Q T K d f = Q 0 0 N N Q i T - - PowerPoint PPT Presentation

q t k d f q 0 0 n n q i t
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Q T K d f = Q 0 0 N N Q i T - - PowerPoint PPT Presentation

Center for Simulation of Advanced Rockets Parallel Solver for Multilayered Structures - FETI Refined Mindlin-Reissner theory u 3 x 3 = x Mindlin kinematic assumptions 3 x 2 x u 2 2 2 u i U i 1 ( x 1 , x 2 ) + x i 3 i 1 ( x 1


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SLIDE 1

Center for Simulation of Advanced Rockets

Parallel Solver for Multilayered Structures - FETI

Refined Mindlin-Reissner theory

h h a b

i

x2 x1 x3

3

x = φ

2

u

2

x

N i 2 1

ψ u3 x1 u1 φ1

2

  • Mindlin kinematic assumptions

ui

1(x1, x2, x3)

= U i

1(x1, x2) + xi 3φi 2(x1, x2)

ui

2(x1, x2, x3)

= U i

2(x1, x2) − xi 3φi 1(x1, x2)

ui

3(x1, x2, x3)

= U i

3(x1, x2),

i = 1, 2, ....N

  • Interface continuity conditions
  • System of equations

  K QT Q     d λ   =   f  

N

  • i=1

Qi Ki−1 QiT λ =

N

  • i=1

Qi Ki−1f i

  • K. Matouˇ

s, J. Kruis and Z. Dost´ al

University of Illinois at Urbana-Champaign

48

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SLIDE 2

Center for Simulation of Advanced Rockets

Numerical examples T-50 graphite : EL = 386.4 GPa

ET = 7.6 GPa GL = 15.2 GPa GT = 2.6 GPa ν = 0.41

6061 Aluminum : E = 72.5 GPa

G = 27.3 GPa ν = 0.33 a = 1.500 m, h = 0.027 m hi = 4.5 mm, layup [0, 60, 90]s

  • 6 CPUs

a a x 1 c h p3 x 2

Convergence behavior

40000 80000 120000 160000 200000 240000

Number of degrees of freedom 20

40 60 80 100

120

140

Number of iterations

5x5 10x10

20x20 30x30

40x40 50x50 60x60

70x70

University of Illinois at Urbana-Champaign

49

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SLIDE 3

Center for Simulation of Advanced Rockets

General domain

hi = 5.0 mm, layup [0, 90, +45, −45, 90, 0], 6 CPUs

Convergence behavior

200000 400000 600000 800000 1000000 1200000

Number of degrees of freedom

40 80

120

160

200 240

Number of iterations

Nel = 712

Nel = 10062 Nel = 40589 Nel = 50366

University of Illinois at Urbana-Champaign

50