1 1 3DS.COM/SIMULIA© Dassault Systèmes Optimization and Robustness Optimization and Robustness DassaultSystemes Deutschland GmbH Analysis Analysis of a Stent AxelReichert 2 2 3DS.COM/SIMULIA© Dassault Systèmes Overview Overview 6 5 4 3 2 1 Robustness Analysis Shape Optimization Parameter Optimization Fatigue Analysis Finite Element Analysis CAD Modeling 3 3 3DS.COM/SIMULIA© Dassault Systèmes CAD Modeling CAD Modeling SolidWorks

2D sketch

2D geometry 4 4 3DS.COM/SIMULIA© Dassault Systèmes Finite Finite Element Analysis 2D mesh 3D 3D mesh Wrapped 3D mesh 5 5 3DS.COM/SIMULIA© Dassault Systèmes Finite Finite Element Analysis Artery (anisotropic-hyperelastic) Stent Stent (elastic-plastic) Expansion/crimping Expansion/crimping cylinders 6 6 3DS.COM/SIMULIA© Dassault Systèmes Finite Finite Element Analysis Crimping Preloading Preloading stress and insertion

Blood loadingpressure Cyclicstress 7 7 3DS.COM/SIMULIA© Dassault Systèmes Fatigue Fatigue Analysis fe

-safe with Gerber (fatigue factor) reserve Brown-Miller (criticalplane method ultimate tensile strength Surgicalstainless steelwith Worst FRF: 1.223 ) Fatigue envelope: (around 20 years) Infinite life estimate: 1 billioncycles Strain (1e−6) Meanstress ( MPa ) ) 8 8 3DS.COM/SIMULIA© Dassault Systèmes Parameter Optimization Parameter Optimization Isight Design Design sweet spot 9 9 3DS.COM/SIMULIA© Dassault Systèmes Parameter Optimization Parameter Optimization Shape Changes

Baseline Baseline Parameter Parameter optimized Comparison Comparison 10 3DS.COM/SIMULIA© Dassault Systèmes

Parameter Optimization Parameter Optimization MisesStress

Baseline Baseline

Parameter Parameter optimized 5%

11 3DS.COM/SIMULIA© Dassault Systèmes

Parameter Optimization Parameter Optimization Fatigue Factor Reserve

Baseline Baseline

Parameter Parameter optimized 8% 8% 12 3DS.COM/SIMULIA© Dassault Systèmes

Shape Optimization Optimization Shape ToscaStructure.shape Geometrical restrictions Objective Method Cyclicsymmetry Preservemanufacturability over all load cases Minimize maximum Misesstress Controller approach

Design Design nodes 13 3DS.COM/SIMULIA© Dassault Systèmes

Shape Optimization Shape Optimization Shape Changes

Parameter Parameter optimized

Shape Shape optimized 14 3DS.COM/SIMULIA© Dassault Systèmes

Shape Optimization Shape Optimization MisesStress

Parameter Parameter optimized

Shape Shape optimized 14%

15 3DS.COM/SIMULIA© Dassault Systèmes

Shape Optimization Shape Optimization Fatigue Factor Reserve

Parameter Parameter optimized

Shape Shape optimized 14%

16 3DS.COM/SIMULIA© Dassault Systèmes

Robustness Robustness Analysis Isight approximation Monte Carlo simulation uses DoE generates approximation Artery dimensionsare varied Radius Inner Outer

1.13 1.62 (mm) Mean

0.018 0.028 (mm) Standard deviation

Outer Outer radius

Inner Inner radius 17 3DS.COM/SIMULIA© Dassault Systèmes

Robustness Robustness Analysis Generating the Approximation DoE DoE

Response Response surface 18 3DS.COM/SIMULIA© Dassault Systèmes

Robustness Robustness Analysis Using the Approximation

Monte Monte Carlo simulation Fatigue reserve factor 19 3DS.COM/SIMULIA© Dassault Systèmes

Summary Summary Process IntegrationProcess with the Power of the Portfolio Non-Parametric Parametric Parametric Optimization Optimization Drives Drives Design Design and and Analysis Finite Elements Finite Elements CAD Modeling Fatigue Fatigue 20 3DS.COM/SIMULIA© Dassault Systèmes