Higher-Order Finite-Element Analysis for Fuzes Subjected to High-Frequency Environments

Transcription

1 Higher-Order Finite-Element Analysis for Fuzes Subjected to High-Frequency Environments Stephen Beissel Southwest Research Institute (210) Presented at: The 60 th Annual Fuze Conference 9-11 May, 2017 Cincinnati, OH Approved for Public Release 1

2 Outline Background Comparison of first-order and higher-order elements in explicit solid dynamics Finite-deformation plasticity Wave propagation Summary and Conclusions 2

3 Background Fuze components subjected to high-frequency waves steel case Al housing Reflections disrupt wave front fuze circuit boards electronics Impact generates wave front potting target 3

4 Background Lagrangian finite-element codes are industry standard for analysis of wave propagation Explicit time integration by central differences First-order elements Computations often can t resolve high-frequency modes, resulting in spurious oscillations (Gibbs phenomenon) Artificial viscosity damps oscillations and high-frequency modes Objective is to improve the accuracy of Lagrangian computations of wave propagation Systematic survey of numerical methods uncovered advantages of higher-order ( > 2 nd order) elements Higher-Order elements formulated and added to the EPIC code 4

5 Background Higher-order elements used successfully for years in CFD Higher-order elements not used for solid mechanics because: Computational efficiency of explicit schemes historically equated to minimizing the floating-point operations (FLOPS) in evaluation of internal-force term, and FLOPs increase with element order. Greater complexity of curved-surface contact algorithms Decades of research invested in various formulaic tradeoffs between locking and zero-energy modes of first-order elements Mass lumping of 2 nd -order serendipity elements yields vertex nodes with zero or negative: Masses Nodal forces due to uniform external traction Lack of meshing and visualization software for higher orders 5

6 Finite-deformation plasticity Square copper rod impacting a rigid surface at 200 m/s plastic strain symmetric order-1 tetrahedra non-symmetric order-1 tetrahedra order-1 hexahedra (Flanagan-Belytschko) 6

7 Finite-deformation plasticity Square copper rod impacting a rigid surface at 200 m/s plastic strain order-2 hexahedra order-3 hexahedra order-4 hexahedra 7

8 Finite-deformation plasticity No volumetric locking 8

9 Wave propagation in 2-D axisymmetry Baseline mesh of simple part loaded by a pulse monitored node near top 16 cm element size: 1x1 cm monitored node in base 4340 steel: c 1 = 5845 m/s c 2 = 4451 m/s 7 cm 5 m/s v z t pulse 2 ms t 9

10 Wave propagation in 2-D axisymmetry t = 5 µs 10 µs 15 µs 20 µs 25 µs 30 µs 35 µs 40 µs 45 µs 50 µs 55 µs 60 µs 65 µs 70 µs 75 µs 80 µs 85 µs 90 µs 95 µs 100 µs 10

