Nonlinear analysis of structural elements under unilateral contact constraints by a Ritz type approach

Ricardo A.M. Silveira (1) , Wellington L.A. Pereira (1) , Paulo Gonçalves (2)

1 Federal University of Ouro Preto
2 PUC-Rio - Pontifícia Universidade Católica do Rio de Janeiro [Brasil] = Pontifical Catholic University of Rio de Janeiro [Brazil] = Université catholique pontificale de Rio de Janeiro [Brésil]

A nonlinear modal solution methodology capable of solving equilibrium and stability problems of uni-dimensional structural elements (beams, columns and arches) with unilateral contact constraints is presented in this work. The contact constraints are imposed by an elastic foundation of the Winkler type, where special attention is given to the case in which the foundation reacts in compression only, characterizing the contact as unilateral. A Ritz type approach with moveable boundaries, where the coordinates defining the limits of the contact regions are considered as additional variables of the problem, is proposed to solve this class of unilateral contact problems. The methodology is illustrated by particular problems involving beams, beam-columns and arches, and the results are compared with available results obtained by finite element and mathematical programming techniques. It is concluded that the Ritz type approach proposed is particularly suited for the analysis of structural problems where the number, but not the length, of the contact regions between the bodies are known a priori. Therefore, it can substitute in these cases finite element applications and be used as a benchmark for more general and complex formulations as well.

Mots clés: Tensionless foundation; Nonlinear structural analysis; Stability; Ritz method; Unilateral contact

Domaines: Vibrations [physics.class-ph]; Systèmes dynamiques [math.DS]; Génie mécanique [physics.class-ph]; Dynamique, vibrations

Ricardo A.M. Silveira, Wellington L.A. Pereira, Paulo Gonçalves. Nonlinear analysis of structural elements under unilateral contact constraints by a Ritz type approach. International Journal of Solids and Structures, 2008, 45 (9), pp.2629-2650. ⟨10.1016/j.ijsolstr.2007.12.012⟩. ⟨hal-01620559⟩