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The application of the TR-BDF2 method to second order problems typical ofstructural mechanics and seismic engineering is discussed. A reformulation ofthis method is presented, that only requires the solution of algebraic systemsof size equal to the number of displacement degrees of freedom. A linearanalysis and numerical experiments on relevant benchmarks show that the TR-BDF2method is superior in terms of accuracy and efficiency to the classical Newmarkmethod and to its generalizations.

The TR-BDF2 method for second order problems in structural mechanics