7 FEM Modeling: Mesh, Loads and BCs IFEM Ch 7 Slide 1 - - PDF document

Introduction to FEM

7

FEM Modeling: Mesh, Loads and BCs

IFEM Ch 7 – Slide 1

Topics in Chapter 7

General Modeling Rules Finite Element Mesh Layouts Distributed Loads NbN Lumping EbE Lumping Displacement BCs

suppressing rigid body motions taking advantage of symmetry and antisymmetry

Introduction to FEM

IFEM Ch 7 – Slide 2

General FEM Modeling Rules

• Use the simplest elements that will do the job
• Never, never, never use complicated or

special elements unless you are absolutely sure of what you are doing

• Use the coarsest mesh that will capture the

dominant behavior of the physical model, particularly in design situations

3 word summary: Keep It Simple

Introduction to FEM

IFEM Ch 7 – Slide 3

Another Justification for Simplicity

In product design situations several FEM models of increasing refinement will be set up as design evolves Ergo, do not overkill at the beginning

Introduction to FEM

IFEM Ch 7 – Slide 4

Where Finer Meshes Should be Used

Introduction to FEM

Cutouts Cracks entrant corners Vicinity of concentrated (point) loads, and sharp contact areas Load transfer (bonded joints, welds, anchors, reinforcing bars, etc.) Abrupt thickness changes Material interfaces weld

IFEM Ch 7 – Slide 5

Avoid 2D/3D Elements of Bad Aspect Ratio

Good Bad

Introduction to FEM

IFEM Ch 7 – Slide 6

Elements Must Not Cross Interfaces

Introduction to FEM

No Physical interface OK

IFEM Ch 7 – Slide 7

Element Geometry Preferences

Other things being equal, prefer in 2D: Quadrilaterals over Triangles in 3D: Bricks over Wedges Wedges over Tetrahedra

(Elements do not file discrimination suits)

Introduction to FEM

IFEM Ch 7 – Slide 8

Node by Node (NbN) Distributed Load Lumping

Introduction to FEM

Finite element mesh Distributed load intensity (load acts downward on boundary) Boundary

• Nodal force f at 3 is set to P, the

magnitude of the crosshatched area under the load curve. This area extends halfway over adjacent element sides

3

f = P

3

1 2 3 4 5 6

IFEM Ch 7 – Slide 9

Element by Element (EbE) Distributed Load Lumping

Introduction to FEM

Force P has magnitude of crosshatched area under load curve and acts at its centroid Distributed load intensity (load acts downward on boundary)

• e

e e e

e

P

centroid C of crosshatched area

P C 3

a b L =a+b

Details of element-level force computations

2

e

f = (b/L )P

e

3

f = (a/L )P

Finite element mesh

1 2 3 4 5 6 f2 f e

3

Boundary

2

IFEM Ch 7 – Slide 10

EbE Shortcut for Linearly Varying Line Load (Bypasses Centroid Calculation)

Introduction to FEM

• j

i

e

L

i

q

j

q

e

i i j

e

f = (2q +q ) L

6

e

j i j

e

f = (q +2q ) L

6 e

IFEM Ch 7 – Slide 11

Boundary Conditions (BCs)

The most difficult topic for FEM program users Two types Essential Natural

  

Introduction to FEM

IFEM Ch 7 – Slide 12

Introduction to FEM

Boundary Conditions Essential vs. Natural

• 1. If a BC involves one or more DOF in a

direct way, it is essential and goes to the Left Hand Side (LHS) of Ku = f

• 2. Otherwise it is natural and goes to the

Right Hand Side (RHS) of Ku = f Recipe:

IFEM Ch 7 – Slide 13

Minimum Support Conditions to Suppress Rigid Body Motions in 2D

Introduction to FEM

• A

B

• A

B x x y y

(b)

• A

B

(c) (a)

IFEM Ch 7 – Slide 14

Minimum Support Conditions to Supress Rigid Body Motions in 3D

• A

B x y z C D

• Introduction to FEM

IFEM Ch 7 – Slide 15

Visualizing Symmetry and Antisymmetry Conditions in 2D

Introduction to FEM

A' A' A A" A A" Symmetry line Antisymmetry line (a) (b) displacement vectors loads

IFEM Ch 7 – Slide 16

Example of Application of Symmetry BCs

y x

A A B B C C D D (a) (b)

• Introduction to FEM

IFEM Ch 7 – Slide 17

Example of Application of Antisymmetry BCs

y x

A A B B C C D D (a) (b)

• Vertical (y) motion of one

node such as C or D may be constrained to suppress y-RBM

Introduction to FEM

IFEM Ch 7 – Slide 18

"Breaking Up" Point Loads at Symmetry BCs

y x A B C D

(a) (b) (c)

Introduction to FEM

P P P/2

• P/2

P/2 P/2 P/2

IFEM Ch 7 – Slide 19

"Breaking Up" Point Loads at Antisymmetry BCs

y x A B C D

Introduction to FEM

P P/2 P/2 P 2P

• (A trickier problem)

IFEM Ch 7 – Slide 20