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Introduction to FEM Modeling

Apoorv Sharmamidas NFX

CAE Consultant

Total Analysis Solution for Multi-disciplinary Optimum Design



1. Introduction

2. Element Types

3. Sample Exercise: 1D Modeling

4. Meshing Tools

5. Loads and Boundary Conditions

6. Sample Exercise 2: Bracket


Objective of Today’s Webinar

Introduction01

• 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.


The Finite Element Method

Introduction01

Physical System

Mathematical model

Discrete model

Discrete solution

Interpretation of solution

Idealization

Discretization


Idealization

Introduction01

• 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.


Discretization

Introduction01

• 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.

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


More on discretization

Material Models02

• 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}


Importance of Engineering judgment

Material Models02

• 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 & cost-effectiveness?

• If not, are there any practical, economical and effective alternatives?

• How much percentage error can we account for, by adopting the more practical alternative?


Why is idealization important?

Introduction01

• 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?


Why is discretization important?

Introduction01

• 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



1. Introduction

2. Element Types


4. Meshing Tools


6. Sample Exercise: Bracket


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 ModelsFinite Element Expressions

(Geometric Properties Defined by Nodes)

Additional Requirements(Actual Vol

ume Calculation)

1DRod (Truss) Beam Length (L)

Area (A, cross-sectional shape)

V = LA

2D

Shell, Plane Stress, Plane Strain, Axisymmetric, etc Area (A)

Thickness (t)

V = At

3D

Solid Volume (V)

None

(volume calculation possible)

Misc. Spring, Mass, Rigid Link, etc. -

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.

02


Input 1D Element Properties

Selecting Cross-sectional Template

Entering Cross-sectional Measurements

Entering Shear Center Distance

1

2

3

Element Types02

Rod/Truss Element:Bending behavior not possibleTotal DOFs: 4

Bar/Beam Element:Bending behavior possibleTotal DOFs: 6


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

02


Input 2D Element Properties

1. Cross-sectional Thickness

2. Nonstructural Mass

3. Include In-plane Rotational DOF

4. Fiber Distance

Top

Bottom

Middle

T/2

T(Thickness)

1

2

34

Element Types02

Total DOFs in shell element: 5Translational: 3Rotational: 2


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

02


Element Types

Types of 3D Elements

Types Tetrahedron Pentahedron Hexahedron

Shape

No. of

Nodes

4 (lower-order elements)

10 (higher-order elements)





DOF

per

Node

3 Translational DOF (Tx, Ty, Tz)

No rotational DOF

02


Element Types

Lower-order and Higher-order Elements

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

interpolation function

Higher-order Elements (2nd-order Elements)1) The shape of a side of an element is either a straight line or a 2nd-order curve, and the element displacement is

expressed as 2nd-order interpolation function

2) Since it is possible to define the shape of a side of an element as a 2nd-order curve, it is effective in models with many curves

3) Compared to 1st-order elements with a similar size, more accurate analysis results can be obtained.

1st-order Elements 2nd-order Elements

Midnode

02


Element Types

Scalar Elements: Spring Elements

Properties of Spring Elements1) 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

축축축

축축축 축축

02


Element Types

Scalar Elements: Damper Elements

Properties of Damper Elements1) 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 analysesExample) 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

감감감감

축축축축

02


Input Scalar Element Properties: Spring, Damper, Mass Elements

Spring1) 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)

Damper1) 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)

Mass1) Input added scalar mass value

2) Can consider the weight of a target, which has not been modeled

1

2

3

Element Types02


Input Scalar Element Properties: Bush Element

Stiffness1) Input spring stiffness value

2) 1, 2, 3, 4, 5 and 6 represent X, Y, Z, Rx, Ryand Rz in the rectangular coordinate system

Damping1) Input viscous damping value

2) 1, 2, 3, 4, 5 and 6 represent X, Y, Z, Rx, Ryand Rz in the rectangular coordinate system

Miscellaneous1) Structural damping

2) Stress calculation factor

3) Strain calculation factor

1

2

3

Element Types02


Element Types

Scalar Elements: Mass Elements

Properties of Mass Elements1) 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 analysesExample) Engine of a car or a motorcycle, pump or motor of machines

RBE2 Element

Mass Element

Mass Element

RBE2 Element

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.

x

y

1

1

2

34

x

y

Independent node

2

34

02


Element Types

Interpolation Elements (RBE3)

Interpolation Element (RBE)

02

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.


