Shape design sensitivity analysis of elastoplastic frictional contact problems with finite deformation

A new shape design sensitivity analysis algorithm oftwo-dimensional multi-body elastoplastic frictional contact problems withfinite deformation was presented in this paper. In the direct analysis ofcontact problems, the variational inequality of contact constraints wereanalyzed with the active set strategies, and the contact interface wasdiscretized by the mortar method. The same nominal penalty parameters wereadopted in the normal and tangential directions of mortar surface'ssegments, and the normal and tangential contact conditions were regularizedby the moving friction cone algorithm based on the nominal penaltyformulation. A new two-dimensional multi-body finite deformation frictionalcontact algorithm was proposed, and the algorithm could inherit the advantagesof the moving friction algorithm and mortar method. In the shape designsensitivity analysis of contact problems, the incremental (path-dependent)sensitivity problem was derived by the direct differentiation of thediscretized equations governing the direct problem. The shape designsensitivity equation was linear and could be solved at each increment stepwithout iterations. In contrast to the classical shape design sensitivityalgorithm, normal and tangential directions was not to be divided in thepresent algorithm and its formulation was more concise to program. Numericalexamples were presented to illustrate the accuracy and efficiency of thisapproach.