A perturbed Lagrangian formulation for the finite element solution of contact problems. (English) Zbl 0552.73097
Making use of a perturbed Lagrangian formulation, a finite element procedure for contact problems is developed for the general case in which node-to-node contact no longer holds. The proposed procedure leads naturally to a discretization of the contact interface into contact segments. Within the context of a bilinear interpolation for the displacement field, a mixed finite element approximation is introduced by assuming discontinuous contact pressure, constant on the contact segment. Because of this piece-wise constant approximation, the gap function enters into the formulation in an ”average” sense instead of through a point-wise definition. Numerical examples are presented that illustrate the performance of the proposed procedure.
MSC:
| 74A55 | Theories of friction (tribology) |
| 74M15 | Contact in solid mechanics |
| 74S99 | Numerical and other methods in solid mechanics |
Keywords:
penalty procedure via perturbed Lagrangian formulation; general case; node-to-node contact no longer holds; bilinear interpolation; displacement field; mixed finite element approximation; discontinuous contact pressure; piece-wise constant approximationReferences:
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