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A robust composite time integration scheme for snap-through problems

Abstract

A robust time integration scheme for snap-through buckling of shallow arches is proposed. The algorithm is a composite method that consists of three sub-steps. Numerical damping is introduced to the system by employing an algorithm similar to the backward differentiation formulas method in the last sub-step. Optimal algorithmic parameters are established based on stability criteria and minimization of numerical damping. The proposed method is accurate, numerically stable, and efficient as demonstrated through several examples involving loss of stability, large deformation, large displacements and large rotations.

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Acknowledgments

The work has been funded in part by AFOSR under the Grant no. FA9550-09-1-0201 and by DOD under the High Performance Computing Modernization Program (HPCMP) under the Grant GS04T09DBC0017. Their support is greatly appreciated. Support was also received from the Data Analysis and Visualization Cyberinfrastructure funded by NSF under Grant OCI-0959097 and the Shared University Grid at Rice funded by NSF under Grant EIA-0216467, and a partnership between Rice University, Sun Microsystems, and Sigma Solutions, Inc.

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Correspondence to Ilinca Stanciulescu.

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Chandra, Y., Zhou, Y., Stanciulescu, I. et al. A robust composite time integration scheme for snap-through problems. Comput Mech 55, 1041–1056 (2015). https://doi.org/10.1007/s00466-015-1152-3

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  • DOI: https://doi.org/10.1007/s00466-015-1152-3

Keywords

  • Time integration
  • Nonlinear dynamics
  • Snap-through
  • Backward differentiation formula