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  • Introduction

    An introduction to mesh generationPart I : Introduction

    Jean-Franois Remacle

    Department of Civil Engineering,Universit catholique de Louvain, Belgium

    Jean-Franois Remacle Mesh Generation

  • Introduction

    Jean-Franois Remacle Mesh Generation

  • Introduction

    Outline

    Jean-Franois Remacle Mesh Generation

  • Introduction

    Scientific computing

    Historically, the principal approaches in engineering design areExperimental and empirical techniquesAnalytical methods

    Recently, those traditional tools have been completed by computer aideddesign.

    Jean-Franois Remacle Mesh Generation

  • Introduction

    Scientific computing

    There are several specialized tools that can be classified in the domain ofscientific computing

    The art of modeling, i.e. finding the relevant set of equations thatdescribe a given process,Geometrical modeling and mesh generation tools,Discretization techniques, numerical methods,Numerical linear algebra, resolution of large systems,Post-processing techniques and visualization of simulation datas.

    Scientific computing consist in the numerical simulation of variousprocesses: physical, chemical, biological, financial... It enables

    To span a wide range of parameters,To model very complex geometries,To couple multiple phenomenon together (multiphisics).

    Jean-Franois Remacle Mesh Generation

  • Introduction

    Why scientific computing ?

    Scientific computing is now considered as a common tool in engineeringdesign offices because of its high benefit/cost ratio. Moreover, scientificcomputing enables to

    Enlarge the range of parameters that can be used in a laboratory,Is not limitated to empirrical relations or analytical tools,Enables to understand the physics of phenomenon for which it isimpossible to do any experience (climate, quantum mechanics,astrophysics...)

    Moreover, scientific computing heavily relies on computer power for whichthe price per flop is decreasing rapidely.

    Yet, scientific computing does not make other methods obsoletes (yet) andusually requires deep knownledge in the processes that are modeled (noblack box).

    Jean-Franois Remacle Mesh Generation

  • Introduction

    Benefits for engineering

    Scientific computing technologies provide reliable tools forEnhancing the quality of products,Lowering the cost of development,Accelerate the design cycle,Enabling an efficent control on fabrication processes,Predicting damages and their consequances (damage tolerentstructures)....

    Jean-Franois Remacle Mesh Generation

  • Introduction

    Historical Background (1940s)

    1941 A. Hrennikoff uses framework method(Journal of Applied Mechanics, Solutionof Problems in Elasticity by theFramework Method).

    1943Whirlwind program simulating aircraftperformance developed at MIT from1943 to 1950.Richard Courant studies St. Venanttorsion problem using FE concepts:proposed breaking a continuum probleminto triangular regions replacing the fieldswith piecewise approximations within thetriangular regions.

    Jean-Franois Remacle Mesh Generation

  • Introduction

    Historical Background (1940s)

    1945 Electronic digital computer gainsexposure.

    1946 Analysis Lab at Caltech builds analogcomputer to solve problems inengineering mechanics.

    1947 W. Prager and J. L. Synge develophypercircle method, in connection withclassical elasticity theory (Q. AppliedMath, Approximation in Elasticity Basedon the Concept of Function Space).

    1948 Transistor invented (Jack S. Kilby, MIT,Nobel Price of Physics, 2000).

    Jean-Franois Remacle Mesh Generation

  • Introduction

    Historical Background (1950s)

    1950 Computer size and speed increase, makingit possible to handle FEA, available onlyto large aircraft.

    1952CEA (Computer Engineering Associates)used FE modeling with a couple ofhundred degrees of freedom.B. Langefors recognizes global behaviorthrough assimilation of local behavior (J.Aeronautical Science, Analysis of ElasticStructures by Matrix Transformation withSpecial Regard to Semi-monologueStructures).

    1953 N. J. Turner at Boeings StructuralDynamics Unit tests plane stress platemodels, which was published in 1956(independent of Argyris).

    Jean-Franois Remacle Mesh Generation

  • Introduction

    Historical Background (1950s)

    1954 John H. Argyris (University of Stuttgart inGermany) publishes series on linearstructural analysis with solutions suitablefor digital computation.

    1956 N. J. Turner, Ray W. Clough, HaroldClifford Martin, and LeRoy J. Topp paperand on direct stiffness method fordetermining FE properties heralded asorigin of FEM.

    1957 Ray W. Clough develops Matrix AlgebraProgram for IBM 701 (1951) and 704(1954) that solves linear equations.

    1959 J. Greenstadts work allows for irregularlyshaped cell meshes (IBM, J. ResearchDevelopment, On the Reduction ofContinuous Problems to Discrete Form).

