Application of Structural Optimization on Lattice Structure Design using Superelastic Material

Application of Structural Optimization on Lattice Structure Design using Superelastic Material Michael Kofler1*, Marius M. Schasching1, Ondˇrej ˇ Cervinek 2, Florian Zwicke1, Daniel Koutn´y 2, Heinz E. Pettermann1, and Melanie Todt1 1Institute of Lightweight Design and Structural Biomechanics, TU Wien, Austria 2Institute of Machine and Industrial Design, Brno University of Technology, Technick´a 2896/2, Brno, Czechia The funding of the project ”Building Actions in Smart Aviation with Environmental Gains” by the European Union Programme Horizon Europe under grant agreement no. 101079091 is gratefully acknowledged. The computational results presented have been achieved using the Vienna Scientific Cluster (VSC). Session: MS022 The 9th European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS Congress 2024 3-7 June 2024, Lisbon, Portugal 1 / 15 Introduction Optimization Framework Results Summary ILSB Outline Introduction Optimization Framework Results Summary 1 / 15 Introduction Optimization Framework Results Summary ILSB Outline Introduction Optimization Framework Results Summary 2 / 15 Introduction Optimization Framework Results Summary ILSB Motivation and Design Goals •Creation of a morphing wing structure to increase aerodynamic efficiency •Soft in rotation, but stiff in translation ⇒Optimization of lattice structure •Superelastic material NiTi •Allows large deformations while ensuring reversibility, but requires considering nonlinear material behavior •Lattice structure consisting of similar sized struts allows efficient beam-based modeling Shape I Shape II Figure: Taken and modified from [1]. [1] Jamshidi, P., et al., Development, characterisation, and modelling of processability of nitinol stents using laser powder bed fusion, J. Alloys Compd., vol. 909, 164681, 2022 2 / 15 Introduction Optimization Framework Results Summary ILSB Motivation and Design Goals •Creation of a morphing wing structure to increase aerodynamic efficiency •Soft in rotation, but stiff in translation ⇒Optimization of lattice structure •Superelastic material NiTi •Allows large deformations while ensuring reversibility, but requires considering nonlinear material behavior •Lattice structure consisting of similar sized struts allows efficient beam-based modeling Shape I Shape II Figure: Taken and modified from [1]. [1] Jamshidi, P., et al., Development, characterisation, and modelling of processability of nitinol stents using laser powder bed fusion, J. Alloys Compd., vol. 909, 164681, 2022 2 / 15 Introduction Optimization Framework Results Summary ILSB Motivation and Design Goals •Creation of a morphing wing structure to increase aerodynamic efficiency •Soft in rotation, but stiff in translation ⇒Optimization of lattice structure •Superelastic material NiTi •Allows large deformations while ensuring reversibility, but requires considering nonlinear material behavior •Lattice structure consisting of similar sized struts allows efficient beam-based modeling Shape I Shape II Figure: Taken and modified from [1]. [1] Jamshidi, P., et al., Development, characterisation, and modelling of processability of nitinol stents using laser powder bed fusion, J. Alloys Compd., vol. 909, 164681, 2022 2 / 15 Introduction Optimization Framework Results Summary ILSB Outline Introduction Optimization Framework Results Summary 3 / 15 Introduction Optimization Framework Results Summary ILSB Overview Optimization 4 / 15 Introduction Optimization Framework Results Summary ILSB Overview Optimization 7 / 15 Introduction Optimization Framework Results Summary ILSB Forward Simulation: Beam-Based FEM •Stress-strain curve of experimental data of uniaxial compression tests of additive manufactured NiTi •Hypoelastic user-interface UHYPEL of ABAQUS •Tangential elastic modulus, ET(ε) •Poisson ratio, ν(ε)→ν •Assumptions of stress-strain relations •Transformation (loading) and re-transformation processes (unloading) ⇒σ(ε) = aε3+bε2+cε •Fully transformed material ⇒σ(ε) = cε •Tangential elastic modulus ET(ε) = ∂σ ∂ε = 3aε2+ 2bε +c •Stress-strain curve of a general loading sequence 8 / 15 Introduction Optimization Framework Results Summary ILSB Forward Simulation: Boundary Conditions 9 / 15 Introduction Optimization Framework Results Summary ILSB Overview Optimization 10 / 15 Introduction Optimization Framework Results Summary ILSB Objective function min αi :F=F(u(αi), αi)= −φ(αi) uv(αi),0≤αi≤π/2, i = 1 . . . ncontrolpoints . 