Currently available welding simulation methodologies provide deterministic
results for the best estimate of the input parameters, such as part geometry,
processing conditions and material properties. If there is an uncertainty
in any of the input parameters, then a reanalysis needs to be performed with
perturbed values of each uncertain variable. However, there can be several
hundred input parameters; therefore, the use of reanalysis in uncertainty
quantification in welding modelling can be time consuming or computationally
prohibitive, especially for three-dimensional modelling. This paper explores
the application of design sensitivity analysis in quantifying uncertainty
in welding residual stress and distortion computations. Analytic sensitivities
are computed by direct differentiation, resulting in a very efficient computational
approach. The variation of temperature, welding residual stress and distortion
with respect to processing parameters is computed from a first order Taylor
expansion of the model output. The approach is demonstrated in a three-dimensional
model of a singe pass weld and validated by comparing sensitivity analysis
results to reanalyses.
HibbittH, MarcalPV: ‘A numerical, thermo-mechanical modelfor the welding and subsequent loading of a fabricated structure’, Comput.Struct., 1973, 3, (5), 1145–1174.
BruD, DevauxJ, BergheauJ, PontD: ‘Influence of material properties athigh temperatures on the modelling of welding residual stress and deformationstate’, in ‘Mathematical modelling ofweld phenomena (3)’, (ed. CerjakH, BhadeshiaH K D H, ed), 456–463; 1997, London, TheInstitute of Materials.
14.
SchwenkC, RethmeierM, DilgerK, MichailovV:‘Sensitivity analysis of welding simulationdepending on material properties value variation’in ‘Mathematicalmodelling of weld phenomena (8)’(
CerjakH, ), 1107–1128; 2007, Graz, Verlagder Technischen Universität Graz.
15.
VenkayyaVB: ‘Structural optimization: a review andsome recomendations’, Int. J. Numer. MethodsEng., 1978, 13, 203–228.
16.
HaugEJ, ChoiKK, KomkovV: ‘Design sensitivity analysis of structuralsystems’; 1986, New York, AcademicPress.
17.
DemsK, MrozZ: ‘Variational approach to sensitivityanalysis in thermoelasticity’, J. Therm. Stresses, 1987, 10, 283–306.
MichalerisP, TortorelliDA, VidalCA: ‘Tangent operators and design sensitivityformulations for transient nonlinear coupled problems with applications toelasto-plasticity’, Int. J. Numer. Methods Eng., 1994, 37, 2471–2499.
22.
MichalerisP, TortorelliDA, VidalCA: ‘Analysis and optimization of weaklycoupled thermo-elasto-plastic systems with applications to weldment design’, Int.J. Numer. Methods Eng., 1995, 38, 1259–1285.
23.
MichalerisP, DantzigJA, TortorelliDA: ‘Minimization of welding residual stressand distortion in large structures’, Weld. J., 1999, 78, (11), 361s–366s.
24.
PaulS, MichalerisP, ShanghviJ: ‘Optimization of thermo-elasto-plasticfinite element analysis using an Eulerian formulation’, Int.J. Numer. Methods Eng., 2003, 56, 1125–1150.
25.
SongJ, PetersJ, NoorA, MichalerisP: ‘Sensitivity analysis of the thermomechanicalresponse of welded joints’, Int. J. Solids Struct., 2003, 40, 4167–4180.
LeblondJB, DevauxJ: ‘A new kinetic model for anisothermalmetallurgical transformations in steels including effect of austenite grainsize’, Acta Metall., 1984, 32, (1), 137–146.
28.
WattDF, CoonL, BibbyMJ, GoldakJ, HenwwodC: ‘An algorithm for modeling microstructuraldevelopment in weld heat-affected zones’, ActaMetall., 1988, 36, (11), 3029–3035.
