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기계항공 공학부 , 서울 대학교 김 승 조 2006, 11, 21 Supercomputing Korea 2006

On Computational Structures Technologies. 기계항공 공학부 , 서울 대학교 김 승 조 2006, 11, 21 Supercomputing Korea 2006. ASTL. A ero ST ructures L ab. Contents. Introduction History of Finite Element Analysis Representative Structural Analysis Codes Large Scale Parallel Structural Analysis Code

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기계항공 공학부 , 서울 대학교 김 승 조 2006, 11, 21 Supercomputing Korea 2006

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  1. On Computational Structures Technologies 기계항공 공학부, 서울 대학교 김 승 조 2006, 11, 21 Supercomputing Korea 2006 ASTL Aero STructures Lab.

  2. Contents • Introduction • History of Finite Element Analysis • Representative Structural Analysis Codes • Large Scale Parallel Structural Analysis Code • Commercial FEM Packages • High-Performance FE Software, IPSAP • Research Trend of Virtual Design and Development • Conclusion

  3. Introduction • Computers have been widely used in structural engineering for: • Structural analysis • Computer-aided design and drafting (CADD) • Report preparation • Typical computer usage by an engineer: • Word-processing • Preparation of tender documents and engineering drawings • Small and intermediate computations • Analysis of structures • Design work • Data reduction and storage • Software development • Email • Etc.

  4. Introduction of Structural Analysis • Computational Structural Analysis : The use of computerized methods to predict the response, performance, failure and service life of structures and materials under various types of loading conditions • The role of Computational Structural Analysis • Allow the simulation of the behavior complex systems beyond the reach of analytic theory. • Provide detailed design information in a timely fashion. • Enhance our understanding of engineering systems by expanding our ability to predict their behavior. • Provide the ability to perform multidisciplinary design optimization. • Increase competitiveness and lower design/production costs.

  5. Introduction of Structural Analysis • 구조해석은 흔히들 생각하는 다리와 건물의 구조를 해석하는 토목공학분야뿐만 아니라 항공우주공학, 기계공학, 선박해양공학, 전자공학 등의 다양한 분야에서 기계적 요소들로 이루어진 구조물의 해석까지 포함 • 구조해석에서 유한요소 해석법(FEM:Finite Element Method)이 가장 보편적으로 사용되는 방법.

  6. Introduction of Structural Analysis • Current Market for CAE Software • Growth of CAE on industrial field • Especially, structural analysis has largest percentage(50%) of it. • This grow up over time going. In Korea, CAE market in 2005 grew 16% larger than that in 2004. Korea market share of CAE in 2004 (45 million $)CAD & Graphics OS % of automotives SC2005 (Top500), ‘Top20Auto Survey of HPC Installations in the Automotive’ the expectation of structural analysis software market

  7. Introduction of Structural Analysis History of Finite Element Analysis • Matrix method : Martin(1966), Meek(1971), Wilson(1960) • Terminology of Finite Element: Clough(1960) • Extended to all kinds of problems described as variational formulation : Zienkiewicz • Development of efficient finite elements, nonlinear and dynamic analysis : Oden, Bathe, Huges, Zienkiewicz, Belytschko, Crisfield et al • Commercial FEA packages : NASTRAN(1963), ABAQUS(1978), ANSYS(1970) • Related Industry : Manufacturing/Machinery, Automotives, Rail/Transportation, Aerospace/Defense, Consumer/Electronics Products, Medical/Biomechanics, Rubber/Sealing

  8. Introduction of Structural Analysis • Iterative method for sparse system • Iterative computations of matrix-vector operations • Jacobi algorithm, Gauss-Seidel algorithm, Conjugate Gradient Method, DDM(FETI), etc. • Converging speed affected by matrix condition • Operation count can not be estimated beforehand • Easy to parallelize efficiently • Direct method for sparse system • Based on Gauss elimination (LU factorization) • Operation counts determined by matrix size and non-zero pattern (mesh connectivity) • Operation count can be estimated beforehand • Band, skyline, frontal, multifrontal solver, etc. • Numerical robustness, Multiple RHS • Difficult to parallelize efficiently

