Course in. FEM ANSYS Classic

Transcription

1 Course in Introduction

2 Introduction Presentation Anders Schmidt Kristensen M.Sc. in Mechanical Eng. from Aalborg University in 1993 Ph.D. in Mechanical Eng. from Aalborg University in 1997 Consultant for PTC Denmark implementation of Pro/ENGINEER 1998 to pt. Associate Prof. at Aalborg University Esbjerg Introduction 2

3 Introduction The course is conducted the following way: minutes lecture followed by minutes exercise (including a break) Questions are allowed at any time Introduction 3

4 References [ANSYS] ANSYS 10.0 Documentation (installed with ANSYS): Basic Analysis Procedures Advanced Analysis Techniques Modeling and Meshing Guide Structural Analysis Guide Thermal Analysis Guide APDL Programmer s Guide ANSYS Tutorials [Cook] Cook, R. D.; Concepts and applications of finite element analysis, John Wiley & Sons [Burnett] Burnett, D. S.; Finite element analysis: From concepts to application, Addison-Wesley [Kildegaard] Kildegaard, A.; Elasticitetsteori, Aalborg Universitet Introduction 4

5 FEM - ANSYS Classic Lecture 1 - Introduction: Introduction to FEM ANSYS Basics Analysis phases Geometric modeling The first model: Beam model Lecture 2 - Preprocessor: Geometric modeling Specification of Element type, Real Constants, Material, Mesh Frame systems Truss systems Element tables Lecture 3 - Loads: Boundary conditions/constraints/supports Loads Mesh attributes, meshing Sections Lecture 4 2D plane models : 2D Plane Solid systems Geometric modeling Postprocessing Lecture 5 Analysis types: Analysis types Modal analysis Buckling analysis Introduction 5

6 FEM - ANSYS Workbench/CAD Lecture 6 3D Solids: 3D solid models Booleans Meshing issues Lecture 7 3D Modeling: Operate Import CAD Advanced topics Lecture 8 Analysis types: Analysis types Postprocessing TimeHistProc Lecture 9 Workbench basics: Workbench basics Geometric modeling Lecture 10 Workbench analysis: Workbench analysis types Introduction 6

7 Overview CAD - Computer Aided Design AutoCAD, Bentley MicroStation, CadKey CAD - Solid Modeling Pro/ENGINEER, Inventor, IDEAS, CATIA, UGS, Solid Works FEM/FEA - Finite Element Method/Analysis ANSYS, ABAQUS, Algor, Altair, MscNastran, Cosmos CAE - Computer Aided Engineering Workbench, Design Space, Pro/Mechanica, CosmosWorks, Inventor/ANSYS BEM - Boundary Element Method Mesh-less systems CFD - Computational Fluid Dynamics ANSYS/Fluent, ANSYS/Flotran, ANSYS/CFX, CF-Design, Altair Multi-scale systems Optimization sizing, shape and topology Introduction 7

8 Introduction to Finite Element Analysis What is Finite Element Analysis? Advantages Disadvantages How to avoid pitfalls History FEM - Resources Examples Introduction 8

9 What is Finite Element Analysis? The FEM is a computer-aided mathematical technique for obtaining approximate numerical solutions to the abstract equations of calculus that predict the response of physical systems subjected to external influences [Burnett] Introduction 9

10 What is Finite Element Analysis? Each point have an infinite number of deformation state variables, i.e. degrees of freedom (dof) Transformation Real model Continuum Each point have a finite number of deformation state variables (u,v), i.e. degrees of freedom Analysis model Discrete Introduction 10

11 What is Finite Element Analysis? Divide a continuum with infinitely degrees of freedom in to finite elements with a given number of degrees of freedom An element is geometrical defined by a number of nodes in which the elements are connected. The directions a node can move in is termed degrees of freedom (dof) Introduction 11

12 What is Finite Element Analysis? Following conditions must always be satisfied Equilibrium conditions Compatibility conditions Constitutive conditions Boundary conditions Introduction 12

13 What is Finite Element Analysis? Most FEA systems are displacement based, i.e. an approximate displacement field is established u(x,y) = a1 + a2 x + a3 y Using a deformation based method yield one unique kinematic determined system to be determined Introduction 13

14 What is Finite Element Analysis? The deformation method yield the FEM characteristic system of equations: Unknown displacement vector [K]{D} = {R} Stiffness matrix Load vector This system of equations is solved for {D} by, e.g. Gaussian elimination Note on matrix algebra is found here Introduction 14

