Basic FEM Webinar 2011

8/6/2019 Basic FEM Webinar 2011

1/130


2/130


3/130


4/130


5/130


6/130


7/130


8/130


9/130


10/130


11/130


12/130


13/130


14/130


15/130


16/130


17/130


18/130


19/130


20/130


21/130


22/130


23/130


24/130


25/130


26/130


27/130


28/130


29/130


30/130


31/130


32/130


33/130


34/130


35/130


36/130


37/130


38/130


39/130


40/130


41/130


42/130


43/130


44/130


45/130


46/130


47/130


48/130


49/130


50/130


51/130


52/130


53/130


54/130


55/130


56/130


57/130


58/130


59/130


60/130


61/130


62/130


63/130


64/130


65/130


66/130


67/130


68/130


69/130


70/130


71/130


72/130


73/130


74/130


75/130


76/130


77/130


78/130


79/130


80/130


81/130


82/130


83/130


84/130


85/130


86/130


87/130


88/130


89/130


90/130


91/130


92/130


93/130


94/130

Introd uc tion to Finite Elem ent Ana lysisDesign, Analysis, and Simul ation


95/130

Or lots of trian les? Introduction Introduction Introduction FEA Process FEA Process FEA Process An Example An Example An Example Complicated Complicated Complicated Models Models Models Choosing

= .00439 = 2558 psi

Elements Interpreting Interpreting Interpreting Results Results Results FEM Codes FEM Codes FEM Codes

Still too stiff

Still low Wrapping Up Wrapping Up Wrapping Up 4-node triangles are too stiff you can use them here and

there in a model, but you dont want a whole model made from them.

1-77-Nastran

NEi Sensitive/Proprietary

www.NEiSoftware.com

,preferentially take the load.



96/130

Introduction Introduction Introduction FEA Process FEA Process FEA Process

How about bad elements?An Example An Example An Example Complicated Complicated Complicated Models Models Models Choosing

=

Elements Interpreting Interpreting Interpreting Results Results Results FEM Codes FEM Codes FEM Codes Bad, but not too bad .

= 2194 psiWrapping Up Wrapping Up Wrapping Up

Same

1-77-Nastran


www.NEiSoftware.com



97/130

How about bad elements with QUADRs?

Introduction Introduction Introduction FEA Process FEA Process FEA Process An Example An Example An Example Complicated Complicated Complicated Models Models Models Choosing

= .00481 = 2937 psi


Much better

Very much better

Wrapping Up Wrapping Up Wrapping Up

QUADR elements tolerate distortions much better then QUAD4s

1-77-Nastran


www.NEiSoftware.com



98/130

What about solid elements? Introduction Introduction Introduction FEA Process FEA Process FEA Process An Example An Example An Example Complicated Complicated Complicated Models Models Models Choosing

= .00499 = 2479 psi


Great for one elment!

Not too bad here either Wrapping Up Wrapping Up Wrapping Up

1-77-Nastran


www.NEiSoftware.com



99/130

Or lots of solid elements Introduction Introduction Introduction FEA Process FEA Process FEA Process An Example An Example An Example Complicated Complicated Complicated Models Models Models Choosing

= .00501


Very nice

= 3006 psi Wrapping Up Wrapping Up Wrapping Up Very nice too.

1-77-Nastran


www.NEiSoftware.com



100/130

Introduction Introduction Introduction FEA Process FEA Process FEA Process Why does everyone tell me to avoid TET4 elements? An Example An Example An Example

Complicated Complicated Complicated Models Models Models Choosing

= .00127Elements Interpreting Interpreting Interpreting Results Results Results FEM Codes FEM Codes FEM Codes

As bad as triangles

Recall that TET elements, like triangles, have different formulations


1-77-Nastran


www.NEiSoftware.com



101/130

Lots of TET elements? Introduction Introduction Introduction FEA Process FEA Process FEA Process An Example An Example An Example Complicated Complicated Complicated Models Models Models Choosing

= .00385


= 2330 psi

Wrapping Up Wrapping Up Wrapping Up Still bad

1-77-Nastran


www.NEiSoftware.com



102/130


But what if I use parabolic TET10 elements? An Example An Example An Example Complicated Complicated Complicated Models Models Models Choosing

= .00490


Not bad for a single element!

= 2403 psiMost meshers automatically create these instead of TET4 elements!

