in the design model at a certain minimum thickness to ensure that applied pressure loads would act on a closed surface, and allow load sharing between skin and internal structure. The thicknesses of these shell elements represented a second part of the design variable vector. Finally, to consider load paths supported by non-design, but load carrying structures, ramp and door were retained in the FE model. Figure 7 depicts the analysis model for topology optimization as a comb ination of a stripped-down version of the original FE model, Figure 5, attached to the topology design space, Figure 6. Again, outer skin thickness and topology design space densities were used as design variables.

Bending

Torsion

Within the topology optimization, the linear combination of the compliances of all load cases is minimized. The constraints consist of a mass constraint limiting the available material to about the same amount as used in the baseline design, and by constraints for the relative displacements between cargo door and rear fuselage.

Bending

All Load Cases

Pressure

All LC

Figure 8: Single and Multi Load Case Topologies


Figure 9 shows the topology optimization results for the internal structure with all relevant load cases considered simultaneously. Material accumulation near the actual longerons, cargo floor, and vertical tail attachment fittings support the necessity of these fe atures of the baseline structure. However, new comp onents are also suggested in form of an “inner skin” following largely the cargo hold envelope, and a special frame structure where the cargo door hinges are lo cated. The former is interpreted to provide more torsional stiffness as well as to minimize weight, the latter to minimize relative deflections between cargo door and rear fuselage. The frame pitch indicated in the figures results from the meshing. Topology optimization results with a refined mesh have been determined as well. They indicate inclined, curved frames as optimum load-path in the tail-plane area.

outer skin is again combined with this 2D shell model, Fig. 10. The thickness of all outer skin shell elements as well as the thickness of certain groups of shell elements (e.g. a complete frame) are defined as sizing design variables. These sizing design variables are combined with density design variables (SIMP) for the complete internal structure (frames, shear webs, inner skin). The objective function (compliance of all load cases) as well as the constraints (mass, relative deflections) remain unchanged compared to the solid topology model. The rear fuselage results determined with the shell topology model are depicted in Figure 11a whilst Figs. 11b, c and d show selected frame results.

Fig 10: Shell Topology Optimization Model

Figure 9: Optimum Solid Model Topology

4.3 Shell (2D) Topology Optimization Results Based on the results of this Topology Optimization with solid elements, a more detailed topology optimization model with 2D shell elements was set up. This model consists of the frames, longerons, shear webs as well as an inner skin modeled by shell elements. The

Figure 11a: Optimum Shell Model Topology


Concentration „0“


Fig 11b: Exemplary Frame Topology Sec. A

Constructive Interpretation Concentration of „2“the Topology

Fig 11c: Exemplary Frame Topology Sec. B


Fig. 12: Variations of the Frame Topology Fig 11d: Exemplary Frame Topology Sec. C 4.4 Single Frame Topology Optimization Study A follow-on study was performed for a selected frame in the tail-plane area. For this purpose, a standalone FE-model of the frame including interface loads was generated. The shell-thickness and the minimummember-size-parameter (MMS; Ref. 2) was varied in order to study the influence on the optimum topology, s. Fig 12. The first picture (concentration 0) was determined without the MMS option. The following pictures (concentration 1 to 3) resulted from topology optimization runs considering a MMS and in creasing shell thickness values. The variations give clear hints about optimum load paths and optimum stiffening trajectories in the different areas of the frame. The material distribution shown in Figure 12 corresponds to the principal stresses in the design driving load cases, Fig. 13.

Maximum Principal Stress

Minimum Principal Stress Fig 13: Principal stresses (Lateral gust superimposed by internal pressure)


The structural analysis is based on a finite element model providing displacements and stresses. The stresses are used in turn as input for the post-buckling analysis, which is based on closed-form, analytical solutions. The sensitivity analysis determines the first order sensitivities of objective and constraints with respect to the design variables (omitted in Fig. 14 for simplicity). It is performed on a semi-analytical basis and provides essential input for the gradient based optimization algorithms.

The topology optimization result for the tail-plane frame were carefully studied and “translated” into a design concept consisting of struts, webs and stiffeners etc. This design concept was then converted into an appropriate finite element model as basis for the subsequent sizing optimization process.

5 Sizing Optimization 5.1 Optimization Procedure LAGRANGE

5.2 Post-Buckling analysis procedure

The sizing optimization process requires the consideration of all relevant strength, fatigue, buckling and deflections constraints. Furthermore, the fuselage skin is allowed to buckle above fatigue loads. Therefore post-buckling effects, like diagonal tension and load redistribution from the skin to the stringers and frames, need to be analyzed and constrained in the optimization process. All constraints mentioned above can be considered within the in-house optimization procedure LAGRANGE, Fig 14. The 3 major columns of the LAGRANGE architecture are (Ref. 3):

The complete shell structure consisting of skin, stringers and frames is sub-structured into so-called buckling fields consisting of 2 skin elements, a stringer element in-between the skins and frame elements supporting the skins in circumferential direction, Fig. 15.

