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

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Example Also, for plane strain strain conditions the constitutive tensor is: ⎡ 1 ν 0 C = E ⎢ ν 1 0 1 − ν 2 ⎣ 1 − ν 0 0 2 ⎤ ⎡ E=5000,ν=0.3 ⎥ ⎢ ⎦ → ⎣ 6731 2885 0 2885 6731 0 0 0 1923 Now, using the assumption of small strain we can use the above constitutive tensor for the relationship between the PK2 stress and the Green-Lagrange strain. Hence from Eqn (1): ⎡ ⎢ ⎣ S 11 S 22 S 12 ⎤ ⎡ ⎥ ⎢ ⎦ = ⎣ 5770t 2 13462t 2 3846t ⎤ ⎥ ⎦ ⎤ ⎥ ⎦ Institute of Structural Engineering Method of Finite Elements II 14
Example Then, the Cauchy stress at time t can be obtained from the PK2 stress as (Lecture 4): t ρ t 0 ρ t τ = 0X t 0S t 0X T ⇒ ⎡ ⎤ ⎡ τ 11 21000t 2 + 54000t 4 ⎤ ⎢ ⎥ ⎢ ⎣ τ 22 ⎦ = ⎣ 13000t 2 ⎥ ⎦ τ 12 3800t + 27000t 3 Institute of Structural Engineering Method of Finite Elements II 15
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: Example Therefore, we ultimately ha
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 and 36: Contact Conditions Usual term Cont
Page 37 and 38: Definitions used in Contact Analysi
Page 39 and 40: Contact Analysis-Interface Conditio
Page 41 and 42: Contact Analysis Complexities In th

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