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Lecture #2 Analytical and Numerical Methods of Structural Analysis

Lecture #2 Analytical and Numerical Methods of Structural Analysis. FLOWCHART OF STRUCTURAL ANALYSIS. 2. FLOWCHART OF STRUCTURAL ANALYSIS. 3. FLOWCHART OF STRUCTURAL ANALYSIS. 4. FLOWCHART OF STRUCTURAL ANALYSIS. 5. METHODS OF STRUCTURAL ANALYSIS. 6.

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Lecture #2 Analytical and Numerical Methods of Structural Analysis

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  1. Lecture #2 Analytical and Numerical Methods of Structural Analysis

  2. FLOWCHART OF STRUCTURAL ANALYSIS 2

  3. FLOWCHART OF STRUCTURAL ANALYSIS 3

  4. FLOWCHART OF STRUCTURAL ANALYSIS 4

  5. FLOWCHART OF STRUCTURAL ANALYSIS 5

  6. METHODS OF STRUCTURAL ANALYSIS 6

  7. ANALYTICAL METHODS OF STRUCTURAL ANALYSIS • Widely used nowadays: • methods of Mechanics of Materials; • methods for statically indeterminate structures: • method of forces; • method of displacements; • beam theory for thin-walled structures; • method of reduction coefficients. • Rarely used nowadays (mostly due to the progress of numerical methods): • methods based on Calculus of Variations; • methods of Theory of Elasticity. 7

  8. EXAMPLE TO COMPARE ANALYTICAL AND NUMERICAL METHODS Aim: Design the steel bracket to minimize the self-weight displacement of the load. Given data: D2=80 mm; L2=500 mm; L1=200 mm; mload=0.5 kg. Objectives: D1, d1, d2. base L2, D2, d2 L1, D1, d1 load 8

  9. BASIC EQUATIONS OF SOLID MECHANICS 9

  10. BASIC EQUATIONS OF SOLID MECHANICS 10

  11. BASIC EQUATIONS OF SOLID MECHANICS 11

  12. BASIC EQUATIONS OF SOLID MECHANICS 12

  13. BASIC EQUATIONS OF SOLID MECHANICS From analytical point of view, every design model can be expressed as a set of three basic equations with corresponding boundary conditions. 13

  14. WAYS TO SOLVE A SOLID MECHANICSPROBLEM 14

  15. EXAMPLE TO COMPARE ANALYTICAL AND NUMERICAL METHODS • Analytical methods used: • Methods of Mechanics of Materials; • Mohr’s integral to calculate displacements. • Software used: • MathCAD V14.0 base L2, D2, d2 L1, D1, d1 load 15

  16. EXAMPLE TO COMPARE ANALYTICAL AND NUMERICAL METHODS 16

  17. EXAMPLE TO COMPARE ANALYTICAL AND NUMERICAL METHODS 17

  18. EXAMPLE TO COMPARE ANALYTICAL AND NUMERICAL METHODS 18

  19. EXAMPLE TO COMPARE ANALYTICAL AND NUMERICAL METHODS 19

  20. EXAMPLE TO COMPARE ANALYTICAL AND NUMERICAL METHODS 20

  21. EXAMPLE TO COMPARE ANALYTICAL AND NUMERICAL METHODS 21

  22. EXAMPLE TO COMPARE ANALYTICAL AND NUMERICAL METHODS 22

  23. EXAMPLE TO COMPARE ANALYTICAL AND NUMERICAL METHODS 23

  24. EXAMPLE TO COMPARE ANALYTICAL AND NUMERICAL METHODS 24

  25. EXAMPLE TO COMPARE ANALYTICAL AND NUMERICAL METHODS 25

  26. METHODS OF STRUCTURAL ANALYSIS 26

  27. NUMERICAL METHODS OF STRUCTURAL ANALYSIS Most widely used nowadays is Finite Element Method (FEM). The structural analysis using FEM is called finite element analysis (FEA). Generally, FEM is just a method to solve differential equations. The physical background of FEM is the same as in analytical methods. 27

  28. FINITE ELEMENT METHOD The smooth field of stresses is calculated using the combination of basic functions, which are constructed on a mesh. 28

