Selective enrichment and modal matrix reduction in the generalized / eXtended Finite Element Method applied to dynamic analysis of plane state problems

The Generalized/eXtended Finite Element Method (G/XFEM) has successfully been applied in the dynamic analysis of a variety of structures such as bars, trusses, beams, and two-dimensional (2D) problems. The G/XFEM has shown high convergence rates to approximate displacements and stresses in many problems, such as in Fracture Mechanics. For free vibration analyses, the G/XFEM also shows high convergence rates to approximate most of the natural frequencies but the error is still considerable for the highest ones. Dealing with transient analysis, the enrichment has usually been done for all elements of the mesh, which requires high computational efforts. Further, those frequencies that were poorly approximated, pollute and affect the final solution precision of the time response. To reduce such issues, a compound strategy is adopted joining selective enrichment and modal matrix reduction. Friberg Indicator is taken in the selective process. The proposed technique is examined for dynamic analysis of plane state problems. Some examples show that, even with a reduced number of degrees of freedom, more accurate approximations are obtained. The additional time for computation of selective parameters is offset by the reduction of the total time solution. Thus, all results have less total computational running time than the traditional G/XFEM.