Kinematic Approach to Dynamic Contact Problems - The Geometrical Soft Way Method
A method of taking into account the geometrical constraints in evolution problems of solid systems that limit the possibility of motion by the history of variation of the velocity field is developed in the paper. The presented formulation can be adapted to numerous problems of solid systems subjected to dynamic effects with large deformations, large displacements1 large rotations. The computational cost of one iteration in the method proposed is the same as in other classical methods because of the frontal approach. However, the iterative process converges faster. If an adaptive space and time meshing were chosen, it could become a less expensive method. A numerical example of the contact analysis in which both the spatial and temporal partition was adapted according to the evolution of the geometry, proved the approach to be more efficient.
J.J. MOREAU and P.D. PANAGIOTOPOULOS, Non-smooth mechanics and applications, Springer Verlag, 1988.
J.J. MOREAU, P.D. PANAGIOTOPOULOS and G. STRANG, Topics in nonsmooth mechanics, Birkhäuser Verlag, 1988.
C. BOHATIER, Unilateral joints in mechanisms: modeling and solution, [in:] Structural Dynamics and Vibrations, A. ERTAS, B.A. OVUNC and I.I. ESAT [Eds.], ASME, vol. PD-52, Houston, Texas, 31 January - 4 February 1993.
C. BOHATIER and J.-L. CHENOT, Finite element formulation for non-steady-state large deformations with sliding or evolving contact boundary conditions, Int. J. Num. Meth. Engng., 28, 753-768, 1989.
C.I. BAJER, Triangular and tetrahedral space-time finite elements in vibration analysis, Int. J. Numer. Meth. Engng., 23, 2031-2048, 1986.
C. BAJER, R. BOGACZ and C. BONTHOUX, Adaptive space-time elements in the dynamic elastic-viscoplastic problem, Comput. and Struct., 391 415-423, 1991.
C.I. BAJER and C.G. BONTHOUX, State-of-the-art in the space-time element method, Shock Vibr. Dig., 23, 5, 3-91 1991.
C. BOHATIER, A large deformation formulation and solution with space-time finite elements, Arch. Mech., 44, 31-41, 1992.
C. BOHATIER, A large deformation formulation from thermomechanical point of view and space-time finite element method, [in:] European Joint Conference on Engineering Systems, Design and Analysis, ASME, Istanbul, 29 June - 3 July 1992.
C. BAJER and C. BOHATIER, Solution of thermomechanical problems by the spacetime finite elements, [in:] Numerical Methods in Industrial Forming Processes, J.-L. CHENOT, R.D. WOOD and O.C. ZIENKIEWICZ [Eds.], pp. 215-219, A.A. Balkema, Valbonne 1992.
C. BAJER and C. BOHATIER, Modélisation des systèmes mécaniques sous sollicitations dynamiques et résolution numérique des problèmes non linéaires associés, [in:] Méth. Inform. de la Conception lndustr., Méc. des Struc., pp. 79-90, Marseille 1993.
C. BAJER and C. BOHATIER, The soft way method and the velocity formulation, Comput. and Struct., 1995.