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

Solution Flowchart
General Solution process in incremental nonlinear FE
Known Solution at t:
Stresses
t σ, strains t ε,
Internal material parameters t κ
Known Quantities at iterations i- 1 :
Nodal Displacements at first Iteration:
and hence
Element strains
t+Δt
ε i−1
t+Δt
U i−1
Calculate at t+ Δt:
t+Δt
Stresses σ i−1
Repat till Convergence
Tangent stress strain matrix C i−1
Internal material parameters
t+Δt
κ i−1
• Elastic Analysis: directly obtain
t+Δt
t+Δt
σ i−1 , C i−1 from ε i−1
• Inelastic Analysis: Integrate to get
t+Δt
σ i−1
t t+Δti−1
= σ + ∫ dσ
t
Calculate:
Incremental Displacement Vector ΔU i:
t+Δt
K i−1 ΔU i =
Then,
t+Δt
R
−
t+Δt
F i−1
t+Δt t+Δt
U i = U i−1 +
ΔU i
Institute of Structural Engineering Method of Finite Elements II 5