The Finite Element Method for the Analysis of Non-Linear and ...

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Definitions used in Contact Analysis Let t f IJ : vector of contact surface traction on body I due to contact with body J then t f IJ = − t f JI . Hence, the virtual work due to the contact traction can be written: ∫ δu I S IJ i fi IJ dS IJ + ∫ δu J S IJ i fi JI dS JI = ∫ δu IJ S IJ i fi IJ dS IJ where where δu IJ i = δu I i − δu J i We call the pair of surfaces S IJ , S IJ a contact surface pair. S IJ is named the ”contactor surface” and S JI is named the ”target surface” Hence, the right hand side of the previous eqn represents the virtual work of the contact tractions over the relative virtual displacements δu I i , δuJ i Institute of Structural Engineering Method of Finite Elements II 36
Definitions used in Contact Analysis Institute of Structural Engineering Method of Finite Elements II 37
Page 1 and 2: The Finite Element Method for the A
Page 3 and 4: Constitutive Relations It is necess
Page 5 and 6: Solution Flowchart General Solution
Page 7 and 8: Elastic Material For an elastic mat
Page 9 and 10: Elastic Material Important Note “
Page 11 and 12: Example Consider the four node elem
Page 13 and 14: Example Therefore, we ultimately ha
Page 15 and 16: Example Then, the Cauchy stress at
Page 17 and 18: Example The Jaumann stress is conne
Page 19 and 20: Hyperelastic Material Hyperelastic
Page 21 and 22: Inelasticity Elastoplasticity, Cree
Page 23 and 24: Elastoplasticity The strain and str
Page 25 and 26: Elastoplasticity Isotropic & Kinema
Page 27 and 28: Thermoelastoplasticity and Creep Th
Page 29 and 30: Relaxation A relaxation test is def
Page 31 and 32: Viscoplasticity The elastic respons
Page 33 and 34: NL FE Special Considerations - The
Page 35: Contact Conditions Usual term Cont
Page 39 and 40: Contact Analysis-Interface Conditio
Page 41 and 42: Contact Analysis Complexities In th

The Finite Element Method for the Analysis of Non-Linear and ...

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