Enriched finite element methods for Timoshenko beam free vibration analysis

Abstract

This work presents free vibration analysis of Timoshenko beam models by using enriched finite element approaches. A conventional C° element is enriched by using finite element enrichment formulations. There are two different formulations employed in this work to enrich mathematical space constructed by conventional finite element shape functions, which are hierarchical approximation and partition of unity method. This work uses Lobatto's functions for hierarchical approximation in the context of Hierarchical Finite Element Method. At the same time, the Lagrange shape functions for partition of unity are adopted in this work, and the local space approximation is constructed by using trigonometric functions in the context of Generalized Finite Element Method. Both enriched finite element methods are applied for free vibration analysis of Timoshenko beam models. The shear locking is briefly investigated in static analysis. The results obtained by both methods are compared to other numerical methods. Efficiency of enriched finite element methods in attaining accuracy results is observed, as well as the elimination of shear locking in higher level of enrichment. An analysis of normalized discrete spectra in enriched C° element is carried out with different levels of enrichment and the results presented perform a remarkable behavior.