Reliability based Design Optimization of Steel-Concrete Structure
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The document discusses the reliability-based design optimization (RBDO) of primary shield structures under seismic loading, focusing on minimizing steel plate thickness while maximizing reliability for pressurized water reactor systems. An experimental test setup and 3D finite element analysis were used to evaluate the structure's seismic performance, leading to optimized design thicknesses that improved reliability significantly. Future work aims to enhance RBDO techniques by incorporating additional failure criteria and design variables.
![Requires Design Process Automation
DV2
Feasible
Region
DV1
(Sample points for DOE)
active constraint
inequality constraint
inactive constraint
Minimized
Objective Function
Contour
Reliable and
Robust Design
Deterministic Optimum
[High Failure Rate]
RBDO [Very Low Failure Rate]
Initial
Design from
DOE
(Approximation)
RBDO Process
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Reliability based Design Optimization of Steel-Concrete Structure
- 1. RELIABILITY BASED DESIGN OPTIMIZATION OF PRIMARY SHIELD STRUCTURE UNDER SEISMIC LOADING 7/20/2017 S. K. Radha, A. Chakraborty Virtual Integrated Analytics Solutions (VIAS) K. C. Sener, A. H. Verma Civil Engineering, Purdue University
- 2. Agenda 2 • Introduction • Background • Problem Statement • Test Setup and Results • FEA Model & Results • Reliability based Design Optimization • Optimization Results ▪ Plate Thickness ▪ Reliability • Conclusions • Future Work
- 3. Introduction • PSW provides support and protection to reactor pressure vessel (RPV) and critical reactor internals of PWR • Consists of several structural members like bearing walls, shear walls, slabs, etc. • Seismic activity can damage critical structural/ shielding components • Modular steel-plate composite (SC) PSW with concrete infills increasingly used • SC structures exhibits excellent structural performance in terms of stiffness, strength and ductility under seismic loading 3 RPV PSW Steel Concrete Steel-Plate Composite PSW Outer Shield Building
- 4. Introduction (Cont.) • Typical SC structure consists of: ▪ Thick concrete walls (infill between plates) ▪ 3 layers of steel plates (interior and exterior surfaces and 1 middle layer to provide additional reinforcement) ▪ Intermediate web plates • SC modules fabricated in production environment and transported to construction site • Erected, welded and finally filled with concrete on-site thereby reducing construction critical path time Exterior Plates Interior Plates Web Plates Concrete Infill Cavity 4
- 5. Background • An experimental test setup of a 1/6th scale PSW specimen and the seismic load-deformation behavior tested • 3D FEA model was developed and validated for deterministic numerical study 5 Current work extends to reliability based design optimization (RBDO) study
- 6. Problem Statement • Objective: ▪ Minimize T and t (minimizes inertia under seismic and cost) ▪ Maximize Reliability (applied stress < yield) • Design Variables: ▪ T: Steel plate thickness at openings ▪ t: Typical steel plate thickness 6 Steel plate thickness at openings (T): Brown plates Typical steel plate thickness (t): Red, Green, Blue, and Black plates Initial Design Dimensions T= 0.17 in (4.32 mm) t= 0.10 in (2.54 mm)
- 7. Test Setup • Experimental test conducted in Japan of 1/6th scale version of the APWR PSW • Polygonal SC structure with three steel liner plates and web plates • Free-standing test specimen rigidly embedded in reinforced concrete base PSW Cross-section and Isometric view of PSW ( no concrete infill) Horizontal Section Cut through Specimen (with concrete infill) Reinforced concrete base (T) (t) 7
- 8. Test Setup (Cont.) • Test setup configured as a free standing structure with top connected to upper concrete loading block and fixed base • Lateral force applied on structure hydraulically • Quasi-static cyclic loading applied • Subjected to three load-controlled cycles in elastic range of response • Final cycle until ultimate failure 8
- 9. Test Results • Ultimate strength controlled by combination of flexure, shear, and axial forces in wall segments • Local buckling and yielding occurred in steel plates adjacent to openings • Specimen showed substantial post yield ductility • Measured shear strains in inner, middle and outer steel plates were relatively equal • Demonstrates that all three steel plates contribute to system strength 9
