Introduction to FEM Modeling

Size: px

Start display at page:

Download "Introduction to FEM Modeling"

Ezra Jerome Sims
6 years ago
Views:

1 Total Analysis Solution for Multi-disciplinary Optimum Design Apoorv Sharma midas NFX CAE Consultant 1

2 1. Introduction 2. Element Types 3. Sample Exercise: 1D Modeling 4. Meshing Tools 5. Loads and Boundary Conditions 6. Sample Exercise 2: Bracket 2

01 Introduction Objective of Today s Webinar Identify the important aspects of FE modeling. Understand the application aspects of different element types in practical FEA.

3 01 Introduction Objective of Today s Webinar Identify the important aspects of FE modeling. Understand the application aspects of different element types in practical FEA. Get acquainted with tools available for effective FE modeling in Midas NFX. Know the importance of loads and boundary conditions. Understand the NFX workflow for modeling an FE problem via live example. 3

4 01 Introduction The Finite Element Method Idealization Discretization Physical System Mathematical model Discrete model Discrete solution Interpretation of solution 4

5 01 Introduction Idealization Understanding the mechanical behavior of the physical system. Establishing a mathematical relationship using concepts of theoretical physics. Understanding the underlying assumptions behind the mathematical model. Obtaining the boundary conditions for the finite element model. 5

01 Introduction Discretization By definition, Discretization refers to the process of translating the material domain of an object-based model into an analytical model suitable for analysis.

6 01 Introduction Discretization By definition, Discretization refers to the process of translating the material domain of an object-based model into an analytical model suitable for analysis. The above circle can be represented as an arrangement of triangles. The representation is more accurate if more triangles are used. Therefore, the above circular geometry has been discretized using triangular elements. 6

02 Material Models More on discretization The finite element model represents a continuous physical system through

This model forms the basis for a mathematical system to emulate real world behavior.

The loads are transferred between interconnected nodes In order to create a mathematical system that predicts real

7 02 Material Models More on discretization The finite element model represents a continuous physical system through a network of nodes and an arrangement of elements. This model forms the basis for a mathematical system to emulate real world behavior. Every node is a source of input/output during the analysis. The loads are transferred between interconnected nodes In order to create a mathematical system that predicts real world behavior with least possible error, it is essential to understand the distribution of nodes and elements along the material domain. Node {f}=[k]{δ} {f}=[k]{δ} {f}=[k]{δ} {f}=[k]{δ} {f}=[k]{δ} {f}=[k]{δ} {f}=[k]{δ} Governing equation of each element: {f}=[k]{δ} 9

02 Material Models Importance of Engineering judgment What kind of behavior is essential to analyze to investigate this problem (linear, nonlinear, static, dynamic, steady, transient etc.)?

8 02 Material Models Importance of Engineering judgment What kind of behavior is essential to analyze to investigate this problem (linear, nonlinear, static, dynamic, steady, transient etc.)? What type of elements should be used? Does the finite element model effectively represent the physics of the system? Does it comply with the theoretical assumptions? Is the best available method in terms of time & costeffectiveness? If not, are there any practical, economical and effective alternatives? How much percentage error can we account for, by adopting the more practical alternative? 12

9 01 Introduction Why is idealization important? Important to understand the factors that affect the system critically. Incorrect assumptions will yield incorrect and unexpected results. Wrong idealization could also cause convergence issues while solving the FE model. Gravity? 13

10 01 Introduction Why is discretization important? To obtain an accurate representation of geometry. To avoid convergence issues due to poor-shaped elements To ensure uniform transfer of load among adjoining nodes. Good Mesh Bad Mesh 14

11 1. Introduction 2. Element Types 3. Sample Exercise: 1D Modeling 4. Meshing Tools 5. Loads and Boundary Conditions 6. Sample Exercise: Bracket 19