Wrapping Up Wrapping Up Wrapping Up Not great, but not terrible

1-77-Nastran


www.NEiSoftware.com

s ng e e emen s goo or sp acemen , u more are nee e or s ress



103/130

And with lots of them Introduction Introduction Introduction FEA Process FEA Process FEA Process An Example An Example An Example Complicated Complicated Complicated Models Models Models Choosing

= .00501=


This is a very good answer, but it required 4129 grids!!!


1-77-Nastran


www.NEiSoftware.com



104/130

A fine mesh cures many ills Introduction Introduction Introduction FEA Process FEA Process FEA Process

It takes a lot of tets to get the right answer Parabolic tets can help a lot, especially for

An Example An Example An Example Complicated Complicated Complicated Models Models Models Choosing

distorted geometries and places where youare forced into tets


,

but still give bad stresses Its ust hard to et ood stresses be


1-77-Nastran


www.NEiSoftware.com wary!



105/130

One last conclusion: Introduction Introduction Introduction FEA Process FEA Process FEA Process The structure looked like a beam The beam model ave the best

An Example An Example An Example Complicated Complicated Complicated Models Models Models Choosing Choosing Choosing

answers with the fewest numberof elements

Elements Elements Elements Interpreting Results FEM Codes FEM Codes FEM Codes Wrapping Up Wrapping Up Wrapping Up

1-77-Nastran


www.NEiSoftware.com



106/130

Now lets revisit step 7, getting Introduction Introduction Introduction FEA Process FEA Process FEA Process results FEM codes really only calculate Gauss


Nastran has no mechanism to get the GaussPoint stresses

Elements Elements Elements Interpreting Results FEM Codes FEM Codes FEM Codes

Nastran interpolates to get centroid values

Nastran extrapolates to get element cornerresults


1-77-Nastran


www.NEiSoftware.com T hese are not Nodal stresses they are

calculated by each element for its own nodes



107/130

Post-Processors plot nodal results Introduction Introduction Introduction FEA Process FEA Process FEA Process The extrapolation usually produces

different values from different


elements for the same nodes Element results therefore must be


single value for the plot Consider this example


1-77-Nastran


www.NEiSoftware.com



108/130

This is a t ical element Introduction Introduction Introduction FEA Process FEA Process FEA Process N4 N3

G4 G3


Centroid Elements Elements Elements Interpreting Results FEM Codes FEM Codes FEM Codes

N1 N2

G2 Wrapping Up Wrapping Up Wrapping Up

1-77-Nastran


www.NEiSoftware.com



109/130

Results are re orted at element Introduction Introduction Introduction FEA Process FEA Process FEA Process corners and centroids like this:

100 90


80

G4 G3 Elements Elements Elements Interpreting Results FEM Codes FEM Codes FEM Codes

G1 G2


1-77-Nastran


www.NEiSoftware.com 70 60



110/130

Consider another element connected Introduction Introduction Introduction FEA Process FEA Process FEA Process to this element:

100 90 110 125


80

G4 G3

95

G4 G3 Elements Elements Elements Interpreting Results FEM Codes FEM Codes FEM Codes

G1 G2G1 G2


1-77-Nastran


www.NEiSoftware.com 70 60 65 80



111/130

And at the connected nodes, the Introduction Introduction Introduction FEA Process FEA Process FEA Process elements have differentanswers!


This is typical (and not necessarilywrong)


processor, it is necessary to comeup with some best guess


1-77-Nastran


www.NEiSoftware.com



112/130

Some t ical wa s to do this: Introduction Introduction Introduction FEA Process FEA Process FEA Process Average the connected elements

110+100/2 = 105


Most common default method Stress Averaging


Pick the largest Max(110,100) = 110


1-77-Nastran


www.NEiSoftware.com



113/130

This is fine as long as the elements Introduction Introduction Introduction FEA Process FEA Process FEA Process are the same thickness and that theresults are something that makes


v x But if they are different?



1-77-Nastran


www.NEiSoftware.com



114/130

A beam made from plates of twoIntroduction Introduction Introduction FEA Process FEA Process FEA Process

t c nesses: An Example An Example An Example Complicated Complicated Complicated Models Models Models Choosing Choosing Choosing


this:


1-77-Nastran


www.NEiSoftware.com


115/130



116/130

The moral of the stor isIntroduction Introduction Introduction FEA Process FEA Process FEA Process

Be careful with what you plot Smooth contours look nice but may


hide high stresses Elements Elements Elements Interpreting Results FEM Codes FEM Codes FEM Codes Wrapping Up Wrapping Up Wrapping Up