P n- 1

1

4 skin panel field No.1

2 Pn

3

1

stringer

4 skin panel field No.2

2

a) side panel

3

b) buckling field

Fig. 15: Shell-sub-structuring into buckling fields

Design Requirements

LAGRANGE

1. Minimum Weight 2. Sufficient Reserve 3. Acceptable Deformations

Reservefactors

MT2-SCHADI Strength and Buckling Analysis

Optimization Algorithm

PRE-SCHADI Strength and Buckling Model

Buckling Field Geometry

KBE

1. Set-up substitute problem 2. Solve substitute problem 3. Check convergence criteria

Finite Element Analysis

Improved Set of Design Variables

C m+1

frame

1) the structural state- and sensitivity analysis (displacements, stresses, buckling loads, post-buckling failure loads, aero-elastic efficiencies, flutter speeds etc. as well as their sensitivities), 2) the optimization model (design variables, objective function and constraints), 3) the optimization algorithms (CONLIN, RQP, SLP, SCP, GRG, etc.). Objective and Constraints

Buckling field

Cm

Displacements

Design Model

DESIGN Material Data

Finite Element Model

1. Update Panel Thickness 2. Update Stringer Sections

ASD Element-IDs

No Convergence ?

Stress Department

Yes

CATIA

Fig. 14: The principal data flow within the structural optimization procedure LAGRANGE 6 American Institute of Aeronautics and Astronautics

KBE

Check Stress and Final Sizing

The combination of longitudinal, circumferential and shear loading can cause different buckling and post-buckling effects within the buckling field. In general, a fuselage skin is allowed to buckle above fatigue loads. After buckling onset, the skin load capacity for compression loads is exceeded, i.e. all compression loads above the skin buckling loads are redistributed to non-buckled skin area, stringers and frames. For shear loads, the situation is slightly different. Diagonal tension effects allow the skin to also carry additional shear loads in a buckled state (Ref. 4). The failure mechanisms considered within the buckling fields are (Ref. 5, 6):

The analysis procedure for these failure mechanisms is based on non-linear analytical solutions, which are solved iteratively. The first step is to determine the initial buckling loads under pure compression and shear loading. The interaction between compression and shear reduces the initial buckling load compared to pure compression or pure shear loading according to the interaction curve, Fig. 18. The actual combined buckling loads depend on the ratio of applied compression and shear loads and follow from the intersection of the straight line with the interaction curve, Fig. 18. After buckling-onset the loads can be increased further until a certain failure occurs. Within the post-buckling range, the non-linear re-distribution of loads between buckled and non-buckled parts of the skin as well as the stringers and frames is calculated by iterative procedures. The non-linear material behavior and plastification effects are considered based on the Ramberg-Osgood theory (Ref. 7). The failure mechanisms mentioned before can be mathematically characterized by non-linear interaction equations considering all stress comp onents. Therefore the actual loads causing a certain failure must be determined iteratively as well.

-

tension failure by exceeding material allowables, skin buckling below fatigue loads, inter-rivet-buckling, shear failure due to diagonal tension loads exceeding the skin material capacities, - stringer crippling due to compression and diagonal tension, - column -buckling (stringer and skins) due to compression and diagonal tension. Compression

Shear

The post-buckling analysis is based on Ref. 4, 5 and 6. Its FORTRAN implementation, MT2-Schadi, was validated by demonstrating good agreement of the design driving reserve factors with the certified Airbus Shell Analysis - and Design-Tool ISSY. The strength and buckling analysis for the frames is performed in a very similar way. Closed, analytical solutions are considered in order to calculate the reserve factors for material failure, inter-rivet buckling, web-buckling and girder buckling due to tension, compression and shear loads. The diagonal tension effects in the skin also cause additional loads on the frames, as already mentioned in the previous section. Furthermore, the skin is not fully effective for circumferential tension loads, also causing load distributions into the frames. All these effects are covered by a frame analysis tool developed and verified by the EADS stress team (Ref. 8). This frame analysis tool was integrated into LAGRANGE in the same way as the shell analysis tool MT2-Schadi.

