# Presentation: 268676

## Coarse and Fine-Grain Parallelism for Inverse Design OptimizationJames St. Ville & Subby RajanHawthorne & York, Intl.Phoenix, AZAshok BelegunduPennsylvania State University

## System Architecture

## Single Processor
Intel P3 and P4 (Windows & Linux)
Itanium (Red Hat Advanced Linux & Windows 2003 Server)
Distributed Processing using MPI (TCP/IP)
CML: 25 nodes, 24 processors at ASU (P4-3.06 MHz, 2 GB RAM, Red Hat Linux)
FEM: 8 nodes, 16 processors at ASU (Dual P4-1.7 GHz, 1 GB RAM, Windows 2000)
HYI: 4 nodes, 4 processors at HYI (P3-1 GHz, 1 GB RAM, Windows 2000)

- Intel P3 and P4 (Windows & Linux)
- Itanium (Red Hat Advanced Linux & Windows 2003 Server)
- Distributed Processing using MPI (TCP/IP)
**CML**: 25 nodes, 24 processors at ASU (P4-3.06 MHz, 2 GB RAM, Red Hat Linux)
**FEM**: 8 nodes, 16 processors at ASU (Dual P4-1.7 GHz, 1 GB RAM, Windows 2000)
**HYI**: 4 nodes, 4 processors at HYI (P3-1 GHz, 1 GB RAM, Windows 2000)

- Computing Platforms

## Objective Functions

- Weight, mass or volume
- Compliance
- Constrained Least-Squares
- Thermal Resistance
- Kinetic Energy, Sound Pressure

## Constraints

- Strength-based (failure criterion based)
- Compliance
- Nodal displacements
- Frequency
- Linearized buckling
- Volume, mass or weight
- Geometry

## Suite of Optimizers

- Method of Feasible Directions
- Specialized Least-Squares Solution
- Optimality Criteria
- Genetic Algorithm

## Gradient-Based Optimization

- 4 Major Steps
- Function Evaluation (FE)
- Gradient Evaluation (GE)
- Direction-Finding (DF) Step
- Line Search (LS)

## 3-Level Parallelism

## Sizing Optimization: Sequential versus Distributed Processing

## Fuel Tank Design

- FE Model
- 2722 nodes
- 5440 elements
- Uniform internal pressure
- Design Model
- 40 design variables
- Von Mises FC
- 30 iterations

## Fuel Tank Design (FEM)

| # of Procs | Parallel
Comps | Time
(seconds) | Speedup |
| --- | --- | --- | --- |
| 1 | NA | 8896 | 1.0 |
| 8 (1PN) | -ge | 4792 | 1.86 |
| 8 (1PN) | -ge –ls | 2265 | 3.93 |
| 8 (1PN) | -ge –df:4 | 2166 | 4.11 |
| 8 (1PN)  | -ge –df:4 –ls:2 | 1594 | 5.58 |
| 16 (2PN) | -ge –df:4 –ls:4 | 1254 | 7.09 |

## Fuel Tank Design (CML)

| # of Procs | Parallel
Comps | Time
(seconds) | Speedup |
| --- | --- | --- | --- |
| 1 | NA | 3602  | 1.0 |
| 8  | -ge | 2395 | 1.50 |
| 8 | -ge –ls | 1652 | 2.18 |
| 8 | -ge –df:4 –ls:2 | 920 | 3.92 |
| 16  | -ge –df:4 –ls:4 | 732 | 4.92 |
| 24 | -ge –df:4 –ls:6 | 783 | 4.60 |

## Fuel Tank Design

## Truss Design

- FE Model
- 1581 nodes
- 4550 elements
- Wind Loads
- Design Model
- 150 design variables
- Axial stress
- 20 iterations

## Truss Design (FEM)

| # of Procs | Parallel
Comps | Time
(seconds) | Speedup |
| --- | --- | --- | --- |
| 1 | NA | 2690 | 1.0 |
| 8 (1PN) | -ge | 1890 | 1.42 |
| 8 (1PN) | -ge –ls | 1196 | 2.25 |
| 8 (1PN) | -ge –df:4 | 1031 | 2.61 |
| 8 (1PN)  | -ge –df:4 –ls:2 | 1025 | 2.62 |
| 16 (2PN) | -ge –df:4 –ls:4 | 1117 | 2.41 |

## Truss Design

## Topology Optimization

## 3D Topology Optimization

- FE Model
- 173663 nodes
- 159763 elements
- Mech. Loads

## 3D Topology Optimization(Mass Fraction = 0.5)

## 3D Topology Optimization(Mass Fraction = 0.3)

## 3D Topology Optimization (FEM)

| # of Procs | Topology Opt. Time (s) | Normalized Time | Parallel FEA Time (s) | Normalized Time |
| --- | --- | --- | --- | --- |
| 8 (1PN) | 7249 | 1.9 | 536 | 1.68 |
| 16 (2PN) | 3813 | 1.0 | 320 | 1.0 |
| 8 (1PN) | 8138 | 1.8 | 558 | 1.73 |
| 16 (2PN) | 4492 | 1.0 | 322 | 1.0 |

