A material/element-defined time integration procedure for dynamic analysis

In this paper, an effective and highly versatile locally-defined time-marching procedure is proposed for dynamic analysis. In this novel technique, the time integration parameters of the method are specified at an element level, adapting themselves to the features of the adopted discretization and to the local proprieties of the model. In this sense, the errors of the co-applied spatial discretization method may be properly counterbalanced by the calculations of the proposed time integration procedure, providing considerably more accurate results. Controllable numerical dissipation is also enabled by the novel approach, allowing the user to determine the regions of the model in which algorithmic damping is to be applied, as well as to define its intensity. Consequently, in the proposed formulation, an additional “material” parameter may be inputted for the analysis (similarly to those defining the physical properties of the model), delineating the numerical features of the considered solution procedure to be locally applied. The proposed formulation is highly accurate, efficient, and simple to implement. It also provides guaranteed stability and improved dissipative analyses, standing as a very effective time-marching technique. At the end of the paper, numerical results are presented and compared to those of standard formulations, illustrating the enhanced performance of the proposed novel procedure.