Introduction to NX Nastran SOL 200 - Design Optimization
- 1. 5/22/2012 Page 1 SDA Webinar Introduction to NX Nastran SOL 200 Design Optimization David Cross Senior Stress Analyst at SDA david@structures.aero July 23, 2015
- 2. 5/22/2012 Page 2Page 2 Webinar Overview • About SDA • What is Design Optimization? • Demonstrations – Thickness optimization of a stiffened rectangular plate • Optimization model setup in Femap • Post-process optimization results • Quick comparison to HyperSizer results – Thickness optimization of wing with buckling constraints • How to add buckling constraints • Adjusting the optimizer’s parameters to improve convergence • Additional Resources • Questions Femap – Model Optimization Dialogue Box
- 3. 5/22/2012 Page 3Page 3 What is Design Optimization • An optimizer is a formal plan, or algorithm, used to search for a “best” design. • “Best” Design – Objective Function – Design Variables – Constraints • NX Nastran uses a gradient-based algorithm – Uses design sensitivities to find “best” search direction – Rate of change of analysis response with respect to changes in the design variables – Finds local optimum, not necessarily the global optimum Geometric Interpretation (Comes from NX Nastran Optimization User’s Manual)
- 4. 5/22/2012 Page 4Page 4 Design Optimization in Femap with NX Nastran • SOL 200 can be used with… Statics (Femap Supports) Normal Modes (Femap Supports) – Buckling – Direct and Modal Frequency – Modal Transient – Acoustic – Aeroelastic • Design variables are defined in relation to property or material entries. • Design constraints are defined in relation to analysis responses. • Basically any field on a property or material card can be set as a design variable. (Limited in Femap) • Shape variables, which allow nodes to move can be defined as well. (Not supported in Femap)
- 5. 5/22/2012 Page 5 Stiffened Plate Model • Orthogrid Stiffened Panel • Metallic • 6 psi External Pressure • Linear Static Analysis • Optimization Problem – Minimize Mass – Subject to: – Stress Constraints – Displacement Constraints – Lower and Upper Bounds (side constraints) Simply-Supported Constraints on all edges 40” 40”
- 6. 5/22/2012 Page 6 Math Programming Problem min 𝒕∈ℝ42 𝑀𝑎𝑠𝑠(𝒕) s. t. 𝒈 𝒕 ≤ 0 𝒈 𝑡 = 𝝈 𝑉𝑀 𝒕 − 25,000 𝜹 𝑍 𝒕 − 0.35 0.05 − 𝑡𝑖 𝑡𝑖 − 0.25 ≤ 0 , 𝑖 = 1,2, … , 42 • Initial Design All thicknesses set to 0.10” • Initial Mass = 22.74 lbs. • Initial design satisfies all constraints • Room for improvement 0.148” Max Displacement 15 ksi Max Stress
- 7. 5/22/2012 Page 7 Optimum Solution – Thickness and Mass Results • Initial Mass = 22.74 lbs. • Optimized Mass = 14.54 lbs. • Percent Relative Decrease of 36% Shows an active constraint 0.03766 slinches View the Webinar
- 8. 5/22/2012 Page 8 Optimum Solution – Stress and Displacement Results Peak stresses close to constraint value in many places Max displacement = Constraint Value of 0.35” Properties that show relatively low peak stresses are those at minimum gauge.
- 9. 5/22/2012 Page 9 Different Initial Design Point Initialized All Properties at Min Gauge (0.05”) • Optimized Mass = 14.62 lbs. (slightly heavier) • Nearly identical optimum design as the first run HyperSizer Result Minimum Margin of Safety • Optimized Weight = 14.08 lbs. • May need additional iterations with FEA • Nastran uses 1e-3 default convergence tolerance
- 10. 5/22/2012 Page 10 Optimum Thicknesses ID Thickness Opt 1 Thickness Opt 2 Thickness HyperSizer 1 0.073 0.073 0.0683 2 0.062 0.062 0.0576 3 0.062 0.062 0.0576 4 0.073 0.076 0.0697 5 0.062 0.062 0.0576 6 0.058 0.058 0.0530 7 0.058 0.058 0.0530 8 0.062 0.062 0.0576 9 0.062 0.062 0.0576 10 0.058 0.058 0.0530 11 0.058 0.058 0.0530 12 0.062 0.062 0.0576 13 0.073 0.073 0.0697 14 0.062 0.062 0.0576 15 0.062 0.062 0.0576 16 0.073 0.073 0.0697 17 0.052 0.05 0.0500 18 0.05 0.05 0.0500 19 0.05 0.05 0.0500 20 0.05 0.05 0.0500 21 0.067 0.068 0.0636 22 0.05 0.05 0.0500 23 0.05 0.05 0.0500 24 0.068 0.067 0.0636 25 0.05 0.05 0.0500 26 0.05 0.05 0.0500 27 0.05 0.05 0.0500 28 0.05 0.05 0.0500 29 0.081 0.082 0.0833 30 0.05 0.05 0.0500 31 0.05 0.05 0.0500 32 0.05 0.05 0.0500 33 0.05 0.05 0.0500 34 0.069 0.067 0.0636 35 0.05 0.05 0.0500 36 0.05 0.05 0.0500 37 0.068 0.067 0.0636 38 0.05 0.05 0.0500 39 0.05 0.05 0.0500 40 0.05 0.05 0.0500 41 0.05 0.05 0.0500 42 0.05 0.055 0.0500
