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

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Types of Response Diagrams Complex Types R U Institute of Structural Engineering Method of Finite Elements II 22
Solution Algorithms for NL equations Root finding for single variable NL problems f (x) = 0 Bisection Method Fixed Point Iteration Assumption: f [a, b] ∈ R and continuous If f (a) > 0, f (b) < 0 ⇒ a ≤ ¯x ≤ b ⇒ f (¯x) = 0 Write f (x) = 0 in the form f (x) = x − q(x), the solution ¯x satisfies ¯x = q(¯x) Recurrence relation: x k+1 = g(x k ) Convergence: If g ′ (x) is defined over [a, b] and a positive constant K exists with |ġ(x)| ≤ K, ∀x ∈ [a, b] then g(x) has a unique fixed point ¯x ∈ [a, b]. Institute of Structural Engineering Method of Finite Elements II 23
Page 1 and 2: The Finite Element Method for the A
Page 3 and 4: Non Linear FE - Background and Moti
Page 11 and 12: Introduction to Nonlinear analysis
Page 13 and 14: Introduction to Nonlinear analysis
Page 15 and 16: Introduction Swiss to Federal Nonli
Page 17 and 18: Example: Simple Bar Structure Area
Page 19 and 20: Example: Simple Bar Structure Secti
Page 21: Types of Response Diagrams Basic Ty
Page 25 and 26: Incremental Analysis The basic appr
Page 27 and 28: Incremental Analysis We may use the
Page 29 and 30: Simple Bar Example - Revisited t t
Page 31 and 32: Simple Bar Example - Revisited Load

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

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