- 10. FEA Model • 3-D half model used since geometry and loading are mirror symmetric • All of the PSW steel plates are modeled using 4-node shell elements (S4R) and multi-axial plasticity material model • Concrete infill is modeled with continuum 3-D 8-node reduced integration (C3D8R) brick elements and elastic fracture (brittle cracking) material model • Composite action between steel and concrete is modeled with non-linear connector elements • Monotonic and cyclic loading conditions are simulated Exploded view of part instances and mesh 1 0
- 11. FEA Model: Results von Mises stress at applied loads of 1000, 2000, 3000 and 4000 kips on inner steel plate von Mises stress at applied loads of 1000, 2000, 3000 and 4000 kips on outer steel plate von Mises stress at applied loads of 1000, 2000, 3000 and 4000 kips on middle steel plate 11 Red indicates yielding (>67.3 ksi)
- 12. FEA Model: Results (Cont.) • Analytical load-displacement response behavior compares well with experimental results • Comparisons also indicate that cyclic load response and behavior of specimen are similar to monotonic analysis results • Cyclic loading is not expected to have major influence on results due to non-ductile shear failure of specimen • Hence only monotonic loading considered in the RBDO study Displacement gradient for monotonic loading Comparison of Experimental and Analytical results 12
- 13. Requires Design Process Automation DV2 Feasible Region DV1 (Sample points for DOE) active constraint inequality constraint inactive constraint Minimized Objective Function Contour Reliable and Robust Design Deterministic Optimum [High Failure Rate] RBDO [Very Low Failure Rate] Initial Design from DOE (Approximation) RBDO Process 13
- 14. RBDO Process (Cont.) 14 Requires Approximation of Response
- 15. Stochastic Analysis • Maximum Von Mises stress (σvm) induced in steel plate considered the most important criteria to evaluate lateral load capacity • T, t – design variables (to be within 20% of T = 0.17 in and t = 0.1 in) • T , t, σy, and u considered as normal random variables with mean values and 10 % as their coefficient of variation (COV) • Performance function defined as g(X)= σvm (T, t, σy, u) - σy • Reaching the yield strength of steel (σy) is considered as structural failure (i.e g(X) >0) (Failure Criteria) • Target reliability 0.99 Normal Random Variable Mean Thickness of steel plate at opening (T) 0.17 in (4.32 mm) Thickness of typical steel plate (t) 0.10 in (2.54 mm) Yield stress of Steel (𝛔 𝐲) 67 ksi (462 MPa) Applied Displacement (𝐮) 0.10 in (2.54 mm) 15
- 16. Response Approximation • Response Surface Method (RSM) is used for optimization and reliability • Response approximated as quadratic function that provided good correlation (mean error< 5%) 60 62 64 66 60 62 64 66 Actual Predicted Actual vs. Predicted values of approximation. 25 FEA runs: For Approximation Function 10 FEA runs: For Error Computing 16 Typical FEA Runtime – 16hrs
- 17. Pareto Effects • U, t has the most pronounced effect on von Mises stress • Higher order and correlation effects are small 17 0 10 20 30 σ_y T t u % effect on maximum von mises stress (Linear) 0 10 20 30 σ_y and T σ_y and u (σ_y)^2 T and u t and u u^2 % effect on maximum von Mises stress (2nd order & correlated)
- 18. Optimization Workflow (Isight) • RBDO workflow setup in Isight based on FEA model response approximations • Second Order Reliability Method (SORM) and Monte Carlo Simulation (MCS) reliability techniques used • Sequential Quadratic Programming (SQP) and Hooke- Jeeves (HJ) direct search approaches used for optimization Sample Size for Optimization – DO : ~ 60 RBDO : ~ 100,000 18
- 19. Results: Optimized Plate Thickness Reliability Method Optimization Method T (in) t (in) SORM SQP 0.16 0.12 HJ 0.16 0.12 MCS SQP 0.14 0.12 HJ 0.14 0.12 RBDO: Optimization Method T (in) t (in) SQP 0.13 0.09 HJ 0.15 0.09 SQP 0.13 0.09 HJ 0.15 0.09 DO: MCS results better suited for non- linear response Original Values T= 0.17 in t= 0.10 in 19
- 20. Results: Reliability Reliability Method Optimization Method DO RBDO SORM SQP 0.48 0.64 HJ 0.49 0.64 MCS SQP 0.55 0.68 HJ 0.55 0.68 Original Model Reliability SORM: 0.56 MCS: 0.62 20
- 21. Conclusions • DO has lowered both thickness values from initial • However, RBDO has lowered the thickness of steel plate at opening (T) by 17.64 % and increased the thickness of typical steel plate (t) by 20 % from the original values • RBDO achieved a reliability of 68 % and increased the reliability of the PSW structure by 9.6 % and 23.6 % when compared to the original reliability and reliability from DO, respectively. 21
- 22. Future Work • Extension for a better RBDO of PSW which considers • Additional failure criteria (concrete casting pressure, thermal loading, etc) • Additional design and stochastic variables 22
- 23. Thank you 23