1-77-Nastran


www.NEiSoftware.com



117/130

Look at the real element results! Dont avera e ad acent elements es eciall if the


are different thicknesses or materials An Example An Example An Example Complicated Complicated Complicated Models Models Models Choosing Choosing Choosing

Elements Elements Elements Interpreting Results FEM Codes FEM Codes FEM Codes Wrapping Up Wrapping Up Wrapping Up

1-77-Nastran


www.NEiSoftware.com



118/130

Not all FEM Codes are created equallyIntroduction Introduction Introduction FEA Process FEA Process FEA Process

Linear codes optimized for infinitesimal

displacements


[K] changes during solution Implicit codes statics, build and solve [K] -1

Elements Elements Elements Interpreting Interpreting Interpreting Results Results Results FEM Codes , e ,

Eulerian codes for fluids (constant volume) Thermal codes heat transfer


1-77-NastranNEi Sensitive/Proprietary

www.NEiSoftware.com



119/130

Infinitesimal displacementsIntroduction Introduction Introduction FEA Process FEA Process FEA Process

e mo on o e no e sinconsequential to the solution of theproblem


Large displacements The motion of the nodes changes the

Elements Elements Elements Interpreting Interpreting Interpreting Results Results Results FEM Codes

so u on

Example fixed-fixed beam Bouncing ball



www.NEiSoftware.com on ac



120/130

Cantilever beamIntroduction Introduction Introduction FEA Process FEA Process FEA Process An Example An Example An Example Complicated Complicated Complicated Models Models Models Choosing Choosing Choosing

Tip motion does not affect root loadsignificantly for small displacements


ect s proport ona to s n t eta

=~ 0 for small deflections (


121/130

Fixed-Fixed Beam Introduction Introduction Introduction

FEA Process FEA Process FEA Process An Example An Example An Example Complicated Complicated Complicated Models Models Models Choosing Choosing Choosing

Initially no bending, no axial load all shear Once center deflects, bending and axial loads

appear and grow


Becomes primary load path!

Motion of the beam center affects the responsessignificantly



www.NEiSoftware.com

An ID code will not show this effect!



122/130

Linear Most FEM codesIntroduction Introduction Introduction FEA Process FEA Process FEA Process

including NEi Nastran do this) Stiffness matrix sta s the same for


the entire solution Single unique static solution


Loads can be applied in any order

Unique steps for other solutions



www.NEiSoftware.com

, ,


123/130



124/130

Implicit (NEi Nastran or NEi Fusion)Introduction Introduction Introduction FEA Process FEA Process FEA Process

u s ness an mass ma r ces assem e ansolved

Variety of solutions


, ,

Explicit (NEI Explicit for example) Solved at element level no big matrices


n y trans ent so ut on ava a e

Good for highly nonlinear problems Good for very large models



www.NEiSoftware.com



125/130

In general, the finite element method Introduction Introduction Introduction

FEA Process FEA Process FEA Process described by partial differentialequations


Thermal Analysis

Fluid flow/wave propagation

Elements Elements Elements Interpreting Interpreting Interpreting Results Results Results FEM Codes FEM Codes FEM Codes

Electromagnetic

Dynamics

Wrapping Up


www.NEiSoftware.com



126/130

Example: Steady-state heat conductionIntroduction Introduction Introduction FEA Process FEA Process FEA Process

Replace the structural stiffness matrix withthe matrix of thermal conductivities


= ,conductivity and T is temperature

Single DOF at each node (temperature)

Elements Elements Elements Interpreting Interpreting Interpreting Results Results Results Wrapping Up

This is why most FEM codes also do thermalproblems!


www.NEiSoftware.com



127/130

K. J. Bathe

Finite Element Procedures in Engineering AnalysisIntroduction Introduction Introduction FEA Process FEA Process FEA Process

ren ce- a , R. D. Cook

Concepts and Applications of Finite Element AnalysisJohn Wiley & Sons, 1989


Harry G. ShaefferMSC/NASTRAN PRIMER, 1998

Richard H. MacNeal


O. C. Zienkiewicz

The Finite Element MethodMcGraw-Hill, 1994


www.NEiSoftware.com J.N. Reddy

An Introduction to the Finite Element MethodMcGraw-Hill, 1984



128/130

Now you should be somewhatIntroduction Introduction Introduction FEA Process FEA Process FEA Process

familiar with some FEM buzzwords: Gauss Points


Shape Functions Continuity


Large Displacements


www.NEiSoftware.com


129/130


130/130

Documents

Basic FEM Webinar 2011