- 11. 5/22/2012 Page 11 Wing Optimization with Skin Buckling • Metallic wing with skins, ribs, spars, and stringers • Uniform pressure load on bottom surface • Linear Static Analysis and Linear Buckling Analysis • Optimization Problem – Minimize Mass – Subject to: – Stress Constraints – Buckling Constraints – Lower and Upper Bounds (side constraints)
- 12. 5/22/2012 Page 12 Math Programming Problem min 𝒕∈ℝ42 𝑀𝑎𝑠𝑠(𝒕) s. t. 𝒈 𝒕 ≤ 0 𝒈 𝑡 = 𝝈 𝑉𝑀 𝒕 − 45,000 λ 𝑏 𝒕 − 1.15 0.03 − 𝑡 𝑠𝑘𝑖𝑛,𝑖 0.05 − 𝑡 𝑟𝑖𝑏,𝑖 0.05 − 𝑡 𝑠𝑝𝑎𝑟,𝑖 𝑡𝑖 − 0.5 ≤ 0 , 𝑖 = 1,2, … , 63 • Initial Design Skins are 0.08” and ribs/spars are 0.10” • Initial Mass = 116 lbs. • Initial design dramatically violates buckling constraint • From this alone, it is easy to see that the design will be mostly if not entirely driven by min gauge and buckling.
- 13. 5/22/2012 Page 13 Best Compromise Infeasible Design Improvement, Converging Not Improving Anymore (Still Positive) • Design is flat-lining, but the buckling constraint is still violated. • Small changes in the design variable result in mode switching. • Only constraining the first buckling mode. • Optimizer treats buckling eigenvalue as a continuous variable. • The optimizer has too little information. Iter 21 Iter 22 Iter 23
- 14. 5/22/2012 Page 14 Converged Optimum • Initial Mass = 116 lbs. • Optimized Mass = 93 lbs. • Percent Relative Decrease of 20% λ1 = 1.139 λ2 = 1.139 λ3 = 1.145 λ4 = 1.149 λ5 = 1.15 • Tracking first five buckling modes • Set looser convergence tolerances Converged within 1e-2 tolerance setting Flat-lining
- 15. 5/22/2012 Page 15 Optimization/Sizing in HyperSizer • HyperSizer evaluates buckling margins with closed form solutions. • Buckling margin calculated for every property (component). • Here I assume simply-supported boundary conditions. • Iterations with FEA are critical to allow loads to redistribute and converge. View the Webinar
- 16. 5/22/2012 Page 16 λ1 = 1.139 λ2 = 1.139 λ3 = 1.145 λ4 = 1.149 λ5 = 1.15 Comparison to HyperSizer Solution NX Nastran SOL 200 Upper Skin Thicknesses HyperSizer Upper Skin Thicknesses HyperSizer Total Weight = 96 lbs Nastran Buckling Analysis of HyperSizer Solution λ1 = 1.20 SOL 200 Total Weight = 93 lbs
- 17. 5/22/2012 Page 17 About SDA (aka “Structures.Aero”) • SDA was founded in 1997 and provides expert aerospace structural analysis • We serve a variety of industries • We specialize in composites, and developing strong, lightweight structures that are readily manufacturable • Low level support up through developing test plans and advanced stress analysis • Typical support programs include small to large UAVs, manned and unmanned spacecraft, naval structures • Our team consists of over a dozen B.S., M.S., and PhD level engineers • SDA is located in Sterling, VA, just north of Dulles Airport near Washington DC Learn more about Structural Design and Analysis
- 18. 5/22/2012 Page 18Page 18 Typical Projects We Support • Some of our previous projects include: – Aircraft • Aurora Excalibur • MHADD ARES • Vanilla VA1 • Lockheed Constellation restoration for Lufthansa – Spacecraft • NASA NESC Composite Crew Module (CCM) • NASA NESC Max Launch Abort System (MLAS) • NASA James Webb Space Telescope/IEC • NASA Orion Heatshield mass reduction for NESC • NASA Orion Crew Module (with Lockheed) • NASA WFIRST Telescope for Goddard Aerosonde Heatshield Shadow M2 CCM Orion Crew Module
- 19. 5/22/2012 Page 19Page 19 Partnerships Siemens Value Added Reseller Collier Research Corporation Reseller FEMAP NX Nastran Fibersim Solid Edge HyperSizer Pro HyperSizer Express
- 20. 5/22/2012 Page 20 Conclusions and Additional Resources What We Covered • Brief introduction to design optimization • Optimization model setup in Femap – Objective function – Design Variables – Constraints • General considerations and post-processing – Function plotting – How to check for convergence – How to help account for modal switching • Comparisons to HyperSizer Questions? As a Siemens PLM Software channel partner SDA provides first line support for Femap with NX Nastran Contact David Cross david@structures.aero Structural Design and Analysis 703-673-1125 46030 Manekin Plaza Sterling, VA 20166