10 / 15 Introduction Optimization Framework Results Summary ILSB Objective function min αi :F=F(u(αi), αi)= −φ(αi) uv(αi),0≤αi≤π/2, i = 1 . . . ncontrolpoints . Pareto front Solutions 11 / 15 Introduction Optimization Framework Results Summary ILSB Overview Optimization 12 / 15 Introduction Optimization Framework Results Summary ILSB Optimization Algorithm •NSGA-II: Non-dominated Sorting Genetic Algorithm3 Figure: Schematic procedure taken from [4] •Pymoo5library for genetic multi objective optimization algorithms [3] Deb et al., A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE transactions on evolutionary computation, vol. 6, 182, 2002 [4] Carles-Bou, J. L. and Gal´an, S. F. Self-adaptive polynomial mutation in NSGA-II. Soft Comput, vol. 27, 17711, 2023 [5] J. Blank and K. Deb, pymoo: Multi-Objective Optimization in Python, IEEE Access, vol. 8, 89497, 2020 12 / 15 Introduction Optimization Framework Results Summary ILSB Outline Introduction Optimization Framework Results Summary 13 / 15 Introduction Optimization Framework Results Summary ILSB Results of Optimization Three different arbitrary stiff and compliant lattice structures are chosen and compared with the pareto optimal solutions. (a) Stiff (b) Mixed (c) Compliant 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Vertical Displacement in mm 0 2 4 6 8 10 Rotational Angle in ° a b c (a) Stiff (b) Mixed (c) Compliant 13 / 15 Introduction Optimization Framework Results Summary ILSB Results of Optimization Three different arbitrary stiff and compliant lattice structures are chosen and compared with the pareto optimal solutions. (a) Stiff (b) Mixed (c) Compliant 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Vertical Displacement in mm 0 2 4 6 8 10 Rotational Angle in ° a b c (a) Stiff (b) Mixed (c) Compliant Pareto front Solutions 15 / 15 Introduction Optimization Framework Results Summary ILSB Summary and Outlook Summary •Framework to optimize lattice structures consisting of nonlinear mechanical material behavior •Uniaxial hypoelastic material model for beam elements via UHYPEL interface of ABAQUS •Integration of open-source geometry tool splinepy and optimization toolbox pymoo with black-box structural analysis software ABAQUS Outlook •Exploration of other optimization algorithms •Validation of optimal designs with experiments of superelastic lattice materials •Adaptation to more realistic loading scenario and corresponding objective function 15 / 15 Introduction Optimization Framework Results Summary ILSB Summary and Outlook Summary •Framework to optimize lattice structures consisting of nonlinear mechanical material behavior •Uniaxial hypoelastic material model for beam elements via UHYPEL interface of ABAQUS •Integration of open-source geometry tool splinepy and optimization toolbox pymoo with black-box structural analysis software ABAQUS Outlook •Exploration of other optimization algorithms •Validation of optimal designs with experiments of superelastic lattice materials •Adaptation to more realistic loading scenario and corresponding objective function 15 / 15 Introduction Optimization Framework Results Summary ILSB Summary and Outlook Summary •Framework to optimize lattice structures consisting of nonlinear mechanical material behavior •Uniaxial hypoelastic material model for beam elements via UHYPEL interface of ABAQUS •Integration of open-source geometry tool splinepy and optimization toolbox pymoo with black-box structural analysis software ABAQUS Outlook •Exploration of other optimization algorithms •Validation of optimal designs with experiments of superelastic lattice materials •Adaptation to more realistic loading scenario and corresponding objective function 15 / 15 Introduction Optimization Framework Results Summary ILSB Summary and Outlook Summary •Framework to optimize lattice structures consisting of nonlinear mechanical material behavior •Uniaxial hypoelastic material model for beam elements via UHYPEL interface of ABAQUS •Integration of open-source geometry tool splinepy and optimization toolbox pymoo with black-box structural analysis software ABAQUS Outlook •Exploration of other optimization algorithms •Validation of optimal designs with experiments of superelastic lattice materials •Adaptation to more realistic loading scenario and corresponding objective function Application of Structural Optimization on Lattice Structure Design using Superelastic Material Michael Kofler1*, Marius M. Schasching1, Ondˇrej ˇ Cervinek 2, Florian Zwicke1, Daniel Koutn´y 2, Heinz E. Pettermann1, and Melanie Todt1 1Institute of Lightweight Design and Structural Biomechanics, TU Wien, Austria 2Institute of Machine and Industrial Design, Brno University of Technology, Technick´a 2896/2, Brno, Czechia The funding of the project ”Building Actions in Smart Aviation with Environmental Gains” by the European Union Programme Horizon Europe under grant agreement no. 101079091 is gratefully acknowledged. The computational results presented have been achieved using the Vienna Scientific Cluster (VSC). Session: MS022 The 9th European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS Congress 2024 3-7 June 2024, Lisbon, Portugal