A novel approach towards optimizing lightweight structures B. Goller, R. Winkler, M. Gratt 3rd Workshop on Structural Analysis of Lightweight Structures Natters, May 15, 2014

INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com Contents Introduction Methods of analysis Implementation in FE-software Examples Conclusions INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com

INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com Introduction Main aspect in the competiveness is the identification of weight saving opportunities. Material, fuel consumptions and hence costs drive the design of lightweight structures. € competiveness weight time Development of novel approaches for optimization are a an approach to meet these challenging requirements. INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com

INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com Introduction RF (composite, metallic, sandwich) > 1.0 Requirements: Displacement constraints Limitations of manufacturing Huge number of design variables Large set of constraints Computational feasibility RFbolt,axial > 1.0 RFbearing,bypass > 1.0 INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com

INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com Introduction Constraint optimization problem: f (x) min gi(x) ≤ ci, for i=1…m subject to x … design variables (number of plies, fiber angle, thickness of metals, etc.) f (x) … objective function (e.g. total mass) gi (x) … constraint function (strength criteria, design constraints, etc.) Classical optimization algorithms might soon reach their feasible limits due to the dimensionality of the problem. INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com

Methods of analysis Proposed novel approach: Iterative adaptation strategy Start configuration Structural analysis with load increment i+1 Local change of thickness, angle Source: W. Liebermeister, University of Berlin Adapted structure for load increment i+1 Final configuration for targeted load level INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com

INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com Methods of analysis Criterion for monolithic composite parts: Strain criterion: max e < 0.35% Strategy: Determine number of plies, stacking sequence and draping angle such that criterion is fulfilled Yamada-Sun: Details will be presented by Egon Verginer INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com

INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com Methods of analysis Criterion for metallic parts: Yielding criterion: t σ11 σ12 RF … reserve factor fy … yield stress σMISES … VON MISES stress σ12 σ22 Strategy: Increase thickness t such that RF>1.0 INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com

INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com Methods of analysis Criterion for fasteners: sn … normal stress of bolt ss … shear stress of bolt Increase bolt diameter Bolt failure: Increase bolt diameter & thickness of connected elements Pull through: nut Increase bolt diameter & thickness of connected elements Bearing failure: INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com

Implementation in FE-software Beginning of Analysis Adaptive change of element properties requires access to element routines (→ re-programming or implementation of improved element routines as a first step. Adaption strategy is integrated in the element routines. Current properties of each iteration of the single elements are to be stored and accessed (→external database) UEXTERNALDB Start of Step Creation of element stiffness matrix UEL Creation of load vector Back to start of step Solution of governing equation UEL Evaluation of elemental output UEXTERNALDB Write output INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com End of step

Implementation in FE-software SQLITE database is a suitable means for storing and accessing efficiently large amount of data For each iteration a new database is created, where the current value of the optimization process are written. For the creation of the element stiffness matrix, the database of the previous step is accessed. INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com

INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com Examples Plate with hole under tension Uniform loading at right edge Fully clamped at left edge Ply type: Fabric Initial stacking: (45/0/0/45) s 3s Analytical solution: INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com

INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com Examples Number of plies The highest number of plies is located in the areas of the stress peaks Maximum number of 50 plies (user defined value) is reached in this area Draping angles The load path can be recognized by the identified draping angles Due to the presence of plies with a0°, the curvature of the solution is not as pronounced as expected from the analytical solution INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com

INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com Examples Illustration of fastener optimization routine: Three shell structures connected by 3 single- and 3 double-lap shear fasteners Two straps are clamped on the left edges, all three are loaded uniformly on the right edges. Fasteners and connected elements are dimensioned against bolt failure, pull through and bypass. Single-lap shear fasteners Double-lap shear fasteners INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com

INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com Examples Diameter of bolts The highest increase of the diameter is performed for those two fasteners, where the initial analysis shows the largest forces. Number of plies The number of plies is updated according to bearing and bypass criterion. The highest number of plies is required for the highest loaded fastener . INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com

INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com Outlook Current example: Optimization of a part of the winglet structure (~ 1 Mio. DOFs) Results after 10 iterations for 3 loadcases each (1.5 h of analysis time): Next step: Smoothing of the results in order to obtain a producible layup INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com

INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com Conclusions A novel approach for the optimization of lightweight structures has been presented. The advantage of this approach is its applicability to FE-models involving a high number of design variables. The results shown in this presentation have been obtained after 10 iterations, which suggests its usability in case of large numerical models. Acknowledgements This project is financially supported by the Austrian Space Applications Programme (ASAP) of the Austrian Ministry for Transport, Innovation and Technology (BMVIT), which is deeply appreciated. INTALES GmbH-Innsbrucker Str. 1 -, A-6161 Natters - www.intales.com