Thegoverningequationsofsurface-deformationinfully-penetratedGTAWweldpoolarederived.ThesolutionschemeoftheLagrangemultiplier,whichmakesthetopsurface-deformationequationbecoupledwiththatforthebottom-surfaceofasingleweldpool,isgivenout.Throughnumericalanalysisofweldpoolsurface-deformationinGTAW,itisfoundthatthereisclearcorrelationbetweenthepenetrationextentandtheLagrangemultiplier,inadditiontotherelationshipbetweenthepenetrationextentandthemaximumdepressionandhumpaswellasthedepressedvolumeofthetopsurfaceofweldpool.Itlaysgoodfoundationfortop-sidesensingbasedweldpenetrationcontrol.
