Quasi-Static Analysis of Raasch Hook with Explicit Solvers RADIOSS and LS-DYNA

Transcription

1 Quasi-Static Analysis of Raasch Hook with Explicit Solvers RADIOSS and LS-DYNA A. Dimitriev, N. Zhurba Abstract. This paper discusses applicability of various RADIOSS and LS-DYNA elements for quasi-static analysis. A well known Raasch Hook problem is used for benchmarking. Numerical results are compared with analytical solution. 1. RADIOSS Bulk (linear static) baseline. Z displacement by analytical solution (ref. 1.): L/t element length to element thickness ratio. Z displacement Error % L/t=0.5 L/t=1.0 L/t=2.0 L/t=3.3 (L/t=1.0) CTRIA CQUAD CTRIA CQUAD CHEXA 1st CHEXA 2nd CPENTA 1st CPENTA 2nd CTETRA 1st CTETRA 2nd Stress for the most accurate solution (CHEXA 1st): 1

2 2. Shell elements. Z displacement by analytical solution (ref. 1.): L/t element length to element thickness ratio. Z displacement Error % L/t=0.5 L/t=1.0 L/t=2.0 L/t=3.3 (L/t=1.0) quad12 (QBAT) quad24 (QEPH) tri1 (C0) tri2 (C0) tri30 (DKT18) tri31 (S3N6) Stress for the most accurate solution (tri30 (DKT18)): Relative to baseline error = 7.8% 2

3 LS-DYNA. Z displacement by analytical solution (ref. 1.): L/t element length to element thickness ratio. Z displacement Error % L/t=0.5 L/t=1.0 L/t=2.0 L/t=3.3 (L/t=1.0) quad tri4 (C0) tri17 error quad16 - fully integrated shell element (very fast) tri17 - fully integrated DKT, triangular shell element Stress for the most accurate solution (tri17): Relative to baseline error = 13.3% 3

4 3. Solid-shell elements. Z displacement by analytical solution (ref. 1.): L/t element length to element thickness ratio. Z displacement Error % L/t=0.5 L/t=1.0 L/t=2.0 L/t=3.3 (L/t=1.0) hex14 (HA8) hex15 (HSEPH) penta15 (PA6) Stress (skinned) for hex14 (HA8): Relative to baseline error = 1.7% 4

5 Stress (skinned) for hex15 (HSEPH): Relative to baseline error = 2.1% Stress (skinned) for the most accurate solution (penta15 (PA6)): Relative to baseline error = 4.0% 5

6 LS-DYNA. Z displacement by analytical solution (ref. 1.): L/t element length to element thickness ratio. Z displacement Error % L/t=0.5 L/t=1.0 L/t=2.0 L/t=3.3 (L/t=1.0) hex hex hex hex1 - one point reduced integration (default) hex2 - selective reduced 2 by 2 in plane integration hex3 - assumed strain 2 by 2 in plane integration Stress (skinned) for the most accurate solution (hex2): Relative to baseline error = 5.3% 6

7 4. Solid elements. Z displacement by analytical solution (ref. 1.): L/t element length to element thickness ratio. Z displacement Error % L/t=0.5 L/t=1.0 L/t=2.0 L/t=3.3 (L/t=1.0) hex14 (HA8) hex24 (HEPH) tetra tetra Stress (skinned) for hex14 (HA8): Relative to baseline error = 1.7% 7

8 Stress (skinned) for the most accurate solution (hex24 (HEPH)): Relative to baseline error = 0.3% Stress (skinned) for tetra10: Relative to baseline error = 1.7% 8

9 LS-DYNA. Z displacement by analytical solution (ref. 1.): L/t element length to element thickness ratio. Z displacement Error % L/t=0.5 L/t=1.0 L/t=2.0 L/t=3.3 (L/t=1.0) fully integrated S/R solid 3 - fully integrated quadratic 8 node element with nodal rotations 4 - S/R quadratic tetrahedron element with nodal rotations 15-2 point pentahedron element 16-5 point 10 node tetrahedron Stress for the most accurate solution (3): Relative to baseline error = 0.0% 9

