1

NONLINEAR ANALYSIS

[ ]K const

2

SOURCES OF NON LINEAR BEHAVIOUR

non-linear supportscontact stresstension/compression only linkselastic foundation

offset or eccentric loadsloads causing the loss of elastic stability (buckling)

geometric non-linearitydisplacements of the structure significantly changes structure's stiffness

material non-linearitystresses exceed elastic limits so stress is no longer proportional to strain

combinedlarge displacements causing plastic flowcrash analysismetal stamping…

3

Non linear supports analysis

EXAMPLES OF NON-LINEAR PROBLEMS

4

cranepotential buckling

stamped steel pulleypotential buckling

angle under bending loadpotential buckling

plate under compressive off-center load; potential buckling

domepotential buckling

Buckling

EXAMPLES OF NON-LINEAR PROBLEMS

5

NL002.SLDPRT

6

NL002.SLDPRT

Linear solution Non-linear solution

7

ROUND PLATE.SLDPRT

8

9Displacement of the center of membrane as function of applied pressure for linear and nonlinear model.

0

5

10

15

20

25

0 50 100 150 200 250 300

Pressure [Pa]

Max

. dis

plac

emen

t [m

m]

nonlinearlinear

Δ F

Δ d

1 cottan

Fkd

10

link 02.SLDPRT

11

Linear solution Non-linear solution

link 02.SLDPRT

12

Horizontal reaction -7.7N

Non-linear solutionLinear solution

Horizontal reaction 3300N

13Chapter 5

14

Fixed support

Sliding support

1,200N normal load to shaded face

NL001 FLAT BEAM

model file NL001model type solidmaterial alloy steelrestraintst built-in to left end

sliding to right end load 1,200 N normal force to top face

objectives• calculate maximum displacement• calculate horizontal displacement of the sliding end • compare linear and non-linear displacement solution

Fixed support

Sliding support

15

ec019.SLDPRT

QUESTION: why does shaft grow in diameter and lugs stretch?

16square hole.SLDPRT

QUESTION: why does hole grow in size. Is there something wrong with the code?

17

This corner must travel along a straight line that is perpendicular to the radius so after deformation it will be here

The same applies to the other three corners. The combined effect gives the illusion of square growing in size even though it is “frozen” in size by rigid links.

Square after deformation

Square before deformation