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Bdf-Like Methods For Nonlinear Dynamic Analysis, S. Dong

PRISM: NNSA Center for Prediction of Reliability, Integrity and Survivability of Microsystems

We present several time integration algorithms of second-order accuracy that are numerically simple and effective for nonlinear elastodynamic problems. These algorithms are based on a general four-step scheme that has a resemblance to the backward differentiation formulas. We also present an extension to the composite strategy of the Bathe method. Appropriate values for the algorithmic parameters are determined based on considerations of stability and dissipativity, and less dissipative members of each algorithm have been identified. We demonstrate the convergence characteristics of the proposed algorithms with a nonlinear dynamic problem having analytic solutions, and test these algorithms with several three-dimensional nonlinear …