Dynamic Analysis of Gap Closing and Contact in the Mixed Lagrangian Framework: Toward Progressive Collapse Prediction

Abstract

Previous research has shown many advantages of the mixed Lagrangian formulation (MLF) for the solution of dynamic problems. In particular, it has shown a very stable and robust behavior with respect to the time step size required for convergence, even in cases where plasticity and fracture were considered. This paper presents another step toward enabling the prediction of progressive collapse of structures using MLF. A new gap element is added to the framework by formulating an additional component in the Lagrangian function. It is shown that by carefully formulating the new component, the optimization problem to be solved in each time step of the MLF algorithm retains its form which is quadratic in the cases considered. Hence, a unified formulation is attained for all stages of the analysis whether contact forces are present or not. After presenting details of the formulation, the proposed method is used for the solution of two examples. 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.