fea_algor

7/27/2019 FEA_ALGOR

1/78

Introduction

7/27/2019 FEA_ALGOR

2/78

Best Practices

FEA requires engineering judgment. In

,

approximate answer before you begin.

, ,

loads, constraints and analysis .

7/27/2019 FEA_ALGOR

3/78

Best Practices

Understand that the computer

only an approximation).

to underestimate the complexity of.

7/27/2019 FEA_ALGOR

4/78

verv ew

7/27/2019 FEA_ALGOR

5/78

The Basic Steps of FEA

Build/Mesh a Model

Define FEA Model

Analysis and Element Types

Define Loads and Constraints

Analyze Model (Solve)

Review Results and Improve Design

7/27/2019 FEA_ALGOR

6/78

Example Using ALGOR

Create Mesh in CAD Solid Model or FEA Editor

Setup Analysis Type, Element Type and

Environment

FE

Materials in the FEA Editor Environment

Apply Loads and Constraints in the FEA Editor

M

P

Analyze Model (Solve)O

Review Results in the Results Environment

and Create an improved Design

7/27/2019 FEA_ALGOR

7/78

FEA Concepts

7/27/2019 FEA_ALGOR

8/78

What is a DOF?

The unknowns in a finite element problem

are referred to as degrees of freedom (DOF).

Degrees of freedom vary by element andanalysis type.

StructuralForce / (M)Displacement / (Rotation)

ApplicationActionDOF Type

ThermalHeat Flow

Rate

Temperature

7/27/2019 FEA_ALGOR

9/78

What is a DOF?

Uy

Rot y

Node Rot x Ux

UzRot z

7/27/2019 FEA_ALGOR

10/78

Node

in space where the DOF are

e ne . e o s po n

represent the possible responseat this point due to the loading of

the structure.

7/27/2019 FEA_ALGOR

11/78

Element

relation that defines how the

o a no e re a e o e

next. These elements can belines (beams), areas

2-D or 3-D lates or solids

(bricks and tetrahedrals).

7/27/2019 FEA_ALGOR

12/78

7/27/2019 FEA_ALGOR

13/78

Element Connectivity

Elements can onl transfer loads to

one another via common nodes.

No Communication

Between the Elements

Communication

Between the Elements

7/27/2019 FEA_ALGOR

14/78

Stress

Basic equations do not require the use of a

.

Computer-based analysis is needed when

Geometric complexity makes the elasticity

e uation diff icult or im ossible to solve.

Variations in material properties exist throughout

the part.

Multiple load cases and complex or combinedloading exists.

ynam cs are o n eres .

7/27/2019 FEA_ALGOR

15/78

General Case

The DOF components of each element

=

[K] = element stiffness components

=

{A} = action value (e.g., force, temperature)

7/27/2019 FEA_ALGOR

16/78

Structural FEA Equation

To determine the displacement of

a simple linear spring under load,the relevant equation is:

{f} = [K] {d}

Known Unknown

where {f} = force vector[K] = stiffness matrix{d} = displacement vector

7/27/2019 FEA_ALGOR

17/78

FEA Equation Solution

matrix algebra by

follows:-

{d} = [K] {f}

7/27/2019 FEA_ALGOR

18/78

Calculation of and

Strains are computed based on

the classical differentialequations.

Stress can then be obtained

law or other constitutive

7/27/2019 FEA_ALGOR

19/78

Dynamic Equation

For a more complex analysis, moreterms are needed. This is true in a

dynamic analysis, which is defined bythe following equation:

{f} = [K] {d} + [c] {v} + [m] {a}where {f} = force vector

[K] = stiffness matrix

{d} = displacement vector

{v} = velocity vector

[m] = mass matrix

{a} = acceleration vector

7/27/2019 FEA_ALGOR

20/78

Analysis Options

7/27/2019 FEA_ALGOR

21/78

Choosing an Analysis Type

The first decision in the FEA process

is to decide what type of analysisyou need to run.

The analysis type will dictate what

t e of results ou will obtain.For example, if you need the

,

will need to run a structural analysis.

7/27/2019 FEA_ALGOR

22/78

Structural

No changes in stiffness.

No changes in loading

direction.Material remains in the linear

elastic ran e.

Small deformation and strain.

7/27/2019 FEA_ALGOR

23/78

Structural

Linear dynamics

a ura requency mo a

Response spectrum

Random vibration

Frequency responseTransient stress (direct integration)

Transient stress (modal superposition)

[Critical buckling load -- eigenvalue]

Dynamic Design Analysis Method

(DDAM)

7/27/2019 FEA_ALGOR

24/78

Element O tions

7/27/2019 FEA_ALGOR

25/78

Choosing an Element Type

will depend on the following:

Analysis type selected.

How ou create our mesh.

Assumptions you can make

.

7/27/2019 FEA_ALGOR

26/78

Element Categories

Line Elements: A line connecting 2

nodes (beams, trusses, springs,actuators, pipes, etc.)

Area (2-D) Elements: A cross-section

of a art. Must be 3 or 4 linesenclosing an area.