## 3D Shape Optimization

## 3D Shape Optimization (FEM)

| # of Procs | Parallel
Comps | Time
(seconds) | Speedup |
| --- | --- | --- | --- |
| 1 | NA | 12525 | 1.0 |
| 8 (1PN) | -ge | 9235 | 1.36 |
| 8 (1PN) | -ge –ls | 4954 | 2.53 |
| 8 (1PN) | -ge –ls –fea:4 | 4269 | 2.93 |

## 3D Shape Optimization (CML)

| # of Procs | Parallel
Comps | Time
(seconds) | Speedup |
| --- | --- | --- | --- |
| 1 | NA | 4616 | 1.0 |
| 8 (1PN) | -ge –ls –fea:4 | 3396 | 1.36 |
| 16 (1PN) | -ge –ls –fea:4 | 2847 | 1.62 |
| 16 (1PN) | -ge –ls –fea:8 | 2122 | 2.18 |
| 24 (1PN) | -ge –ls –fea:4 | 2608 | 1.77 |
| 24 (1PN) | -ge –ls –fea:8 | 1895 | 2.44 |

## Topology & Shape Optimization of an L-Bracket

## Design Flow Diagram

- Create solid model,
- FEA and design data

- Prep3D

- Topology
- optimization

**Design3D/MP**

- Post3D

- Create shape and
- sizing optimization data
- using parametric solid modeling

- Prep3D

- Shape and/or
- sizing optimization

- Update solid model

- Prep3D

- User prepares for
- manufacturing

**Design3D/MP**

## Slide 27

## Shape Optimization of an Automotive Torque Arm

## Torque Arm Design

- FE Model
- Plane stress
- Tip loading
- Design Model
- 4 design variables
- Von Mises FC (800 MPa)
- Frequency constraint (> 400 Hz)
- Linear buckling constraint (> 750 N)

## Torque Arm Problem

- Stress Constraint

- Stress + Frequency

- Stress + Frequency + Buckling

## Torque Arm Problem

| Type | Max. VMFC (MPa) | Freq. (Hz) | Buckling Load (N) | Volume (mm3) |
| --- | --- | --- | --- | --- |
| Stress | 800 | - | - | 83818 |
| Stress + Freq. | 776 | 401 | - | 99036 |
| Stress + Freq. + Buckling | 751 | 421.5 | 750.1 | 102179 |

## Acoustics Optimization

## Acoustics Optimization

-  Focus has been on experimentally verified, passive noise radiation, from vibrating plates and shells – e.g., appliance covers or side panels, oil pan, timing chain cover plate, trim panels in aircraft
-  Objective is based on multiple attributes (sound power over a frequency band, weight, cost, amount of damping)
-  Design Idea: *attach* masses, vibration absorbers, air-filled cavities etc *to* the existing structure
-  Design variables are the parameters of the attachment structures

## Acoustics Optimization

-  Simulation Codes: In-house boundary element for sound power, FEA for vibration
-  New fast re-analysis techniques have been developed for obtaining response spectrum;
- modal calculations of original structure done once only, outside optimization loop
-  Efficient for broadband objectives since there are no peak searches
-  Absorber frequencies can be closely spaced
-  Coupled structure-acoustic vibration analysis method has now been developed – can now attach a thin air-filled cavity to structure

**Acoustics Optimization**

## Pressure Vessel

- A reduced eigenvalue method for broadband analysis of a structure with vibration absorbers possessing rotatory inertia, *J. of Sound and Vibration*, 281, pp. 869-886, 2005. [Grissom, Belegundu, et al]
- Conjoint  Analysis  Based  Multiattribute Optimization : Application  in  Acoustical  Design, To Appear, *J. of Structural Optimization*, 2005. [Grissom, Belegundu, et al]

- Finite element depiction of the curved pressure vessel

**Pressure Vessel**

## SOUND PRESSURE LEVEL 1 METER FROM THE VESSEL 

**SOUND PRESSURE LEVEL 1 METER FROM THE VESSEL**
- The problematic noise occurs at around 360 Hz, a harmonic of the motor frequency, and at the next three harmonics, 720, 1080, and 1440

## Method for Broadband Acoustic Response

**Method for Broadband Acoustic Response**

## Results

**Results**

## The “Optimized Product”

**The “Optimized Product”**

**A set of optimized Broadband Vibration Absorbers with a variable number of beams, n****b**

## Concluding Remarks

- Future of engineering analysis and design is in some form of a combined desktop-distributed computing paradigm
- Challenges lie ahead for inverse analysis and design
- Tightly integrated multi-physics design optimization offers an attractive solution to reducing design cycle times