  9. Introduction of Structural Analysis • 세계적 최신 전산 해석 프로그램의 개발 및 적용 사례 • EU • Dassault사 Falcon 7x • AirBus 사 가상구조시험 • 미국 • 각종 유명 상용코드 독점 • SALINAS 프로젝트 • 일본 • Adventure 프로젝트 • GeoFEM

  10. Large Scale Parallel Structural Analysis Code • SALINAS project - USA • 미국 에너지성의 ASCI 프로젝트의 일환 • Developed by Sandia National Laboratory in 1999 • 1~10억 자유도를 필요로 하는 매우 복잡한 구조물의 응력, 진동, 과도응답 유한요소 모델에 대한 확장성이 강한 계산 도구의 제공을 목적 • Implicit Solver를 기반으로 하여 수천개 이상의 프로세서로 구성된 ASCI 시스템에서 활용 • DDM에 기반을 둔 Multigrid 알고리듬과 coarse auxiliary 알고리듬과 같은 Multilievel iterative scheme을 참고한 FETI-DP 알고리듬을 이용 • Scalability를 중시하여 1,000여개 계산 노드를 가지는 ASCI Red, white등의 시스템에서 순환적으로 운용

  11. Large Scale Parallel Structural Analysis Code • ADVENTURE Project - JAPAN • ADVanced ENgineering analysis Tool for Ultra large REal world • Development of Computational Mechanics System for Large Scale Analysis and Design • 1997 ~ 2002 • 목표 : 슈퍼 컴퓨터(MPP, PC Cluster)로 천만~일억 자유도를 가지는 임의의 모델 형상을 1시간~하루 정도의 시간으로 해석 가능 • 약 20여개의 pre-processing, post-processing 모듈을 구성 Pantheon Model(1.5M DOF)Solid Analysis Fluid Analysis

  12. Large Scale Parallel Structural Analysis Code • GeoFEM - JAPAN • Parallel FE Solid Earth Simulator • 1997 ~ 2003 • Localized operation & optimum data structures for massively parallel computation • Pluggable design • Platform : linear solver, I/O, visualization GeoFEM Platform Geodynamo process and fluid dynamics in the Earth’s outer core A test dataset on the ES with 5,886,640 unstructured elements Modeling of Philippine Sea plate boundary

  13. Commercial FEA Packages FE model vibration analysis • MSC NASTRAN • Developed by NASA as analysis tools for the structural analysis of spacecraft. (1963) and managed by MSC • Through 40 years of R&D, MSC/NASTRAN has been regarded as a standard analysis system in most area of industry. • Capable of linear static analysis, buckling analysis, vibration and thermal analysis. • Sparse matrix solver, Automated Component Modal Synthesis • Analysis results of aerospace structural parts are used as the certification of quality. • Certificated by FAA (USA) stress analysis nonlinear analysis < Structural analysis of VAN > Stress analysis of Car Bumper Turbine blade thermal stress analysis

  14. Commercial FEA Packages - Parallel Performance • MSC NASTRAN 출처 : www.mscsoftware.com , Ver. : 2004

  15. Commercial FEA Packages • ABAQUS • Developed by Hibbitt, Karlsson & Sorrensen in 1978 • In 2005, Dassault Systems(CATIA) acquired ABAQUS : SIMULIA • Linear and nonlinear structural analysis • Multifrontal solver, Block Lanczos eigen solver • Vectorized Explicit Time Integration for the dynamic analysis • Conduction, convection and heat transfer problem • Analysis of offshore structure • wave-induced inertial force, buoyant force and drag of fluid Stress analysis of airplane engine

  16. Commercial FEA Packages - Parallel Performance • ABAQUS E1: Car crash (274,632 elements) E2: Cell phone drop (45,785 elements) E3: Sheet forming (34,540 elements) E4: Projectile penetration (237,100 elements) 단위 :sec 출처 : www.abaqus.com , Abaqus ver. 6.6