7/27/2019 FEA_ALGOR

27/78

Element Categories

Area (3-D Planar) Elements:

Midplane of a part in space. Mustbe 3 or 4 lines enclosing an area.

3-D Solid Elements: Must be 4, (5),

6 or 8 nodes enclosin a volume.

7/27/2019 FEA_ALGOR

28/78

es ng an

7/27/2019 FEA_ALGOR

29/78

Proper Modeling Techniques

For any region (3, 4, 5, 6 or 8-nodes)

to be a valid element, it must:Consist of either three (triangular) orfour (quadrilateral) undivided line

segments. If a side consists of multiple

, .

Not have curved or arched sides.

7/27/2019 FEA_ALGOR

30/78


Certain shapes can create elements

which are not recommended for FEAanalysis. The following regions will

be eliminated:

Re ions with an collinear orconcave sides.

Re ions with a hi hl nonflat

curvature in a 3-D drawing.

7/27/2019 FEA_ALGOR

31/78


7/27/2019 FEA_ALGOR

32/78

Meshing Guidelines

Meshing can be completed either by

using automatic mesh engines or bycreating a mesh by hand .

Automatic mesh generation is usually

com leted on CAD solid models. Hand meshing is usually done on

structured mesh.

7/27/2019 FEA_ALGOR

33/78

7/27/2019 FEA_ALGOR

34/78

7/27/2019 FEA_ALGOR

35/78

Introduction to Loads and Constraints

You will have to decide what type of

loads and constraints will properly

define the engineering criteria for the

mo e .

In FEA, there are different types of loads

.

Applying the proper loads and

factors in getting the correct answer.

.

7/27/2019 FEA_ALGOR

36/78

Types of Loads and Constraints

There are multiple ways to

apply different loads andconstraints to a model:

Nodal

Surface

Element

7/27/2019 FEA_ALGOR

37/78

Structural Nodal Loads

Displacements (N.L.)

Forces

Temperatures (thermal stress)

Voltages (piezoelectric materials)

7/27/2019 FEA_ALGOR

38/78

Structural Nodal Constraints

Boundary Conditions:

Prevent specified DOF fromundergoing translation or

rotation in a specified

direction.Boundary Elements: Act like

stiffness along a specified

7/27/2019 FEA_ALGOR

39/78


Using Boundary Conditions to

Good only for symmetrical problems and

Along the line of symmetry, boundary

condit ions must be applied to representthe symmetrical part:

Out-of-plane displacement = 0

Two in- lane rotations = 0

7/27/2019 FEA_ALGOR

40/78


P PP

Line ofSymmetry

ane o ymmetry

7/27/2019 FEA_ALGOR

41/78

Boundary Conditions

Proper boundary conditions are

.

The global stiffness of the system must

behavior to be captured correctly.

7/27/2019 FEA_ALGOR

42/78

Boundary Conditions

The two most unwanted FEA effects to

Overstiffening

Rigid Body Motion

- ,

constraints in FEA are perfect.

S f

7/27/2019 FEA_ALGOR

43/78

Linear Surface Loads

Uniform or Hydrostatic Pressure

and TractionApplied to the face of plate, composite

and brick elements.

Applied to the edge of 2-D and

.

Surface Force

a force that wil l be evenly distributed

over a given surface.

Li S f L d

7/27/2019 FEA_ALGOR

44/78

Linear Surface Loads

Variable Pressure or TractionDefine a function of the position that

controls the magnitude of the load over

.

Li

7/27/2019 FEA_ALGOR

45/78

LinearElement Loads

Gravit

Can specify gravitational value anddirection. You must have a mass density

e ne or eac par .

Centrifugal Loads

,

and acceleration values.

Specify the magnitude and direction ateach end of beam elements.

7/27/2019 FEA_ALGOR

46/78

Truss Elements

Truss Elements

7/27/2019 FEA_ALGOR

47/78

Truss Elements

Truss elements are two-node

,

orientation in the X, Y, Zsystem.

The truss transmits axial force

only, and in general, is a three

e emen .e., ree g o a

translation components at each

end of the member . Trusses

are used to model structuressuch as towers, bridges and

u ngs.

Truss Elements

7/27/2019 FEA_ALGOR

48/78

Truss Elements

Guidelines for using

russ e emen s:

The length of the element is much

greater than the width or depth

(approximately 8-10 times).

It is connected to the rest of the model

with hinges that do not transfer

momen s.The external applied forces are only at

o n s.

7/27/2019 FEA_ALGOR

49/78

Beam Elements

Beam Elements

7/27/2019 FEA_ALGOR

50/78

Beam Elements

Beam elements are slender

structural members that offer

resistance to forces and bending

under applied loads.

eams are oun n u ng

frames, transmission towers and

.

A beam differs from a truss in that

a beam resists moments twistin

and bending) at the connections.

Beam Elements

7/27/2019 FEA_ALGOR

51/78

Beam Elements

Beams use a third node to

define the orientation of thecross-section.