Question Time

Question Time00

What is the difference between Rigid Body & Interpolation elements?

Send in your answers to [email protected] best answers shall be featured on the next webinar (April 15)

mailto:[email protected]


1. Introduction

2. Element Types


4. Meshing tools





개요

해석목적

Sample Exercise: 1D Modeling

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?

03Objective


예제 목적

실습 개요

Step개요

Analytical Model Boundary conditions Load conditions

concentrated load of 20000 N

each

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

03

Fixed condition

Objective of example problem

Summary

Sample Exercise: 1D Modeling


1. Introduction

2. Element Types


4. Meshing tools





Meshing in Midas NFX

Meshing Tools04

Mesh ribbon bar : Create your own nodes and elements

Generate mesh straight from the geometry

Modify mesh and check mesh quality

Mesh Tree: Detailed list of all the mesh sets in the project Property works tree : For the material and section parameters of the mesh

Elements: 110,146

Nodes: 113,235


Create 2D Elements

Auto – Surface, Mapped - Surface1) 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

Auto – Domain, Mapped – Domain1) 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

1 2

Mapped-Surface, 2D Mesh

Auto-Surface, 2D Mesh

Meshing Tools04


Create 3D Elements

Auto – Solid, Mapped - Solid1) 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 Generator1) 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).

2D 3D1) 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.

1

2

3

Hexahedron Mesh

Tetrahedron Mesh

Meshing Tools04


Manual Meshing Functions

Meshing Tools04

Sweep

ExtrudeProject 2D-3D

Fill

OffsetProject nodes Change material orientation

Merge Nodes

2D 3D


Map-mesh

Meshing Tools04

Surface Map-mesher (Quad)

Solid Map-mesher(Hexa, Penta)

Quad Mesh

Hexa Mesh


Hybrid Mesher

Meshing Tools04

Elements: 84,629

Nodes: 63,395

Elements: 83,136

Nodes: 162,319

Hexahedral elements

Pyramid elements

Tetrahedral elements

Prism elements

General higher order tetrahedral mesh

Hexahedral-Tetrahedral Hybrid Mesh

(same number of elements with approximately 1/3 of the nodes )

Shortened analysis time & improved analysis results

Element distribution of hybrid mesh

(Color representation of each element type)

Hexahedral

Element

Pyramid Element

Tetrahedral Element

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.


Check mesh quality

Meshing Tools04

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


Opinion Time

Question for all00

Which is better – Manual meshing or Automatic meshing?

Why? / Why not?

Send in your opinion to [email protected] best responses shall be featured on the next webinar (April 15) and also be featured on our blog (www.feaforall.com).

Automatic Mesh Manual Mesh

mailto:[email protected]

http://www.feaforall.com/


1. Introduction

2. Element Types


4. Meshing Tools

5. Loads & Boundary Conditions




Degrees of Freedom (DOF)

Analysis Type Stress AnalysisTemperature

Analysis

Degree of freedomDisplacement

(vector)Temperature

(scalar)

Number of DOF(components)

3 translational DOF(Tx, Ty, Tz)

3 rotational DOF(Rx, Ry, Rz)

1 per node

Loads and Boundary Conditions05

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.


Types of Constraint Conditions

Pin Constraint

Pin constraint in which only rotation is possible

Pin

Symmetry Constraint

Symmetry plan: ZX-plane

Constrained DOF(Ty, Rx, Rz)

X

X

X

X

Y

Z


Roller SupportObject free to slide

Fixed ConstraintNo movement possible


Input Constraints

Conditions to limit/constrain the motion and deformation of analysis model

Input basic constraint conditions

Input advanced constraint conditions



Definition of Gravity

Gravity & Direction of Gravity

• Set local coordinates by using “curve” or “surface” of the geometric shape

• Input the gravity direction load component in the direction of self-weight of the model

• 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



Static Loads


GravityRotational displacement /

TorqueTranslational displacement /

Concentrated Force

Remote Load

W

W

Bolt Load

Pressure

Static Load ribbon bar in midas NFX

Bearing Load


1. Introduction

2. Element Types


4. Meshing Tools





예제 목적

실습 개요

Step개요

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

06Objective of example problem

Summary

Sample Exercise 2: Bracket


How to get more training material ?


How to get more learning resources

www.midasNFX.com

19

http://www.midasnfx.com/


Thank you very much for attending the webinar !

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Laminar and turbulent flows using Midas NFX

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