  17. Commercial FEA Packages • Developed by John Swanson in 1970 • Utilized in conceptual design of the product and the manufacturing process • Provides general graphic utilities • Various analysis utilities • Basic structural analysis, CFD, Electro-magnetic analysis • Thermal stress, Acoustic analysis, Piezoelectric analysis • Multi-physics • AI*NASTRAN solver • Wavefrontal solver based on sparse matrix solver, • Substructuring analysis option for large structures • Block Lanczos eigen solver • Distributed Pre-conditioned Conjugate Gradient (DPCG) Distributed Jacobi Conjugate Gradient (DJCG) Engine analysis Infrared camera analysis

  18. Commercial FEA Packages - Parallel Module • The solvers are: • Distributed Domain Solver (DDS) • Distributed Jacobi Conjugate Gradient (DJCG) • Algebraic Multigrid (AMG) • Distributed Pre-conditioned Conjugate Gradient (DPCG) 출처 : www.ansys.com , ANSYS ver. 10.0

  19. Commercial FEM Packages • Comments • Most of commercial FEA packages use direct method : multifrontal (ABAQUS), sparse matrix solver (NASTRAN), Sparse Matrix, Frontal Solver(ANSYS) • Commercial packages need to guarantee the end users the practicality and reliability • Practicing engineers do feel comfortable with the direct method • However, the parallel performance of these packages are very poor. • ANSYS is trying to add the iterative solver optionally in new version of the code : an alternative method to increase the parallel performance.

  20. STRESS ANALYSIS High-Performance Parallel Software IPSAP High-Performance Hardware (Supercomputer, Clusters, GRID) VIBRATION ANALYSIS Grand Challenge Applications (Large Scale) IPSAP/ EXPLICIT High-Performance FE Software, IPSAP • IPSAP : Internet Parallel Structural Analysis Program • General purpose FEA program • Generality, Single CPU & Parallel Performance • Written by C and C++ • Performance : Faster than commercial softwares like MSC/Nastran and ABAQUS, etc

  21. High-Performance FE Software, IPSAP • IPSAP : Standard • Linear Static, Vibration Analysis : open on WEB • Nonlinear, Thermal Analysis : under development • FE Model : 8 node solid, 4 node solid, 4 node plane, 3 node plane, 2 node beam, Rigid body element • Nodal force, Acceleration, Temperature load • Multifrontal Linear Equation solver, Lanczos Eigenvalue extractor • Library : BLAS(Basic Linear Algebra Subroutine), LAPACK(Linear Algebra Package), METIS • MPP Parallelization

  22. High-Performance FE Software, IPSAP • IPSAP : Explicit • Explicit Time Integration, Automatic Time Step Control • Elastic, Orthotropic, Elastoplastic, Johnson-Cook • EOS (Equation of State) : Polynomial Model, JWL, Grüneisen • FE Model : 8 node Hexahedron, 4 node BLT Shell 1 point integration with Hourglass Control • Object Stress Update : Jaumann rate stress update • Artificial Bulk Viscosity • Contact Treatment : • Contact Search : Bucket Sorting • Master-Slave Algorithm, Penalty Method • Single Surface Contact (or Self Contact) • Element Erosion and Automatic Exterior contact surface update • MPP Parallelization

  23. IPSAP – Multifrontal Solver • Procedure for modified multifrontal solver Step1-2 • Using data structure of Element connectivity Step3-4 • Element Computation is smeared in this step • computed using the memory hierarchy • Optimized for finite element method Step1. Domain partitioning Step2. Symbolic factorization Step3. Numerical factorization Step4. Triangular solve

  24. IPSAP – Multifrontal Solver • Domain partitioning with graph partitioning • Converting the FEM mesh into graph data • Various graph building scheme • WEM (Weighted Edge Mapping) • WEVM (Weighted Edge and Vertex Mapping) • I-WEVM (Iterative Weighted Edge and Vertex Mapping) • Dividing the graph into k parts • Graph regularity checking • Exact spectral algorithm implemented • State-of-the-art techniques incorporated • METIS 4.0 • ParMETIS 3.1

