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 φ x u 2 2 2 u i U i 1 ( x 1 , x 2 ) + x i 3 φ i ψ 1 ( x 1 , x 2 , x 3 ) = 2 ( x 1 , x 2 ) x 1 N a i h i h 2 u i U i 2 ( x 1 , x 2 ) − x i 3 φ i 2 ( x 1 , x 2 , x 3 ) = 1 ( x 1 , x 2 ) 1 x 1 b u 1 φ 1 u i U i 3 ( x 1 , x 2 , x 3 ) = 3 ( x 1 , x 2 ) , i = 1 , 2 , ....N • Interface continuity conditions • System of equations       Q T  K  d  f  =   Q λ 0 0 N N Q i � T λ = K i � − 1 � K i � − 1 f i � � Q i � Q i � i =1 i =1 • K. Matouˇ s, J. Kruis and Z. Dost´ al 48 University of Illinois at Urbana-Champaign

Center for Simulation of Advanced Rockets Numerical examples x 2 c a T-50 graphite : E L = 386 . 4 GPa E T = 7 . 6 GPa x 1 p3 G L = 15 . 2 GPa h G T = 2 . 6 GPa a Convergence behavior ν = 0 . 41 6061 Aluminum : E = 72 . 5 GPa 140 70x70 60x60 50x50 G = 27 . 3 GPa 120 40x40 ν = 0 . 33 100 Number of iterations 30x30 80 20x20 a = 1 . 500 m , h = 0 . 027 m 60 h i = 4 . 5 mm , layup [0 , 60 , 90] s 40 10x10 5x5 20 • 6 CPUs 0 40000 80000 120000 160000 200000 240000 Number of degrees of freedom 49 University of Illinois at Urbana-Champaign

Center for Simulation of Advanced Rockets General domain Convergence behavior 240 Nel = 50366 Nel = 40589 200 Nel = 10062 Number of iterations 160 Nel = 712 120 80 40 0 0 200000 400000 600000 800000 1000000 1200000 Number of degrees of freedom h i = 5 . 0 mm , layup [0 , 90 , +45 , − 45 , 90 , 0] , 6 CPUs 50 University of Illinois at Urbana-Champaign