02 Element Types Standard of Classification Elements can be classified based on

Type Actual Models Finite Element Expressions (Geometric Properties Defined by

Length (L) Area (A, cross-sectional shape) V = L A 2D Shell, Plane Stress,

12 02 Element Types Standard of Classification Elements can be classified based on geometric dimensions (properties), which are defined by lower-ranked nodes (coordinate information). Element properties (additional requirements) must be entered. Type Actual Models Finite Element Expressions (Geometric Properties Defined by Nodes) Additional Requirements(Actual Vol ume Calculation) 1D Rod (Truss) Beam Length (L) Area (A, cross-sectional shape) V = L A 2D Shell, Plane Stress, Plane Strain, Axisymmetric, etc Area (A) Thickness (t) V = A t 3D Solid Volume (V) None (volume calculation possible) Misc. Spring, Mass, Rigid Link, etc. - 20

13 02 Element Types 1D Elements Also referred to as line elements. Often used to represent members, which are too long compared to the measurement of the cross-section (L/r >20). Useful when bending is the root cause of failure. Fundamental assumption: Changes in material properties along the cross-section are negligible. 21

Entering Shear Center Distance 1 Rod/Truss Element: Bending behavior

14 02 Element Types Input 1D Element Properties Selecting Cross-sectional Template Entering Cross-sectional Measurements Entering Shear Center Distance 1 Rod/Truss Element: Bending behavior not possible Total DOFs: 4 2 Bar/Beam Element: Bending behavior possible Total DOFs:

02 Element Types 2D Elements Also referred

Often used when thin, sheet structures are

Changes in material properties along the

15 02 Element Types 2D Elements Also referred to as shell elements. Often used when thin, sheet structures are under bending deformation Can consider 2D stress conditions and bending and shear deformations Fundamental assumption: Changes in material properties along the thickness of the structure are negligible. Mesh Creation Using 2D Elements 24

16 02 Element Types Input 2D Element Properties 1. Cross-sectional Thickness 2. Nonstructural Mass 3. Include In-plane Rotational DOF 4. Fiber Distance Total DOFs in shell element: 5 Translational: 3 Rotational: 2 1 Top T/2 2 Middle T(Thickness) 3 4 Bottom 26

17 02 Element Types 3D Elements Also referred to as solid elements Since actual tasks deal with 3D model using CAD, they are used in analyses the most. Mesh Creation Using 3D Elements 27

18 02 Element Types Types of 3D Elements Types Tetrahedron Pentahedron Hexahedron Shape No. of Nodes 4 (lower-order elements) 10 (higher-order elements) 6 (lower-order elements) 15 (higher-order elements) 8 (lower-order elements) 20 (higher-order elements) DOF per Node 3 Translational DOF (Tx, Ty, Tz) No rotational DOF 28

02 Element Types Lower-order and Higher-order Elements Lower-order Elements (1 st -order Elements) 1) The shape of a side of an element is a straight line, and the element displacement is expressed

19 02 Element Types Lower-order and Higher-order Elements Lower-order Elements (1 st -order Elements) 1) The shape of a side of an element is a straight line, and the element displacement is expressed as 1 st -order interpolation function Higher-order Elements (2 nd -order Elements) 1) The shape of a side of an element is either a straight line or a 2 nd -order curve, and the element displacement is expressed as 2 nd -order interpolation function 2) Since it is possible to define the shape of a side of an element as a 2 nd -order curve, it is effective in models with many curves 3) Compared to 1 st -order elements with a similar size, more accurate analysis results can be obtained. Midnode 1 st -order Elements 2 nd -order Elements 29

02 Element Types Scalar Elements: Spring Elements Properties of Spring Elements 1) Simple 1D line element that connects two nodes within a mesh 2) Typically used to express springs but are variously

Node-connecting springs: basic spring element that connects two nodes 6) Ground spring: spring element in which all degrees of freedom of a node are automatically constrained 7) Degree of freedom

20 02 Element Types Scalar Elements: Spring Elements Properties of Spring Elements 1) Simple 1D line element that connects two nodes within a mesh 2) Typically used to express springs but are variously utilized to realize assembly modeling or contact as well 3) Can support load in the torsional direction in addition to the axial direction 4) Possible to set simply by entering spring constant 5) Node-connecting springs: basic spring element that connects two nodes 6) Ground spring: spring element in which all degrees of freedom of a node are automatically constrained 7) Degree of freedom spring: retains spring stiffness in reference to only a specific direction or specific degree of freedom. : spring load is generated only during translation or rotation of a specified degree of freedom 축축축축축 축축축 30