    Jean-Franois Remacle Mesh Generation

  • Introduction

    Historical Background (1960s)

    1960R. J. Melosh addresses convergence of GEM and variational method(e.g., Ritz-Galerkin method).Ray W. Clough coins FE term (ASCE paper The Finite Element Methodin Plane Stress Analysis).John H. Argyris with Sydney Kelsey publishes in Aircraft EngineeringJournal (London), from 1954-55 research.

    1962 K. O. Friedrichs uses the Dirichlet variation principle.1963 SADSAM (Structural Analysis by Digital Simulation of Analog

    Methods) developed by Richard MacNeal and Robert Schwendler,forerunner of MSC/NASTRAN.

    1964 IBM 7094, Univac 1107, etc., used for American aircraft FE programs.

    Jean-Franois Remacle Mesh Generation

  • Introduction

    Historical Background (1960s)

    1965ASKA (automatic system for kinematics analysis) commercial softwareproduct based on Argyris work.Variational form develops, opening FEM to all fields of application; O.C. Zienkiewicz and Y. K. Cheung give it broader interpretation in article(Engineer, Finite Elements in the Solution of Field Problems).Wright-Patterson Air Force Base holds its first Conference on MatrixMethods in Structural Mechanics (AFFDL-TR-66-80) with 200 scientistsincluding early pioneers Turner, Clough and Argyris.Portable, desktop and microcomputers marketed.NASTRAN (NASA Structural Analysis Program) developed byMacNeal-Schwendler Corp., as early effort to consolidate structuralmechanics into a single program (proprietary version announced in1971).

    1967M. J. L. Hussey applies theory of cyclical symmetry to FEM (ASCE,Journal of Structural Division)Two-dimensional analysis of the Concorde wing with approximately1,000 degrees of freedom was made on an analog computer in France.

    Jean-Franois Remacle Mesh Generation

  • Introduction

    Historical Background (1970s)

    1970ANSYS (from ANSYS, Inc., formerly SwansonAnalysis Systems Inc.) grew out of nuclearindustry.Automotive industry begins to use FEM.FE software still limited to mainframecomputers, with transition from pre andpost-processing mostly being done by hand tointeractive pre-and post-processing programsbecoming generally available.First public release of NASTRAN. NASTRANSystems Management Office est. at NASALangley Research Center. Dr. J. P. Raney, Head.

    1971INF-SUP condition identified and proved (alsocalled Babuska-Brezzi condition).First NASTRAN Colloquim held at NASALangley Research Center. Over 300 attendees.Papers presented covering many applications ofNASTRAN.

    Jean-Franois Remacle Mesh Generation

  • Introduction

    Historical Background (1970s)

    19721,004 papers published during year.First version of MARC program introduced(general-purpose nonlinear FEA program),developed by Brown University researchers.

    1974 Prof. R. D. Cook writes textbook for Universityof Wisconsin FE class (Concepts andApplications in Finite Element Analysis, Wiley).

    1975 Interactive FE programs on small computersleads to rapid growth of CAD systems.

    1976 CRAY supercomputer developed, which canhandle flow analysis.

    Jean-Franois Remacle Mesh Generation

  • Introduction

    Historical Background (1980s)

    1980 Trends include electromagnetic applications(e.g., high-frequency power supplies), thermalanalysis, greater emphasis on model generation.

    1983 Fluid Dynamics introduces FIDAP for industrialfluid flow and heat and mass transfer.

    1989CFD (Computational Fluid Dynamics) and othernonstructural applications increase routine useof FE.Fluid flow analysis becomes more widespread,extending beyond work by large aerospacefirms, and turbulent flow analysis expected todevelop.

    Jean-Franois Remacle Mesh Generation

  • Introduction

    Mesh Generation

    Scope of the presentationHistory of mesh generation,Classification of meshes, definitions,Structured mesh generation techniques(elliptic, hyperbolic),Unstructured techniques (delaunay andfrontal),Hybrid meshes,Surface mesh generation,Data structures,Adaptive meshes.

    Jean-Franois Remacle Mesh Generation

  • Introduction

    History of Mesh Generation

    In early 70s, the Finite Element Method(FEM) was starting to become a majoractor in engineering design officesCAD systems are the basis of engineeringdesign. They represent parts withinmanufacturing tolerancesThe FEM requires an alternativerepresentation of the partsVery quickly, it was clear that some kindof automatization was required in meshgeneration procedures.

    Jean-Franois Remacle Mesh Generation

  • Introduction

    History of Mesh Generation

    The plane-2D mesh generation problemwas solved withine 5 years.Planty of robustmethods/codes/algorithms have beenproduced. Triangular and quadran