OPTIMIZATION OF ENERGY DISSIPATION PROPERTY OF ECCENTRICALLY BRACED STEEL FRAMES

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1 OPTIMIZATION OF ENERGY DISSIPATION PROPERTY OF ECCENTRICALLY BRACED STEEL FRAMES M. Ohsaki (Hiroshima Univ.) T. Nakajima (Kyoto Univ. (currently Ohbayashi Corp.))

2 Background Difficulty in optimization in building structures: Structures are not mass products cannot spend much cost on optimization Shape optimization of special structures (long-span truss, free-form shell, etc.) Structural parts are mass products optimization of parts of building frame

$(fraction = -1.0) (Ave. Crit.$ : 75%) +2.436e+08 +2.

3 Optimization of structural parts Optimization of beam-flange shape to improve plastic energy dissipation property S, Mises SNEG, (fraction = -1.0) (Ave. Crit.: 75%) e e e e e e e e e e e e e ODB: Case2-STEP1680.odb ABAQUS/Standard Mon Oct 17 16:04:32 GMT+09: Step: STEP1680, STEP1680 Increment 7: Step Time = Primary Var: S, Mises Deformed Var: U Deformation Scale Factor: e+00 Ohsaki, Pan, Tagawa (2007, 2010)

4 Optimization of structural parts Reduce weight of clamping device of membrane structure Ohsaki, Fujiwara, Nakajima (2010)

5 Purpose of study Optimization of Eccentrically Braced Frame (EBF) Eccentricity between beam-brace connection Dissipate seismic (earthquake) energy in link member between connections Link member

6 Design specification of EBF Demand for large rotation (γ p : plastic rotation of link, θ p : interstory drift angle of frame) Specification by AISC: 0.02 ~ 0.08 (rad) (AISC:American Institute of Steel Construction) Rotation γ p [rad] Length of link : e/(m p /V p )

7 Optimization approach Mathematical programming Optimization of structural parts Geometrical/material nonlinearity Poor convergence Populationbased heuristic approach High computational cost Evaluate response many times Tabu search: single-point search heuristics based on local search

Optimize location and thickness of stiffeners 2.

8 Optimization of link member Increase plastic energy dissipation Prevent buckling and collapse near connections 1. Optimize location and thickness of stiffeners 2. Optimize length of link member in a frame 3. Tabu search: Approximate optimal solution with small number of analyses Forced disp

9 Analysis model Wide-flange section (H ) Elastic modulus: GPa, Yield stress: Mpa Tensile strength: MPa Link length: e =1219 mm (intermediate length) Stiffeners: four, 10mm Shell element: nominal size 25mm Forced vertical displacements FEM code: ABAQUS Boundary A flange stiffener Boundary B web Forced disp.

10 Failure Index Index for low cycle fatigue Defined by stress triaxiality ( σ m / σ e ) p Equivalent plastic strain von Mises equivalent stress Mean stress Critical plastic strain: Fracture occurs if FI=1.0 Compute FI of all elements and find the max. value

11 Verification with experimental results FE-analysis Local buckling of flange and web Cyclic softening Location of element with If =1.0 Good accuracy von Mises stress experiment Shear force analysis Plastic rotation Equivalent plastic strain

of stiffeners Discretize real variables x

12 Optimization problem Objective function Plastic energy dissipation Constraint Max. value f I of FI is less than 1.0 Design variables Location and thickness of stiffeners Discretize real variables x i to integer variables J i Rotation 振幅 [rad] angle

13 Tabu search (TS) 1. Randomly generate initial seed solution Initialize tabu list T as empty list 2. Generate neighborhood solutions N = { J N j j =1,...,q } 3. Evaluate objective functions and constraints (penalty function for constraints) 4. Best solution in N that is not included in tabu list T Next seed solution 5. Add the seed solution to T 6. Go to step 2 if termination conditions are not satisfied; otherwise, output the best solution satisfying constraints.

14 Parameters of TS 1. Number of neighborhood solutions: 3 2. Number of steps: 5 3. Length of tabu list: 5 4. Carry out TS five times from different random seeds. 5. Total number of analyses: 5 x 5 x 3 = 75

15 Optimization using ABAQUS TS Algorithm Generate coordinates, thickness, length Postprocessing (Python Script) Preprocessing (Python Script) (1) Flange, web, plate parts (2) Material and section (3) Assemble beam part (4) Boundary and load (5) FE-mesh (6) Submit to ABAQUS Dissipated energy Equivalent plastic Strain Compute objective and constraint functions Simulation ABAQUS/Standard

16 Optimization of location and thickness of stiffeners Stiffeners are located near center and ends Shear (reaction) force is incerased standard optimal Standard Max. If Force-rotation relation Optimal Location (mm) Thickness (mm)

17 Optimization of location and thickness of stiffeners Increase E p, decrease f I Dissipated energy E f p before failure is 42% larger than standard model Objective function Failure index Dissipated energy before failure E p I f E p f Standard Optimal E pf : dissipated energy before I f reaches 1.0 (kn m) +42%

Brace: truss element Assign story drift (=1/50) and maximize

18 Eccentrically braced portal frame Span L=4.0m, height 2.0m FE-model: Link: shell element; Beam, column: beam element; Brace: truss element Assign story drift (=1/50) and maximize dissipated energy E f p before reaching f I =1.0 Forced disp Rotation angle

19 Relation between length and responses Rotation Shear force Link length Link length Dissipated energy before I f =1.0 No. of cycles before I f =1.0 Link length Link length

20 Optimization problem Objective function Plastic energy dissipation before reaching I f =1.0 Design variables Location and thickness of stiffeners Length of link beam Discretize real variables x i to integer variables J i Upper bound of length: e =1400 mm

21 Optimization of link length, location and thickness of stiffeners standard optimal Location Thickness Model Length Plastic energy Cycles Angle Shear force e (mm) E p f (kn m) N cycle (times) γ max (rad) V L max (kn) Standard Optimal %

22 Conclusions 1. Shape optimization of link beam Combine FEM (ABAQUS) and optimization algorithm (TS) Maximize energy dissipation under constraint on failure index Optimize location and thickness of stiffeners Tabu search for improvement: Approximate optimal solution with small computational cost 2. Optimization of portal EBF Optimize length of link beam Energy dissipation has been drastically improved

Optimization of Energy Dissipation Property of Eccentrically Braced Steel Frames

9 th World Congress on Structural and Multidisciplinary Optimization June 13-17, 2010, Shizuoka, Japan Optimization of Energy Dissipation Property of Eccentrically Braced Steel Frames Makoto Ohsaki 1,