15 What is Finite Element Analysis? Formulation techniques to determine the stiffness matrix [K] Direct method Variational methods, i.e. principle of stationary potential energy Weighted Residual methods, e.g. the Galerkin formulation Introduction 15

16 What is Finite Element Analysis? The unknown displacements (can be any field variable, e.g. temperature) {D} = {u1, v1, u2, v2 } T in the element nodes (nodal values) are determined from Unknown displacement vector [K]{D} = {R} v3 u3 Stiffness matrix Displacement field variables: In 2D: (u,v) In 3D: (u,v,w) Load vector y v1 x ndof = 6 v2 u2 u1 Introduction 16

17 What is Finite Element Analysis? It is assumed that displacements within an element can be interpolated from known nodal values ui=? u2 u N1 u1 + N2 u2 ui u2 u1 u1 x1 xi x2 N1 = (1 x/l) N2 = x/l x1 xi x2 Linear case Introduction 17

18 What is Finite Element Analysis? The element stiffness matrix for a beam element with 2 nodes and 2 dof at each node [Cook], see also note: ndof = 4 Found by the Direct Method Unknown displacement vector ndof x 1 [K]{D} = {R} {D} = [K] -1 {R} Known stiffness matrix ndof x ndof Known load vector ndof x 1 Introduction 18

19 Advantages Irregular Boundaries General Loads Different Materials Boundary Conditions Variable Element Size Easy Modification Dynamics Nonlinear Problems (Geometric and/or Material) Introduction 19

20 Disadvantages NB: Always document assumptions! An approximate solution An element dependent solution Shape quality of elements affect the solution, e.g. poorly shaped elements (irregular shapes) reduce accuracy of the FE solution Element density affect the solution, i.e. the element size should be adjusted to capture gradients Example: plate with a circular hole Errors in input data Introduction 20

21 Disadvantages [Cook] Introduction 21

22 Disadvantages [Cook] Introduction 22

23 How to avoid pitfalls Carry out: Hand calculations (Navier, Airy, Timoshenko ) Norm based calculations (Euro-Code, EN, API ) Experiments (strain-gauge, accelerometer ) Evaluate the kinematic behaviour (deformations) Introduction 23

24 History A. Hrennikoff [1941] - Lattice of 1D bars McHenry [1943] - Model 3D solids R. Courant [1943] - Variational form Levy [1947, 1953] - Flexibility & Stiffness M. J. Turner [1953] - FEM computations on a wing Boeing [1950's] Engineer's at Boeing apply FEM to delta wings Argryis and Kelsey [1954] - Energy Prin. for Matrix Methods Turner, Clough, Martin and Topp [1956] - 2D elements R. W. Clough [1960] Coins the term Finite Elements Introduction 24

25 History Mathematical validity of method established - applied to non-structural problems 1960's - First general purpose FEA code developed 1970's - Non-linear solvers developed 1980's - Graphical pre-/postprocessors are developed 1990's - FEM tools integrated in CAD software Introduction 25

26 FEM - Resources ALGOR ANSYS COSMOS/M STARDYNE/FEMAP MSC/NASTRAN SAP90/2000 ADINA NISA GT Strudl ABAQUS Plaxis Matlab based: CalFem FemLab CAE products: Pro/ENGINEER Pro/FEA Pro/MECHANICA Cosmos/Works Inventor/ANSYS IDEAS Resources Introduction 26

27 Introduction to ANSYS What is ANSYS Facilities in ANSYS Interfacing with ANSYS Common terms Introduction 27

28 What is ANSYS ANSYS finite element analysis software enables engineers to perform the following tasks: Build computer models or transfer CAD models of structures, products, components, or systems. Apply operating loads or other design performance conditions. Study physical responses, such as stress levels, temperature distributions, or electromagnetic fields. Optimize a design early in the development process to reduce production costs. Do prototype testing in environments where it otherwise would be undesirable or impossible (for example, biomedical applications). Introduction 28

29 Facilities in ANSYS Structural Linear Structural Nonlinear Structural Contact/Common Boundaries Structural Dynamic Structural Buckling Thermal Analysis CFD Analysis Electromagnetic - Low Frequency Electromagnetics - High Frequency Field and Coupled-Field Analysis Introduction 29

30 Facilities in ANSYS Solvers Iterative Sparse Frontal Explicit Preprocessing Postprocessing General Features Introduction 30

