PSI - Issue 6

V.A. Meleshko / Procedia Structural Integrity 6 (2017) 115–121 Meleshko V.A./ StructuralIntegrity Procedia 00 (2017) 000–000

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Appendix B. Program nonlinear analysis of a cantilever rod

:=

ε 10 0 ← x 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 ( ) T ←

KONSOL(n)

i 0 n ∈ .. for

ε ε s

←

τ

k 0 10 ∈ .. for

←

T

σ s b ⋅ h 3 ⋅ 2 2 ⋅ ε s ⋅ σ s b ⋅ h 3 ⋅ 2 2 ⋅ ε s ⋅

1 3 τ k ( ) ⋅

τ k ( )

 

 

 

 

3 1 −

  

  

←

⋅

1 a1 ⋅ +

τ k

1 >

if

T1 k

3

1 3

⋅

otherwise

T1

←

∆ M

k 0 10 ∈ .. for

k

0 k x k F ⋅ ( ) ∑ =

∆ M1 k

←

∆ M1

∆ M T ← ∆ε ∆χ , ←

h

∆χ

⋅

2

ε ← ε + ∆ε , χ ← χ + ∆χ σ σ EPL ⋅∆ε + τ k if σ E + ⋅∆ε otherwise ←

1 >

←

k 0 10 ∈ .. for

∆

10 ∑ =

χ m 1 − χ m + 2

  

  

m 1 − k − ( ) Φ m 1 − 1.01k − ( ) ⋅ [

m k − ( ) Φ m 1.01k − ( ) ⋅ +

]

←

∆ 1 k

0.1 ⋅ ⋅

0.1 ⋅

2

m

1

∆ 1

← k 0 10 ∈ .. for

θ

←

x , ←

k 0 10 ∈ .. for

cos θ k ( ) 0.1 ⋅ k 0 > if 0 otherwise

x1 k

10 ∑ =

χ m 1 − χ m + 2

  

  

Φ m 1.01k − ( ) 1 ⋅

θ 1 k

0.1 ⋅

←

m

1

x1

θ 1

T χ ε σ ∆ M ∆ θ x ( ) T

T –section stiffness; χ – curvature; ε –deformation ; σ – stress; ∆ M – increment of bending moment; ∆ – displacement; θ – rotation angle ; x – length of the integration section.

Stress

Displacement

1.2 10 9 × 1.6 10 9 × 2 10 9 ×

0.1 0.2 0.3 0.4 0.5

KONSOL(n) 3 ( ) k

KONSOL(n) 5 ( ) k

4 10 8 × 8 10 8 ×

0 1 2 3 4 5 6 7 8 9 10 0

0 1 2 3 4 5 6 7 8 9 10 0

k

k