  25. IPSAP – Multifrontal Solver • Symbolic factorization • elimination ordering from partitioned graph(mesh) • front matrix size estimation • Core memory usage is known before real factorization • Floating point operation count is estimated 1 2 5 6 1 2 3 7 3 4 7 8 4 6 5 9 10 13 14 11 12 15 16 Domain Order Factorization Order

  26. IPSAP – Multifrontal Solver • Numerical factorization • Serial stage : domains are merged with factorized domains • Automatic Matrix assembly • Operations are performed on dense frontal matrices • Hierarchical memory architecture of modern computers can be fully utilized 7 3 6 1 2 4 5 3 4 5 6 7 8 1 2 Elimination Tree

  27. IPSAP – Multifrontal Solver • Parallel Stage : Distributed memory parallelization • Merging makes the distributed frontal matrix • Factorization is performed with distributed matrix Proc 0 Proc 1 Proc 0,1 Proc 0,1,2,3 Factorization Factorization Proc 2 Proc 3 Proc 2,3 • 2 dimensional processor map is used p0 p2 p0 p2 p1 p3 p1 p3

  28. IPSAP – Multifrontal Solver • Parallel Stage : Distributed memory parallelization • Block cyclic distribution with 2 dimensional processor map P 0 P 2 P 1 P 3 Block size is not fixed p0 p2 Block Cyclic p1 p3 • Owner of sub-matrix is dependent on ordering index • Matrix re-distribution is performed by one-to-one communication • pBLAS & SCALAPACK cannot handle variable block size

  29. IPSAP – Block-Lanczos Eigensolver • Large-scale eigen analysis of 3D complex structures • Finite element method • Prediction of dynamic stability of structures • Up to millions of DOF (Degree of Freedom) • Huge-size computing/resources required • Repetition of linear equation solving • Feasible algorithm : Block Lanczos Eigenvalue Solver Equipped with Efficient Direct Equation Solver

  30. IPSAP – Block-Lanczos Eigensolver • Block Lanczos algorithm with multifrontal solver • Use of Lanczos method with shift and inverting technique for eigen solution • Most of operations in Lanczos steps are required in solution procedure for (K - M)-1 and M inner product • Efficient direct equation solver is needed for the Lanczos process • Multiple RHS (Right Hand Side ) operation is needed for the block Lanczos process (K -lM) x= 0 (K -M)-1 Mx=x = shift , =(shifted eigenvalue) -1

  31. IPSAP – Block-Lanczos Eigensolver Block Lanczos Iteration with MFS Effetive Mass Multiplication Multifrontal Solver Uj = MVj (K-  M)Wj = Uj W’j = Wj - Vj-1 BTj-1 Cj = VTj MW’j W’’j = W’j - Vj Cj GEQRF in PLASC W’’j = Vj+1 Bj : QR factorization

  32. IPSAP – Block-Lanczos Eigensolver Block version of CGS2 : classical Gram-Schmidt with reorthogonalization

  33. Subroutine ContactForce Subroutine InternalForce IPSAP – IPSAP/Explicit • Contact/Impact Analysis • Nonlinear explicit time integration • Contact search ISSUE (1) Increasing Efficiency of Contact Force Vector Calculation (2) Increasing Efficiency of Internal Force Vector Calculation Subroutine ContactForce Subroutine InternalForce

  34. 1 2 3 4 5 6 7 8 9 IPSAP – IPSAP/Explicit • Parallelization of Internal Force 1. Each processor computes internal forces of own nodes 2. Commuication and addition for interface nodes (Swap,Add) - unstructured efficient communication is implemented

  35. IPSAP – IPSAP/Explicit • Parallelization of Contact Force Define 3D box Slave node update Communication of slave nodes’ coordinates Contact Force computed in each processor Communication of Contact Force