02 Element Types Scalar Elements: Damper Elements Properties of Damper Elements 1) The property to prevent the motion of an object is called damping 2) Used to reflect damping effects of a buffer in

21 02 Element Types Scalar Elements: Damper Elements Properties of Damper Elements 1) The property to prevent the motion of an object is called damping 2) Used to reflect damping effects of a buffer in a dynamic analysis model; in other words, they are not used in static analyses Example) The shock absorber attached to the suspension system of a car 3) Unit: force/velocity 4) Can support axial load and torsional load 5) Used instead of an external damper 축축축축 감감감감 31

02 Element Types Input Scalar Element Properties: Spring, Damper, Mass Elements Spring 1) Input spring constant and stress coefficient 2) Since the value entered in the initially set unit system is

22 02 Element Types Input Scalar Element Properties: Spring, Damper, Mass Elements Spring 1) Input spring constant and stress coefficient 2) Since the value entered in the initially set unit system is used as it is, it must be analyzed based on the input unit system (does not support unit conversion) Damper 1) Input damping value 2) Since the value entered in the initially set unit system is used as it is, it must be analyzed based on the input unit system (does not support unit conversion) Mass 1) Input added scalar mass value 2) Can consider the weight of a target, which has not been modeled

viscous damping value 2) 1, 2, 3, 4, 5 and 6 represent X, Y, Z, Rx, Ry and Rz in the rectangular coordinate

23 02 Element Types Input Scalar Element Properties: Bush Element Stiffness 1) Input spring stiffness value 2) 1, 2, 3, 4, 5 and 6 represent X, Y, Z, Rx, Ry and Rz in the rectangular coordinate system Damping 1) Input viscous damping value 2) 1, 2, 3, 4, 5 and 6 represent X, Y, Z, Rx, Ry and Rz in the rectangular coordinate system Miscellaneous 1) Structural damping 2) Stress calculation factor 3) Strain calculation factor

02 Element Types Scalar Elements: Mass Elements Properties of Mass Elements 1) Used by idealizing mass of a component that has a

In analyses without gravitational force/accelerating force, mass element effects are not possible 4) Since mass element is imposed

locating it at the center of gravity of the shape 6) Mass elements are used since mass distribution is crucial in modal

24 02 Element Types Scalar Elements: Mass Elements Properties of Mass Elements 1) Used by idealizing mass of a component that has a very large stiffness or is too complicated to be expressed in meshes 2) Single-node elements that do not retain geometric models 3) In analyses without gravitational force/accelerating force, mass element effects are not possible 4) Since mass element is imposed on a single point, it does not affect stiffness 5) May link the model with a rigid body element after adding to a mesh node and locating it at the center of gravity of the shape 6) Mass elements are used since mass distribution is crucial in modal analyses/dynamic analyses Example) Engine of a car or a motorcycle, pump or motor of machines Mass Element RBE2 Element Mass Element RBE2 Element 34

25 02 Element Types Rigid Elements Also known as multi-point constraint. Assigned at a single node. Establishes a kinematic relationship between the nodes connected to the rigid body, also called slave nodes. Rigid body element has very high stiffness. The deflection of slave nodes is dependent on the deflection of the rigid body. y y x 1 Independent node 2 x 35

26 02 Element Types Interpolation Elements (RBE3) Also a type of multi-point constraint. Also assigned at a single node. Also establishes a kinematic relationship between the nodes connected to the it.. The deflection of interpolation element is dependent on the deflection of the nodes it is connected to. Interpolation Element (RBE) 36

27 00 Question Time Question Time What is the difference between Rigid Body & Interpolation elements? Send in your answers to The best answers shall be featured on the next webinar (April 15) 37

28 1. Introduction 2. Element Types 3. Sample Exercise: 1D Modeling 4. Meshing tools 5. Loads and Boundary Conditions 6. Sample Exercise 2: Bracket 38

29 개요 03 Sample Exercise: 1D Modeling Objective 해석목적 Pylons are mounted under the ground to assess whether they can support the weight of the frame or not. What are the load and boundary conditions of the Tower Body? What is the weight of the upper pylons? Do the pylons support the bottom of the frame in any way? 39