11 Wave propagation in 2-D axisymmetry Velocities of node in base at equal mesh refinement 11

12 Wave propagation in 2-D axisymmetry Velocities of node in base at equal mesh refinement 12

13 Wave propagation in 2-D axisymmetry Velocities of node in base at equal mesh refinement 13

14 Wave propagation in 2-D axisymmetry Summary of errors at node in base (0-12 µs) 5x 10x 20x order = 5 40x 80x

15 Wave propagation in 2-D axisymmetry Convergence of top-node velocity with element order 15

16 Wave propagation in 2-D axisymmetry Convergence of top-node velocity with element order 16

17 Wave propagation in 2-D axisymmetry Convergence of top-node velocity with element order 17

18 Wave propagation in 2-D axisymmetry Convergence of top-node velocity with element order 18

19 Wave propagation in 2-D axisymmetry Convergence of top-node velocity with element order 19

20 Wave propagation in 2-D axisymmetry Convergence of top-node velocity with refinement of first-order quads 20

21 Wave propagation in 2-D axisymmetry Convergence of top-node velocity with refinement of first-order quads 21

22 Wave propagation in 2-D axisymmetry Convergence of top-node velocity with refinement of first-order quads 22

23 Wave propagation in 2-D axisymmetry Convergence of top-node velocity with refinement of first-order quads 23

24 Wave propagation in 2-D axisymmetry Convergence of top-node velocity with refinement of first-order quads 24

25 Wave propagation in 2-D axisymmetry Convergence of top-node velocity with refinement of first-order quads 25

26 Wave propagation in 2-D axisymmetry Convergence of top-node velocity with refinement of first-order quads 26

27 Wave propagation in 2-D axisymmetry Convergence of top-node velocity with refinement of first-order quads 27

28 Wave propagation in 2-D axisymmetry Convergence of top-node velocity with refinement of first-order triangles 28

29 Wave propagation in 2-D axisymmetry Convergence of top-node velocity with refinement of first-order triangles 29

30 Wave propagation in 2-D axisymmetry Convergence of top-node velocity with refinement of first-order triangles 30

31 Wave propagation in 2-D axisymmetry Convergence of top-node velocity with refinement of first-order triangles 31

32 Wave propagation in 2-D axisymmetry Convergence of top-node velocity with refinement of first-order triangles 32

33 Wave propagation in 2-D axisymmetry Convergence of top-node velocity with refinement of first-order triangles 33

34 Wave propagation in 2-D axisymmetry Convergence of top-node velocity with refinement of first-order triangles 34

35 Wave propagation in 2-D axisymmetry Comparison of velocity convergence with order and refinement 35

36 Wave propagation in 2-D axisymmetry Comparison of velocity convergence with order and refinement 36

37 Wave propagation in 2-D axisymmetry Comparison of velocity convergence with order and refinement 37

38 Wave propagation in 2-D axisymmetry Comparison of velocity convergence with order and refinement 38

39 (1) Wave propagation in 2-D axisymmetry Summary of errors in velocity at node near top 3x first-order quads 5x 3x 10x 7x 4x 15x 8x first-order triangles order = 3 20x 30x 12x 15x higher-order elements 4 40x 20x 5 80x 40x (1) Errors relative to data from 20 th - order elements for t = µs 39

40 (1) Wave propagation in 2-D axisymmetry Summary of errors in velocity at node near top 3x 3x 5x 4x 7x 10x 3 8x 15x 4 12x 20x order = x 10 30x (2) 20x (1) Errors relative to data from 20 th - order elements for t = µs (2) Intel Core i7: 2.93 GHz 15 GB RAM 40

41 (1) Wave propagation in 2-D axisymmetry Summary of errors in velocity at node near top 8x 3 15x 20x 12x 4 15x 30x order = 5 20x 40x (1) Errors relative to data from 20 th - order elements for t = µs 41

42 Wave propagation in 3D Baseline mesh of simple part loaded by a pulse monitored node (same location as 2D) mesh on plane of symmetry identical to 2-D mesh 5 m/s v z t v z t model differs from 2D due to facets along hoop direction 2 ms t 42

43 Wave propagation in 3D Comparison of 2-D and 3-D node velocities 43

44 Wave propagation in 3D Convergence of top-node velocity with element order 44

45 Wave propagation in 3D Convergence of top-node velocity with element order 45

46 Wave propagation in 3D Convergence of top-node velocity with element order 46

47 Wave propagation in 3D Convergence of top-node velocity with element order 47

48 Wave propagation in 3D Convergence of top-node velocity with refinement of first-order hexes 48

49 Wave propagation in 3D Convergence of top-node velocity with refinement of first-order hexes 49

50 Wave propagation in 3D Convergence of top-node velocity with refinement of first-order hexes 50

51 Wave propagation in 3D Convergence of top-node velocity with refinement of first-order hexes 51

52 Wave propagation in 3D Convergence of top-node velocity with refinement of first-order hexes 52

53 Wave propagation in 3D Convergence of top-node velocity with refinement of first-order hexes 53

54 Wave propagation in 3D Convergence of top-node velocity with refinement of first-order hexes 54

55 Wave propagation in 3D Convergence of top-node velocity with refinement of first-order hexes 55

56 Wave propagation in 3D Comparison of convergence with order and refinement 56

57 Wave propagation in 3D Comparison of convergence with order and refinement 57

58 Wave propagation in 3D Comparison of convergence with order and refinement 58

59 (1) Wave propagation in 3D Summary of velocity errors at monitored node 3x first-order hexahedra 7x 5x 4x 15x 12x 10x first-order quads order = 3 20x 3-D higher-order elements D higher-order elements (1) Errors relative to data from 7 th - order elements for t = µs 59

60 (1) Wave propagation in 3D Summary of velocity errors at monitored node 3x 4x 5x 2 7x 10x 12x order = (2) 6 (1) Errors relative to data from 7 th - order elements for t = µs (2) AMD Opteron: 2.31 GHz 15.7 GB RAM 60

61 (1) Wave propagation in 3D Summary of velocity errors at monitored node 3x 4x 5x 2 7x 10x 12x order = 3 15x (1) Errors relative to data from 7 th - order elements for t = µs 61

62 Summary and conclusions Analysis of wave propagation is essential to fuze design 1D, 2D and 3D higher-order elements have been formulated and implemented in EPIC The higher-order elements show no signs of volumetric locking Accuracy of higher-order elements is compared to standard first-order elements in simulations of wave propagation. Higher-order elements provide much greater accuracy at equal: Mesh refinement Computing time Allocated memory 62

63 Acknowledgment This work was funded by the DoD Joint Fuze Technology Program. 63