FEM ACCURACY ASSESSMENT (*)
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1 ASME_2018_V_V_Symp_Minneapolis_MN_May_17_1:30_pm_Session_12-1 Paper_9320 (Fong) FEM SOLUTION UNCERTAINTY, ASYMPTOTIC SOLUTION, AND A NEW APPROACH TO FEM ACCURACY ASSESSMENT (*) Jeffrey T. Fong, P.E., F.ASME Physicist and Project Manager National Institute of Standards & Technology (NIST) Gaithersburg, MD (*) Contribution of NIST, not subject to copyright. Co-authored by J. T. Fong, P. V. Marcal, R. Rainsberger, L. Ma, N. A. Heckert, and J. J. Filliben. 1
2 ASME_2018_V_V_Symp_Minneapolis_MN_May_17_1:30_pm_Session_12-1 Paper_9320 (Fong) Outline of Talk ( 30 slides, ~ 25 minutes ) 1. Theory of an Asymptotic Solution of FEM. 2. FEM Uncertainty as Metric-1 for Accuracy. 3. Relative Error Rate of Decay as Metric Calibration of Metric-1 and Metric Applications. 6. Conclusion. 2
3 1. Theory of an Asymptotic Solution of FEM. Pierre Francois Verhulst (1845) 3-parameter 3
4 1. Theory of an Asymptotic Solution of FEM. 4
5 1. Theory of an Asymptotic Solution of FEM. Fine Fine 5
6 1. Theory of an Asymptotic Solution of FEM. Element Size: Fine 24,606 elements 123,657 d.o.f. 6
7 1. Theory of an Asymptotic Solution of FEM. Element Size: Fine MPa 7
8 1. Theory of an Asymptotic Solution of FEM. Element Degrees of Max. Mises % of Stress Size Freedom (d.o.f.) Stress (MPa) (100 for fine) (Log_10 (dof)) Fine 123, (100 %) (5.0922) Normal 74, (97.4 %) (4.8706) Coarse 47, (93.1 %) (4.6723) Coarser 31, (89.7 %) (4.4980) Extremely Coarse (88.5 %) (4.0311) 8
9 1. Theory of an Asymptotic Solution of FEM. A Non-Linear Least Square Fit using an S-curve Logistic Function: MPa s.d. = 2.0 MPa 9
10 1. Theory of an Asymptotic Solution of FEM MPa sd = 2.0 MPa 10
11 1. Theory of an Asymptotic Solution of FEM. Predicted Max. Mises Stress = MPa, s.d. = 2.0 MPa. Question: Is that good enough? 11
12 1. Theory of an Asymptotic Solution of FEM. Max. Mises Stress = MPa = = 6,932,883 (d.o.f.) 12
13 1. Theory of an Asymptotic Solution of FEM MPa, s.d. = 0.6 MPa No. of slides Subtotal Residual S.D. = 1.38 ( Fit is GOOD.) 6,932,883 Ans. Max. Mises Stress at 95 % confidence level = ( 368.0,....., MPa ) 13
14 2. FEM Uncertainty as Metric-1 for Accuracy. 14
15 2. FEM Uncertainty as Metric-1 for Accuracy. 15
16 2. FEM Uncertainty as Metric-1 for Accuracy. No. of slides Subtotal
17 ASME_2018_V_V_Symp_Minneapolis_MN_May_17_1:30_pm_Session_12-1 Paper_9320 (Fong) 3. Relative Error Rate of Decay as a 2 nd Metric. 17
18 3. Relative Error Rate of Decay as Metric-2. No. of slides Subtotal
19 4. Calibration of Metric-1 and Metric-2. 19
20 4. Calibration of Metric-1 and Metric-2. 20
21 4. Calibration of Metric-1 and Metric-2. No. of slides Subtotal
22 5. Applications. 22
23 5. Applications. 23
24 5. Applications. 24
25 5. Applications. 25
26 5. Applications. 26
27 5. Applications. ABAQUS Hexa-08 27
28 5. Applications. ABAQUS Hexa-08 28
29 5. Applications. ABAQUS Hexa-20 ABAQUS Hexa-08 29
30 5. Applications. 30
31 5. Applications. No. of slides Subtotal ABAQUS Hexa-20 ABAQUS Hexa-08 31
32 ASME_2018_V_V_Symp_Minneapolis_MN_May_17_1:30_pm_Session_12-1 Paper_9320 (Fong) 6. Concluding Remarks No. of slides Subtotal FEM accuracy assessment is feasible using Metrics 1 and FEM asymptotic solution with Metrics 1 and 2 is a useful tool for partial verification. 3. To complete FEM verification, we need to use a second tool, namely, design of experiments. 32
33 Disclaimer Certain commercial equipment, instruments, materials, or computer software are identified in this talk in order to specify the experimental or computational procedure adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards & Technology, nor is it intended to imply that the materials, equipment, or software identified are necessarily the best available for the purpose. 33
34 Speaker s Biographical Sketch Dr. Jeffrey T. Fong has been Physicist and Project Manager at the Applied and Computational Mathematics Division, Information Technology Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, MD, since He was educated at the University of Hong Kong (B.Sc., Engineering, first class honors, 1955), Columbia University (M.S., Engineering Mechanics, 1961), and Stanford (Ph.D., Applied Mechanics and Mathematics, 1966). Prior to 1966, he worked as a design engineer ( ) on numerous power plants (hydro, fossil-fuel, nuclear) at Ebasco Services, Inc., in New York City, and as teaching & research assistant ( ) on engineering mechanics at Stanford University. During his 40+ years at NIST, he has conducted research, provided consulting services, and taught numerous short courses on mathematical and computational modeling with uncertainty estimation for fatigue, fracture, high-temperature creep, nondestructive evaluation, electromagnetic behavior, and failure analysis of a broad range of materials ranging from paper, ceramics, glass, to polymers, composites, metals, semiconductors, and biological tissues. A licensed professional engineer (P.E.) in the State of New York since 1962 and a chartered civil engineer in the United Kingdom and British Commonwealth (A.M.I.C.E.) since 1968, he has authored or co-authored more than 100 technical papers, and edited or co-edited 17 national or international conference proceedings. He was elected Fellow of ASTM in 1982 and Fellow of ASME in In 1993, he was awarded the prestigious ASME Pressure Vessels and Piping Medal. Most recently, he was honored at the 2014 International Conference on Computational & Experimental Engineering & Sciences (ICCES) with a Lifetime Achievement Medal. Since 2006, he has been Adjunct Professor of Mechanical Engineering and Mechanics at Drexel University and taught a graduate-level 3-credit course on Finite Element Method Uncertainty Analysis. Since Jan. 2010, he has given every 6 months an on-line 3-hour short course at Stanford University on Reliability and Uncertainty Estimation of FEM Models of Composite Structures. In 2012, he was appointed Adjunct Professor of Nuclear and Risk Engineering at the City University of Hong Kong, and Distinguished Guest Professor at the East China University of Science & Technology, Shanghai, China, to teach annually a 1- credit 16-hour short course on Engineering Reliability and Risk Analysis. 34
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