30 Step 개요 03 Sample Exercise: 1D Modeling Objective 예제목적 of example problem Use and applications of 1D elements - Learn how to use 1D elements and create a frame structure - Learn how to simply change the cross-sectional shape features using a section of 1D elements - Learn how to set the direction of the section of the 1D elements 실습 Summary 개요 Analytical Model Boundary conditions Load conditions concentrated load of N each Fixed condition 40

31 1. Introduction 2. Element Types 3. Sample Exercise: 1D Modeling 4. Meshing tools 5. Loads and Boundary Conditions 6. Sample Exercise 2: Bracket 41

04 Meshing Tools Meshing in Midas NFX Mesh

elements Generate mesh straight from the

quality Elements: 110,146 Nodes: 113,235

sets in the project Property works tree :

32 04 Meshing Tools Meshing in Midas NFX Mesh ribbon bar : Create your own nodes and elements Generate mesh straight from the geometry Modify mesh and check mesh quality Elements: 110,146 Nodes: 113,235 Mesh Tree: Detailed list of all the mesh sets in the project Property works tree : For the material and section parameters of the mesh 42

04 Meshing Tools Create 2D Elements Auto Surface, Mapped - Surface

size after selecting a surface or a shell.

of triangular, quadrilateral or triangular + quadrilateral shapes.

Auto Domain, Mapped Domain 1) After creating a closed curve from the

selected element on the surface drawn by the closed curve.

Auto-Surface, 2D Mesh Mapped-Surface, 2D Mesh 44

33 04 Meshing Tools Create 2D Elements Auto Surface, Mapped - Surface 1) Automatically creates 2D mesh as much as the specified element size after selecting a surface or a shell. 2) Auto: based on the selected mesh method, the 2D mesh is consisted of triangular, quadrilateral or triangular + quadrilateral shapes. 3) Mapped: 2D mesh is constituted by quadrilateral shapes only 1 2 Auto Domain, Mapped Domain 1) After creating a closed curve from the selected curves, automatically creates 2D mesh in the size of the selected element on the surface drawn by the closed curve. 2) Auto: based on the selected mesh method, the 2D mesh is consisted of triangular, quadrilateral or triangular + quadrilateral shapes. 3) Mapped: 2D mesh is constituted by quadrilateral shapes only Auto-Surface, 2D Mesh Mapped-Surface, 2D Mesh 44

04 Meshing Tools Create 3D Elements Auto Solid, Mapped - Solid 1)

tetrahedron or tetrahedron + hexahedron shapes.

Mesh Generator 1) Tetrahedron mesh generator: creates 3D mesh by

2) Hybrid mesh generator: creates 3D mesh by combining tetrahedron

34 04 Meshing Tools Create 3D Elements Auto Solid, Mapped - Solid 1) Auto: according to the selected mesh method, it creates 3D mesh in tetrahedron or tetrahedron + hexahedron shapes. 2) Mapped: creates 3D mesh in hexahedron shapes only. Mesh Generator 1) Tetrahedron mesh generator: creates 3D mesh by only using tetrahedron elements in reference to the selected shape. 2) Hybrid mesh generator: creates 3D mesh by combining tetrahedron and hexahedron elements in reference to the selected shape (hexahedron elements are usually used) Tetrahedron Mesh 2D 3D 1) Creates tetrahedron mesh in the space enclosed by 2D mesh. 2) If tetrahedron elements exist in the selected 2D mesh, the program arbitrarily divides a tetrahedron element into 2 triangular elements and then a tetrahedron element is created. Hexahedron Mesh 45

35 04 Meshing Tools Manual Meshing Functions Extrude Project 2D-3D Fill Merge Nodes 2D 3D Sweep Project nodes Change material orientation Offset 48

36 04 Meshing Tools Map-mesh Surface Map-mesher (Quad) Quad Mesh Solid Map-mesher (Hexa, Penta) Hexa Mesh 49

04 Meshing Tools Hybrid Mesher Tetrahedral

number of elements with approximately 1/3

improved analysis results Composition of

generated at interiors where stiffness and

37 04 Meshing Tools Hybrid Mesher Tetrahedral Element Pyramid Element Elements: 83,136 Nodes: 162,319 General higher order tetrahedral mesh Elements: 84,629 Nodes: 63,395 Hexahedral Element Hexahedral-Tetrahedral Hybrid Mesh (same number of elements with approximately 1/3 of the nodes ) Shortened analysis time & improved analysis results Composition of hybrid element mesh Hexahedral elements producing superb results are primarily generated at the boundaries where maximum displacements/stresses are resulted. Tetrahedral elements are partially generated at interiors where stiffness and mass calculations are more meaningful. Hexahedral elements Pyramid elements Tetrahedral elements Prism elements Element distribution of hybrid mesh (Color representation of each element type) 50

04 Meshing Tools Check mesh quality Because the

Automatically detect poor elements by a simple

Export the poor elements to a separate mesh set.