Fig. 16: Initial Skin Buckling Effects Stringer-Crippling

Column Buckling Inter-rivet buckling

σx

Fig. 17: Post-Buckling Failure Mechanisms τ τcr0

σc τ + c σ cr0 τ cr 0

2

=1

Failure Load Interaction curve

τcr0 τcr τ appl

σappl

σcr

σcr0

σ σcr0

Fig. 18: Buckling Load Interaction


6.2 Sizing Optimization of the A400M Rear Fuselage

6.3 Sizing of topology optimized frame concepts

The application of LAGRANGE in order to determine skin, stringer and frame sizes meeting all strength, fatigue, buckling, post-buckling and displacement constraints with minimum weight is in progress. Table 1 characterizes the size of a typical optimization model of the rear fuselage section C.

The topology optimization results for the tail-plane frame described in chapter 4.4 were converted into a first design concept. Fig. 20 shows the FE-Model generated based on this concept.

Section C

Fig. 20: FE-Model of a truss-like tail-plane frame Fig. 19: A400M Rear Fuselage FE-Model

Comp onent Design Variables Skin 247 Stringer 28 Longeron 42 Frames 1009 Sum / LC 1326 Total Sum 1326

Fatigue constr./FLC 494 247 72 1210 2023 10115

Failure constr./ ULC 1976 741 144 5400 8261 603053 Fig. 21: Baseline design of the tail-plane frames

Table 1: Sizing Optimization Model for Section C This truss-like design concept requires strength and buckling analysis tools different from those needed for the baseline frame design, Fig. 21. Those analysis tools have been developed and are currently being integrated into LAGRANGE in order allow a proper sizing optimization of the new design concept. Preliminary asses sments indicate a significant weight reduction potential compared to the baseline concept. However, comprehensive investigations considering all design criteria (strength, fatigue, buckling, damage tolerance, manufacturing etc.) have not been completed yet. In particular, damage tolerance requirements need to be studied carefully in order to demo nstrate, that the truss-like frame has enough load carrying capability after failure of a single strut or a joint (crossing of two struts). A final assessment and conclusion regarding the weight saving potential is therefore still to be done.

The load case spectrum for sizing optimization comprises 5 Fatigue Load Case (FLC) and 73 Ultimate Load Cases (ULC). First sizing optimizations for skin, stringer and longerons have been completed. These runs have successfully demonstrated the functionality and convergence behavior of the enhanced optimization procedure considering displacement-, strength-, fatigue-, bucklingand post-buckling-constraints. The first results indicate significant changes of the load paths. However, in order to complete the optimization task it is very important to consider all structural comp onents simultaneously in the optimization model (skin, stringer, longerons and frames). In other words, it is necessary to optimize all load-sharing components together whilst the first optimization runs did not include design variables and constraints for the frames. The sizing optimization runs including all structural components in the optimization model are in progress. Results will be reported in a follow-on paper.


7 Summary and Conclusion References

Topology and structural optimization methods were successfully applied during the concept- and predesign phase of the A400M Military Aircraft. The paper shows the subsequent steps of the optimization assisted design process and its topology optimization results. The successful application of topology optimization methods at a system level (complete rear fuselage of the A400M) rather than on component level has moved the limits of topology optimization applications in aerospace. The sizing optimization procedure LAGRANGE was enhanced in order to consider post-buckling design constraints for stringer and frame supported fuselage shells. It also has been demonstrated that the enhanced procedure works successfully. The sizing optimization process for the A400M rear fuselage is still in progress and the results will be reported in a follow-on paper. The possibilities offered by topology- and structural optimization methods provide a very valuable support for the development process. Application of topology optimization methods during the concept phase opens new possibilities for tremendous weight savings, whilst the sizing optimization process ensures that the weight saving possibilities remaining in the preliminary design phase will be fully utilized. Furthermore, the application of sizing optimization methods reduces development cost by reducing the number of design cycles.

1

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2

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3

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4

Kuhn, Paul, Peterson, James P., Levin, L. Ross: „A summary of Diagonal Tension“. Part 1 – Methods of Analysis. NACA Report 2661, Washington, May 1952.

5

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6

ASSACOS/SCHADI Strength Analysis of Shells. Theoretical Manual. Deutsche Aerospace Airbus GmbH, Hamburg, Germany.

7

Ramberg, W., Osgood, W.R.: Description of stressstrain-curves by three Parameters. NACA-TN 902, April 1943.

8

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ACKNOWLEDGEMENT The authors acknowledge the valuable cooperation and support of the ALTAIR Engineering team. The ALTAIR project engineers Christian Förtsch, Hans Gruber and Ekkehard Rieder have shown great enthusiasm and dedication and they have provided a very valuable contribution to the project. Furthermore the ALTAIR software development team has been very helpful whenever help was needed. The co-operation with the stress teams and the very valuable contributions of Jeff Ratcliffe are acknowledged as well. Last but not least, the management decision to establish an optimization department in order to improve the structural development process is highly appreciated.