10 5. Relative cost of Raasch Hook dynamic relaxation solution run. Only solutions with error <= 5% are considered: Number of integration points through thickness tri30 (DKT18) hex14 (HA8) (solid-shell 3X3) hex15 (HSEPH) penta15 (PA6) hex14 (HA8) (solid 3X3) hex24 (HEPH) 0.2 (1 integration point) tetra (4 integration points (all)) LS-DYNA. Only the most accurate solutions are considered: Number of integration points through thickness tri hex (1 integration point) tri17 - fully integrated DKT, triangular shell element hex2 - selective reduced 2 by 2 in plane integration 3 - fully integrated quadratic 8 node element with nodal rotations 6. s summary. For quasi-static analysis (dynamic relaxation) of sheet metal structures use elements listed below. Shell elements. tri30 (DKT18) /PROP/SHELL/ I shell =12 I smstr =4 I sh3n =30 h m h f h r d m d n N=5 I strain =1 Thick=2.000 A shear I thick =1 I plas =1 10

11 Solid-shell elements in order of decreasing preference. hex15 (HSEPH) /PROP/TSHELL/ I solid =15 I smstr =4 I cpre I cstr I npts =5 I int d n =0.1 q a q b h Δt min penta15 (PA6) /PROP/TSHELL/ I solid =15 I smstr =4 I cpre I cstr I npts =5 I int d n =0.1 q a q b h Δt min hex14 (HA8) /PROP/TSHELL/ I solid =14 I smstr =4 I cpre I cstr =0 I npts =3,5,3 I int d n =0.1 q a q b h Δt min Solid elements in order of decreasing preference. hex14 (HA8) /PROP/SOLID/ I solid =14 I smstr =4 I cpre =2 I npts =3,5,3 I rot I frame d n q a q b h Δt min I strain 11

12 hex24 (HEPH) (for in plane problems only) /PROP/SOLID/ I solid =24 I smstr =4 I cpre =2 I npts I rot I frame d n q a q b h Δt min I strain tetra10 (for in plane problems only) /PROP/SOLID/ I solid I smstr I cpre I npts I rot I frame d n q a q b h Δt min I strain Shell elements for skin. quad12 (QBAT) or tri30 (DKT18) /PROP/SHELL/ I shell =12 I smstr =4 I sh3n =30 h m h f h r d m d n N=1 I strain =1 Thick= A shear I thick =1 I plas =1 LS-DYNA. For quasi-static analysis (dynamic relaxation) of sheet metal structures use elements listed below. Shell elements. tri17 - fully integrated DKT, triangular shell element (elements with L/t < 1.0 not allowed) SECID ELFORM=17 SHRF NIP=5 PROPT QR/IRID ICOMP SETYP T1=2.000 T2 T3 T4 NLOC MAREA IDOF EDGSET Solid-shell elements. hex2 - selective reduced 2 by 2 in plane integration SECID ELFORM=2 SHRF NIP=5 PROPT QR ICOMP 12

13 Solid elements. 3 - fully integrated quadratic 8 node element with nodal rotations (for in plane problems only) SECID ELFORM=3 AET Shell elements for skin. quad9 - fully integrated Belytschko-Tsay membrane SECID ELFORM=9 SHRF NIP PROPT QR/IRID ICOMP SETYP T1= T2 T3 T4 NLOC MAREA IDOF EDGSET 7. Material. /MAT/PLAS_JOHNS/ mat_title ρ i =7.300e-04 E= ν=0.350 a=1.000e+30 b= n=1.000 max σ max c ICC F smooth F cut m T melt ρc p T i LS-DYNA. *MAT_SIMPLIFIED_JOHNSON_COOK MID RO=7.300e-04 E= PR=0.350 VP A=1.000e+30 B= N=1.000 C PSFAIL SIGMAX SIGSAT EPSO 8. Dynamic relaxation controls. /DYREL LS-DYNA NRCYCK DRTOL DRFCTR DRTERM TSSFDR IRELAL EDTTL IDRFLG =250 =5.000e-06 = =1 13

14 9. Load function. LS-DYNA. 10. Reference. 1. H. Schoop, J. Hornig, T. Wenzel Remarks on Raasch s Hook,