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Introduction to Contact Mechanics
Contact problems: roller bearing and impact of a lorry.
Introduction to Contact Mechanics
Sheet metal forming Crash of a car against a deformable barrier
Introduction to Contact Mechanics
Self-contact of a car component during crash,
Crash of a car against a deformable barrier
Introduction to Contact Mechanics
Contact of tyres with a road surface,
Introduction to Contact Mechanics
Contact in a Mass Spring System
Energy of the mass spring systemPoint mass supported by spring
Contact in a Mass Spring System
The Energy of system
The variation of Energy
The second variation of Π
The minimum of u
The restriction of the motion of the mass by a rigid support
Contact in a Mass Spring System
the point mass contacts the rigid surface, a reaction force RN appears.
two cases within a contact problem
Both cases can be combined
Kuhn–Tucker condition
Contact in a Mass Spring System
Lagrange multiplier method
the Lagrange multiplier method adds to the energy of the system a term which contains the constraint
the Lagrange multiplier λ is equivalent to the reaction force RN .
for contact: u = h
for does not contact: RN =0
u=mg/k
Contact in a Mass Spring System
Penalty method
or an active constraint one adds a penalty term to the energy
the solution
penalty spring due to the penalty term
The variation of the energy
Contact in a Mass Spring System
Penalty method
in the contact,
The reaction force
Penetration of the point mass into the rigid support occurs.
the unconstrained solution.
the correct solution obtained with the Lagrangemultiplier method.
Finite Element Analysis of the Contact of Two Bars
Lagrange method
F
Finite Element Analysis of the Contact of Two Bars
Lagrange method
Finite Element Analysis of the Contact of Two Bars
Lagrange method
Finite Element Analysis of the Contact of Two Bars
Lagrange method
Finite Element Analysis of the Contact of Two Bars
Lagrange method
Finite Element Analysis of the Contact of Two Bars
Penalty method
1
2
3
2 0
0
u FEA EAl l
u gEA EAl l
EAl u g
εε ε
ε εε
− − + − = − + −
2 2
2
3
EA EAF g Fl luEA EAl l
ε
ε
+ + =
+
ε →∞
2
21 23 3
EA g F Fllu gEA EAl
+ = = +
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