Contact analysis in the mixed lagrangian framework

Abstract eng:
Previous research has shown many advantages of the Mixed Lagrangian Formulation (MLF) for the solution of dynamic problems. Unlike standard approaches, MLF leads to a convex well-behaved optimization problem with forces as primary variables. The solution of dynamic problems by using the MLF has shown to be robust in the case of yielding structures, hence allowing larger time steps than those usually considered. In this paper a new contact element is introduced. The new contact element allows compression forces only, when the relative displacement between its edges is zero. By adding a linear spring and a slider in series with the new contact element, the contact force could be modeled to have an elastic-plastic behavior, thus, plasticity in the contact can be accounted for in a natural manner. Additional elements could be added in series or in parallel to this system to result in different behavior of the contact force. After presenting details of the formulation and computational algorithms, the new element is used for the solution of two examples. In the first example, pounding between adjacent buildings is considered, while the second example analyses a base isolated structure with gap elements. These examples illustrate that relatively large time steps can be considered even for contact problems. Furthermore, the reasons for this capability of the algorithm are discussed in the paper.

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