  29. FINITE ELEMENT METHOD Finite element software calculates exactly what you tell… 29

  30. FINITE ELEMENT METHOD Finite element software calculates exactly what you tell... 30

  31. FINITE ELEMENT METHOD Finite element software calculates exactly what you tell... 31

  32. FINITE ELEMENT METHOD Even if the result is realistic, you should always check it. It’s not a big problem to create a “nice picture” using FEA. The problem is to get the reliable and verified result. That’s a difference between professional and beginner. FEA is a way to find a stress state, but not the way to design or to check the strength! 32

  33. EXAMPLE TO COMPARE ANALYTICAL AND NUMERICAL METHODS Object FEM model base load 33

  34. EXAMPLE TO COMPARE ANALYTICAL AND NUMERICAL METHODS Assignment of parameters 34

  35. EXAMPLE TO COMPARE ANALYTICAL AND NUMERICAL METHODS 35 finite elements in model Deformed shape 35

  36. EXAMPLE TO COMPARE ANALYTICAL AND NUMERICAL METHODS Optimization took 7 minutes on average office PC. 990 points were studied. 36

  37. EXAMPLE TO COMPARE ANALYTICAL AND NUMERICAL METHODS 37

  38. METHODS OF STRUCTURAL ANALYSIS 38

  39. EXAMPLE ILLUSTRATING THE DESIGN OF FINITE ELEMENT MODEL Shell model. 12K elements in model, around 5 minutes to solve on poor office PC 39

  40. EXAMPLE ILLUSTRATING THE DESIGN OF FINITE ELEMENT MODEL Solid model. 250K elements, around 20 minutes to solve on powerful PC (4x4.2GHzprocessor, 16 GB memory). 40

  41. EXAMPLE ILLUSTRATING THE DESIGN OF FINITE ELEMENT MODEL Difference? Certain there is a difference, but for some results it is negligible. Thus, the model should be built according to problem, as in analytical methods 41

  42. FINITE ELEMENT SOFTWARE • Widely used nowadays: • ANSYS; • Patran/Nastran; • ABAQUS; • Solidworks Simulation (former COSMOS); • And many-many others, freeware and proprietary… Any difference? Generally, no difference. FEA packages are often customized to be more convenient for some specific problems. But for most cases, differences between packages and limitations have marketing but not the technical reason. 42

  43. FINITE ELEMENT METHOD HISTORICAL PROGRESS 43

  44. PRINCIPAL COMPONENTS OF FEA SOTWARE 44

  45. FINITE ELEMENT METHOD – OLD INTERFACE 45

  46. FINITE ELEMENT METHOD – MODERN INTERFACE 46

  47. CONCLUSIONS • “Analytical method” does not mean “by hand” or “on paper”, modern software can give large benefits. • Numerical methods are very exacting in terms of software and hardware. • FEA is not a magic key that opens every door. It’s just a versatile and effective tool to calculate stresses. • Deep insight is required for successful structural analysis, no matter is it analytics of FEA. • Generally, analytical methods are good for designing, FEA – for checking. However, in many cases both of methods can be used for both phases of analysis. 47

  48. CONCLUSIONS What does it mean to be a professional in structural analysis? Knowledge of complex formulas? Usage of modern software? Neither of it is an answer. Answer is a deep understanding of how the structure works, and application of proper methods according to the given problem. Analytical and numerical methods loss their disadvantages when they are combined together. 48

  49. WHERE TO FIND MORE INFORMATION? BOOKS AND USEFUL LINKS Good book about structural analysis and Ansys is E. Madenci, I.Guven. The Finite Element Method and Applications in Engineering Using ANSYS, 2006 Very useful links are: Official website resourse library ansys.com Resourse for Ansys users ansys.net Perfect forum (not for beginners, though) xansys.org Youtube (it’s not a joke, search “Ansys” for amazing training videos) youtube.com … Internet is boundless … 49

  50. TOPIC OF THE NEXT LECTURE Statically determinate trusses All materials of our course are available at department website k102.khai.edu 1. Go to the page “Библиотека” 2. Press “Structural Mechanics (lecturer Vakulenko S.V.)” 50

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