Derivation of the variational inequalities and extremum principles of the frictionless elastic contact problem
For two contacting elastic bodies with arbitrary (sufficiently smooth) shapes the statical and kinematical conditions are established assuming small deformations and allowing the contact region to be large. From these ones the principles of virtual displacements and virtual force as well as the corresponding complementary variational principles are derived in two different versions: In the first one only integrals over the contact surfaces, in the second one also integrals over the volumes of both bodies are involved. Alternatively an equivalent derivation based on a mixed principle of virtual work and a saddle-type functional is presented. Several representations known in the literature are contained as special cases.
mixed principle of virtual work and a saddle-type functional
scientific article; zbMATH DE number 3889078
scientific article