  36. Rack-20 Node & Multi Trunking (4 GB Uplink) -Nortel 380-24T (Giga) & Intel 24T (Fast) Gigabit Ethernet- Nortel 5510-48T Fast ethernet- Intel 24T Local Gigabit Local Fast Rack ( 20 Node ) NFS & Gatekeeper External Network Performance of IPSAP • Computing Environment • PEGASUS System

  37. IPSAP Stress Analysis Serial performance comparison with NASTRAN 70.7 and ABAQUS 6.3 32x32x32 hexagonal elements (DOFs = 107,811) Performance of IPSAP 2.1 Gflops

  38. IPSAP Stress Analysis Serial performance comparison with MSC/NASTRAN 2004 and ABAQUS6.4 PC : Pentium-4(northwood), 3GHz, 1G memory Performance of IPSAP 2.6 Gflops

  39. Performance of IPSAP • IPSAP Vibration Analysis Serial performance comparison with MSC/NASTRAN 2004 and ABAQUS 6.4 • PC : Pentrium-4, 3GHz, 1G memory

  40. Performance of IPSAP • IPSAP Vibration Analysis : Cycloidal Blade Model • Pentium IV 3.2GHz, 2.0 GB RAM, Windows XP • Elapsed time (30 modes extracted) • IPSAP : 2855 sec, NASTRAN2004 : 3251 sec, ABAQUS 6.4 : 4870 sec NASTRAN ABAQUS IPSAP 48.566Hz (1st mode) 175.07Hz (3rd mode) 48.015Hz(1st mode) 169.29Hz (3rd mode) 47.854Hz (1st mode) 167.09Hz (3rd mode)

  41. Performance of IPSAP • IPSAP Stress Analysis • Scalability test in Pegasus system • 2D Mesh topology Specification of data for 2-D scalability test and results

  42. Performance of IPSAP • IPSAP Stress Analysis • Scalability test in Pegasus system • 3D Mesh topology Specification of data for 3-D scalability test and results

  43. Performance of IPSAP • IPSAP Stress Analysis • Scalability test • Computing Environment : IBM p690+ (power 4 1.7GHz) • 3D Mesh Topology

  44. Performance of IPSAP • IPSAP Stress Analysis • Parallel performance comparison with ABAQUS • IBM Power4 1.3GHz system

  45. Performance of IPSAP • IPSAP Vibration Analysis : Simple wing structure • Parallelperformance comparison with NASTRAN • PEGASUS Cluster • Distributed memory parallel • 4 node shell elements • 0.5 million DOF Solution time only

  46. Performance of IPSAP • IPSAP/Explicit • Taylor Impact Test • Comparison with LS-DYNA 970 • PEGASUS Cluster • Distributed Memory Parallel • 10.0 Million DOF

  47. Performance of IPSAP IPSAP/Explicit Oblique Impact of Metal Sphere PEGASUS Cluster Distributed Memory Parallel Sphere : 21,600 elements Plate : 7,488 elements Total : 29,088 elements 33,329 nodes 99,987 DOF Mild Steel Sphere : diameter : 6.35mm mass : 1.04g Mild Steel Plate : 50mm x 40mm thickness : 1.5 mm Impact Velocity : 610m/s@60degree Termination Time : 50 micro seconds Material Model : Johnson-Cook

  48. released IPSAP • 홈페이지 : http://ipsap.snu.ac.kr • Modules included : Stress analysis, vibration analysis • Elements : solid, shell, beam • Downloadable IPSAP executables • Windows, Linux, OS-X • Serial, parallel version

  49. Virtual Design Development • AIRBUS – Aircraft Virtual Structural Testing • 항공기 전기체 가상구조시험 에어버스 가상구조시험 체계 계획(2005년 8월) 가상구조시험의 멀티 스케일 해석 접근

  50. Virtual Design Development • Boeing • “Virtual Mockup facilities the exploration of a larger design solution space, at the same time that it helps catch problems before they become very expensive. This enabled Boeing’s 777 program to achieve unprecedented levels of rework reduction, product quality and customer satisfaction.” William A. McNeely Senior Principal Scientist Boeing Information and Support Services Boeing 777 Virtual Reality Application

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