Quasistatic frictional contact problems with finitely many degrees of freedom.

• In the present paper results on existence and uniqueness of solutions to discrete frictional quasi-static unilateral contact problems are given under a condition that the coefficients of friction are smaller than a certain upper bound. This upper bound is defined in terms of an influence matrix for the contact nodes. The results of existence and uniqueness may be ordered into two classes depending on whether regularity conditions for the applied forces are imposed or not. For general loading which has a time derivative almost everywhere it is shown that a solution exists which satisfies governing equations for almost all times. Uniqueness of the solution has been shown only when the problem is restricted to two degrees of freedom. For a loading which is right piecewise analytic, additional results can be obtained. For instance, if each contact node has only two degrees of freedom a unique solution which satisfies governing equeations for all times exists. For the constructed solutions a priori estimates of the displacement field and its time derivate in terms of the applied forces are also given.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Coulomb friction; unilateral contact; linear elasiticity; quasistatic; existence; uniqueness; finite-dimensional; real analytic

MATHEMATICS

MATEMATIK

Publikations- och innehållstyp

vet (ämneskategori)

rap (ämneskategori)