31 Facilities in ANSYS.. ANSYS Commands reference ANSYS Element reference.. Basic Analysis Procedures Advanced Analysis Techniques.. Structural Analysis Guide.. ANSYS Tutorials Introduction 31

32 Facilities in ANSYS During an analysis, you may want to modify or delete commands entered since your last SAVE or RESUME. You can access the following file operations from the session editor dialog: OK: Enters the series of operations displayed in the window below. You will use this option to input the command string after you have modified it. Save: Saves the command string displayed in the window below to a separate file. ANSYS names the file Jobnam000.cmds, with each subsequent save operation incrementing the filename by one digit. You can use the /INPUT command to reenter the saved file. Cancel: Dismisses this window and returns to your analysis. Help: Displays the command reference for the UNDO command. The Session Editor is available in interactive (GUI) mode only. Introduction 32

33 Facilities in ANSYS Introduction 33

34 Interfacing with ANSYS Matlab, Excel CAD Pro/ENGINEER IGES Log-file editing Application Programming Interface (API) Introduction 34

35 Interfacing with ANSYS Introduction 35

36 Common terms Processor Function GUI Path Command PREP7 Build the model (geometry, materials, etc.) Main Menu> Preprocessor /PREP7 SOLUTION Apply loads and obtain the finite element solution Main Menu> Solution /SOLU POST1 Review results over the entire model at specific time points Main Menu> General Postproc /POST1 POST26 Review results at specific points in the model as a function of time Main Menu> TimeHist Postpro /POST26 OPT Improve an initial design Main Menu> Design Opt /OPT PDS AUX2 AUX12 Quantify the effect of scatter and uncertainties associated with input variables of a finite element analysis on the results of the analysis Dump binary files in readable form Calculate radiation view factors and generate a radiation matrix for a thermal analysis Main Menu> Prob Design Utility Menu> File> List> Binary Fi les Utility Menu> List> Files> Binary F iles Main Menu> Radiation Matrix /PDS /AUX2 /AUX12 AUX15 Translate files from a CAD or FEA program Utility Menu> File> Import /AUX15 RUNSTAT Predict CPU time, wavefront requirements, etc. for an analysis Main Menu> Run-Time Stats /RUNST Introduction 36

37 Basics Launching of ANSYS Graphical User Interface (GUI) Menus, dialogs and toolbars Working area Preferences Files used by ANSYS ANSYS Menus ANSYS File menu ANSYS PlotCtrls menu Units Undo Hints Introduction 37

38 Analysis phases Build the model. Apply loads and obtain the solution. Review the results. PREPROCESSOR SOLUTION POSTPROCESSOR Introduction 38

39 Analysis phases Element Type select appropiate element type to model the structural response/behaviour most accurately. Real Constants properties depending on the element type, e.g. cross-sectional properties, area, area moment of inertia Material Props material properties, e.g. modulus of elasticity E and Poisson s ratio n Sections cross-section definition Modeling define the geometry of the structure - it is essential to make some modeling considerations in this phase Meshing divide the geometry of the structure into elements take care of element distribution/density Introduction 39

40 Analysis phases Analysis Type specify the character of the problem Define Loads apply loads to the element model Solve run the solution process, e.g. for linear static systems solve (Gaussian elimination) for the unknown displacements: Unknown displacement vector ndof x 1 [K]{D} = {R} {D} = [K] -1 {R} The global stiffness matrix [K]: ndof = total number of nodes x number degrees of freedom per node Known global stiffness matrix ndof x ndof Known load vector ndof x 1 Introduction 40

41 Geometric modeling Create geometrical entities Operate perform Boolean operations Move / Modify move or modify geometrical entities Copy copy geometrical entities Delete geometrical entities Update Geom update the geometry in relation to for example buckling analysis Introduction 41

42 Modeling - Create The hierarchy of modeling entities is as listed below: Elements (and Element Loads) Nodes (and Nodal Loads) Volumes (and Solid-Model Body Loads) Areas (and Solid-Model Surface Loads) Lines (and Solid-Model Line Loads) Keypoints (and Solid-Model Point Loads) Introduction 42

43 Examples - content Example0100 s: Link and/or beam models Example0200 s: Plane 2D models Example0300 s: Solid 3D models Example0400 s: Vibration/dynamic models Example0600 s: Thermal models Introduction 43

44 The first model Introduction 44