38 04 Meshing Tools Check mesh quality Because the outer contour does not present the full picture Automatically detect poor elements by a simple mouse click. Export the poor elements to a separate mesh set. Mesh Quality Parameters: Aspect Ratio Skew Angle Warpage Taper Jacobian Ratio Twist Angle Element Length 51

00 Question for all Opinion Time Which is better

next webinar (April 15) and also be featured on

39 00 Question for all Opinion Time Which is better Manual meshing or Automatic meshing? Why? / Why not? Send in your opinion to apoorv@midasit.com The best responses shall be featured on the next webinar (April 15) and also be featured on our blog ( Automatic Mesh Manual Mesh 52

40 1. Introduction 2. Element Types 3. Sample Exercise: 1D Modeling 4. Meshing Tools 5. Loads & Boundary Conditions 6. Sample Exercise 2: Bracket 53

41 05 Loads and Boundary Conditions Degrees of Freedom (DOF) The degree of freedom determines the freedom of movement of an object or a system. The motion could be translational, rotational or vibrational in nature. Analysis Type Degree of freedom Stress Analysis Displacement (vector) Temperature Analysis Temperature (scalar) Number of DOF (components) 3 translational DOF (Tx, Ty, Tz) 3 rotational DOF (Rx, Ry, Rz) 1 per node 54

05 Loads and Boundary Conditions Types of

plan: ZX-plane Z X X Y Constrained DOF (Ty, Rx,

42 05 Loads and Boundary Conditions Types of Constraint Conditions Pin Pin constraint in which only rotation is possible Fixed Constraint No movement possible Pin Constraint Symmetry plan: ZX-plane Z X X Y Constrained DOF (Ty, Rx, Rz) X X Roller Support Object free to slide Symmetry Constraint 55

43 05 Loads and Boundary Conditions Input Constraints Conditions to limit/constrain the motion and deformation of analysis model Input basic constraint conditions Input advanced constraint conditions 56

05 Loads and Boundary Conditions Definition of Gravity Set local coordinates

load component in the direction of selfweight of the model Gravity & Direction

importantly during the analysis after setting a number of load cases

44 05 Loads and Boundary Conditions Definition of Gravity Set local coordinates by using curve or surface of the geometric shape Input the gravity direction load component in the direction of selfweight of the model Gravity & Direction of Gravity Input name of the load set Specify a load set and use it importantly during the analysis after setting a number of load cases Individually input the set name if the analysis results for the number of loads want to be known 57

45 05 Loads and Boundary Conditions Static Loads Static Load ribbon bar in midas NFX Gravity Translational displacement / Concentrated Force Rotational displacement / Torque Pressure W W Remote Load Bolt Load Bearing Load 58

46 1. Introduction 2. Element Types 3. Sample Exercise: 1D Modeling 4. Meshing Tools 5. Loads and Boundary Conditions 6. Sample Exercise 2: Bracket 59

47 Step 개요 06 Sample Exercise 2: Bracket Objective 예제목적 of example problem Manual solid FE modeling - Learn how to create 3D mesh without geometry - Learn how to use manual meshing tools - Learn how to apply a load that varies as a function of distance 실습 Summary 개요 60

48 How to get more training material? 61

49 19 How to get more learning resources 62

50 Next Webinar ( ): Laminar and turbulent flows using Midas NFX Thank you very much for attending the webinar! Q&A Join us 63

midas NFX An insight into midas NFX

midas NFX An insight into midas NFX Total Analysis Solutions for Multi-disciplinary Optimum Design Part 1. Work environment Multi-disciplinary CAE solutions in one unique work environment 1 Part 1. Work