Finite Element based optimization of form and material orientation of fiber-reinforced composites

Transcription

1 Finite Element baed optimization of form and material orientation of fiber-reinforced compoite H. Maching, M. Ficher, K.-U. Bletzinger Techniche Univerität München Faculty of Civil Engineering and Surveying Chair of Structural Analyi Hannover Mee 2013 Werktoff-Forum

2 Outline 1. Introduction to 2. Finite element baed tructural optimization 3. The compoite hell element 4. Fiber-optimization of a ingle-layer orthotropic plate 5. Combined hape and fiber optimization 5.1 Navier upported plate 5.2 Preure bulkhead 6. Concluion Hannover Mee 2013 Werktoff-Forum 2 / 23

3 1. Introduction to Computer Aided Reearch and Analyi Tool A flexible finite element oftware for: Simulation: (Non-)Linear Static and (Non-)Linear Dynamic Eigenfrequency Analyi, Buckling Analyi Contact Analyi Analyi for Reduced Model Controlled Structure Interface to FSI analyi, Formfinding and cutting patterning of membrane Iogeometric analyi Structural Optimization inflated tructure membrane deign aeropace automotive Hannover Mee 2013 Werktoff-Forum 3 / 23

4 2. Finite element baed tructural optimization Parameterization and deign CAGD Computer Aided Geom. Deign Optimization variable: geometry parameter CAGD free (= FE-baed) Optimization variable: baed on FE model: coordinate, thickne, material orientation time conuming limited deign pace optimization run out of the box maximum deign pace regularization neceary Hannover Mee 2013 Werktoff-Forum 4 / 23

5 Hannover Mee 2013 Werktoff-Forum 5 / Finite element baed tructural optimization Senitivity analyi: Adjoint emi analytic approach Programming iue concerning of gradient computation: Efficiency No deign variable pecific code i i i i i e x = + K K K K ) ( Low coding effort Can be ued for any deign variable type Semi-analytical enitivitie of element propertie: Adjoint formulation of derivative: i i i d d ψ ψ ψ + = d d 1 T h ψ with ; ψ ψ = + = d d λ h λ i i i d d avoid explicit derivative of primary variable adjoint 2 1 ; 2 1 direct int int 1 ext ext T ext ext T ext T ext f K f u f f f u f f f K Λ = Λ + = + = Τ T T d dψ d dψ

6 2. Finite element baed tructural optimization Natalia Camprubi Gradient filtering baed on convolution Fernaß Daoud Matthia Firl filter type and ize (deign deciion) 3 d f ( d) = 20 3π r 5 2 d 10 π r π r 2 r r Filter function of 3 rd order f m [2] [2]: onvolution_animation_ (Gauian).gif&filetimetamp= Hannover Mee 2013 Werktoff-Forum 6 / 23

7 2. Finite element baed tructural optimization Gradient filtering baed on convolution noie eliminated local effect filter radiu: 0.5 The filter i not jut a mathematical moothener, it i a deign tool! input function filter radiu: 1.5 overall deign moothened global effect filter radiu: 2.0 Hannover Mee 2013 Werktoff-Forum 7 / 23

8 2. Finite element baed tructural optimization Gradient filtering baed on convolution Filter radiu: 100 Filter radiu: 200 Filter radiu: 400 Hannover Mee 2013 Werktoff-Forum 8 / 23

9 3. The compoite hell element Single-layer hell formulation: Mainly baed on the PhD of Manfred Bichoff at the Univerität Stuttgart 7-parameter-hell (3x tranl., 3x diff. of director, 1x EAS) Thickne change are conidered DOF: 6 x number of node RM-kinematic EAS and ANS improvement 2d-geometry, 3d-phyic Material law i pre-integrated over the thickne: Unmodified three dimenional material law can be ued Hannover Mee 2013 Werktoff-Forum 9 / 23

10 3. The compoite hell element Multi-layer hell formulation: Formulation wa extended to a ingle director multi layer hell: till 6 DOF per node Material law and tree are integrated over the complete thickne [3] [3]: Baed on: Berthelot, Jean-Marie: Compoite Material Mechanical Behaviour and Structural Analyi, Springer-Verlag, New York, 1999 Hannover Mee 2013 Werktoff-Forum 10 / 23

11 4. Fiber-optimization of a ingle-layer orthotropic plate under preure load X E = MPa E = MPa G =5 600 MPa G =5 100 Mpa ν = 0.25 ρ = 2000kg/m 3 Tickne: 10cm Load: Preure Hannover Mee 2013 Werktoff-Forum 11 / 23

12 4. Fiber-optimization of a ingle-layer orthotropic plate under preure load Optimization of fibre orientation variable Repone function: train energy CG-Algorithm max. change of angle: 10 per tep 3-point lineearch Hannover Mee 2013 Werktoff-Forum 12 / 23

13 4. Fiber-optimization of a ingle-layer orthotropic plate under preure load Diplacement of initial deign Diplacement of optimized deign Hannover Mee 2013 Werktoff-Forum 13 / 23

14 5. Combined hape and fiber optimization 5.1 Navier upported plate Orthotropic material Uniform fiber orientation Mixed et of deign variable - nodal poition of all unupported node - fiber orientation in each element Different filter for different deign variable: - linear filter for fiber variable (R=0.8) - cubic filter for hape variable (R=3.0) Hannover Mee 2013 Werktoff-Forum 14 / 23

15 5. Combined hape and fiber optimization 5.1 Navier upported plate Hannover Mee 2013 Werktoff-Forum 15 / 23

16 5. Combined hape and fiber optimization 5.1 Navier upported plate Load carrying pathe of optimal deign Hannover Mee 2013 Werktoff-Forum 16 / 23

17 5. Combined hape and fiber optimization 5.2 Preure bulkhead Formfinding Topology Optimization CAGD-baed hape optimization Hannover Mee 2013 Werktoff-Forum 17 / 23

18 5. Combined hape and fiber optimization 5.2 Preure bulkhead Optimization of hape and fiber orientation while the tack ha to remain ymmetric. Objective: train energy 1 deign variable per node 2 deign variable per element Compoite tructure with ymmetric tack: Hannover Mee 2013 Werktoff-Forum 18 / 23

19 5. Combined hape and fiber optimization 5.2 Preure bulkhead Optimization of hape: Change of geometry Hannover Mee 2013 Werktoff-Forum 19 / 23

20 5. Combined hape and fiber optimization 5.2 Preure bulkhead Optimization of fiber orientation: Outer plie Optimization of fiber orientation: Inner plie Hannover Mee 2013 Werktoff-Forum 20 / 23

21 5. Combined hape and fiber optimization 5.2 Preure bulkhead Buckling load increaed by 70% Hannover Mee 2013 Werktoff-Forum 21 / 23

22 6. Concluion FE-baed tructural optimization with minimum modeling effort large deign pace (adjoint enitivity analyi) large application field: (non-)linear tiffne, ma, eigenfrequency, buckling, huge model via parallelization (hared and ditirbuted memory) abtract definition of deign variable allow an eay change of optimization dicipline (nodal coordinate, nodal hell thickne, ply material angle, ) Hannover Mee 2013 Werktoff-Forum 22 / 23

23 Finite Element baed optimization of form and material orientation of fiber-reinforced compoite Thank you for your attention Hannover Mee 2013 Werktoff-Forum 23 / 23