Cross-sectional properties

about both the strong and

Beam Elements

7/27/2019 FEA_ALGOR

52/78

Beam Elements

Guidelines for using beam elements:

The length of the element is muchreater than the width or de th.

The element has constant cross-

sectional ro erties.The element must be able to transfer

moments.

The element must be able to handle aload distributed alon its len th.

7/27/2019 FEA_ALGOR

53/78

2-D Elements

2-D Elements

7/27/2019 FEA_ALGOR

54/78

2 D Elements

Two-dimensional

e emen s are ree- or

four-node elements thatare ormu a e n e -

plane. They are used to

mo e an ana yze

objects such as bearings,

sea s or s ruc ures sucas dams.

2-D Elements

7/27/2019 FEA_ALGOR

55/78

2 D Elements

2-D Geometry Types

Axisymmetric: For parts that are

Plane strain: No deflection

(e.g., a large dam).

to the cross-section (e.g., a plate

.

2-D Elements

7/27/2019 FEA_ALGOR

56/78

Create wireframe sketches for each part

.

Use the 2-D mesh engine to generate the- .

Do not create slender elements. Not

more an : ra o e ween s es or

diagonals.

7/27/2019 FEA_ALGOR

57/78

Plate Elements

Plate/Shell Elements

7/27/2019 FEA_ALGOR

58/78

Plate/shell elements are three- or

-

three-dimensional space. These

analyze objects such as pressure

vessels, aircraft skin andautomotive body parts.

A thickness is assigned to the

elements. Stresses will vary linearly through

t e t c ness.

Plate/Shell Elements

7/27/2019 FEA_ALGOR

59/78

Guidelines for using plate/shell

elements:

The thickness is small in relation tothe len th and width about 1/10 .

Good for small displacements and

rotations.Elements remain (almost) planar (i.e.,

no war a e .

No rotation about the direction normalto the element.

Membrane Elements

7/27/2019 FEA_ALGOR

60/78

Three- or four-node elements

formulated in three-dimensional

space. No moment resistance.

Used to model " fabric-like"

objects such as tents or cots, or

structures such as the roof of a

sports stadium.

Model solids of a specified

c ness, w c ex no

stress normal to the thickness.

7/27/2019 FEA_ALGOR

61/78

Brick Elements

Solid (Brick) Elements

7/27/2019 FEA_ALGOR

62/78

Solid elements are

, ,

eight-node elements

dimensional space.

be used when the

thickness of a part is

. : ra o

7/27/2019 FEA_ALGOR

63/78

Mesh Convergence

Mesh Convergence

7/27/2019 FEA_ALGOR

64/78

For mesh convergence

testing, it is suggested that

you run at least three

analyses at different mesh

sizes:

Coarse

Fine

Somewhere in between coarseand fine

Mesh Convergence

7/27/2019 FEA_ALGOR

65/78

Usually, you will not see the

direct equation solutions (such

as displacements) change with

the different mesh sizes.

You will see the numericalmethod answers (such as

stresses conver e to an answer

as the mesh gets finer.

7/27/2019 FEA_ALGOR

66/78

Meshing CAD Solid

Models

7/27/2019 FEA_ALGOR

67/78

Mesh Refinement

7/27/2019 FEA_ALGOR

68/78

To optimize solution time, it is

useful to create a fine mesh in

areas where the results are

critical and a coarser mesh in

areas where the results will not

be as high.

You can add refinement oints

to achieve localized refinement.

Assembly Meshing

7/27/2019 FEA_ALGOR

69/78

When working with multiple parts in

,

meshes match between the parts if.

If the area where the parts come

toget er s ou not e on e ,

then contact should be used to

accoun or e r n erac on.

Combining Element Types

7/27/2019 FEA_ALGOR

70/78

Any combination of element types is possible

in an assembly.

Nodes must be matched where the parts meet

in order for loads to be transferred.

The available DOF of the element types that

are connected must be considered and

matched to avoid unstable geometry.

7/27/2019 FEA_ALGOR

71/78

Solving Options

Introduction to Solvers

7/27/2019 FEA_ALGOR

72/78

There are many different ways to

discussed earlier.u , w

technologies are used that create

.

You should usually accept the default

settings, which are optimized for thefastest processing.

7/27/2019 FEA_ALGOR

73/78

Results

Result Options

7/27/2019 FEA_ALGOR

74/78

The types of results depend on

the type of analysis that is

performed.

For example, a structural analysis

will ive ou dis lacement andstress results while a thermal

anal sis will ive ou tem erature

and heat flux results.

How Results are Calculated

7/27/2019 FEA_ALGOR

75/78

The results are either calculated

directly (D.O.F.s) through linear

equations or derived from them.

For example, displacements are

derived through numerical

Structural Results

7/27/2019 FEA_ALGOR

76/78

Displacement

Stress

Reaction forces

n erna orces

Motion

7/27/2019 FEA_ALGOR

77/78

resentat on

Presentation Options

7/27/2019 FEA_ALGOR

78/78

Contour images

Animations-

fea_algor

Documents