Dynamic Analysis of Gap Closing and Contact in the Mixed Lagrangian Framework: Toward Progressive Collapse Prediction
Publication: Journal of Engineering Mechanics
Volume 136, Issue 8
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.
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Acknowledgments
Support for the work described in this paper was provided in part by the Multidisciplinary Center for Earthquake Engineering Research under a cooperative agreement from the National Science Foundation (Grant No. NSFEEC-9701471) as well as by the Kajima Corporation through the CUREE-Kajima joint program Phases VI and VII. The writer gratefully acknowledges this support.
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© 2010 ASCE.
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Received: Feb 5, 2009
Accepted: Feb 4, 2010
Published online: Jul 15, 2010
Published in print: Aug 2010
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