a b s t r a c tThis 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 °ele-ment is carried out with different levels of enrichment and the results presented perform a remarkable behavior.
This work contributes to the generalized finite element approach in free vibration, dynamic elastic, and elastoplastic analysis of plane frame subjected to random excitation generated by the wind action. The wind velocity is modeled mathematically by using power spectral density method in combination with Shinozuka’s model, along with the commonly employed wind spectra. From these spectra, the dynamic wind loading is determined from the sum of the mean and floating wind velocities. The governing equation is formulated by Euler–Bernoulli beam theory, and it is discretized by using the enriched beam element. The enrichment is done by employing enriched finite element shape function to construct the enriched mathematical space. This strategy is constituted by the enrichment space, which is constructed by trigonometric functions, and the conventional space, which is constructed by conventional two-node Lagrange–Hermite shape function. The time increment procedure is carried out by Hilber-Hughes-Taylor algorithm and the material nonlinearity is modeled by von Mises isotropic hardening model, solved by the Newton–Raphson algorithm. A flowchart is presented to summarize the proposed numerical modeling procedure. Finally, several applications are presented, and the results obtained by the generalized finite element method are compared with those obtained by conventional beam element. Natural frequencies are determined in a one-story plane frame and are compared with reference results. The relative error in displacement is determined in h-refine strategy for quadratic beam element (FEM3), while the generalized finite element method adopts the enrichment increment strategy. The results demonstrate the competitiveness and numerical stability of generalized finite element method in this type of application. Even in comparison to the quadratic beam element, the generalized finite element method presents good performance and accuracy in numerical modeling.
This work proposes a methodology for defective pipe elastoplastic analysis using the Euler Bernoulli beam-pipe element formulation. The virtual work equation is modified to incorporate the stress concentration factor in beam-pipe element formulation. The stress concentration factor is evaluated a priori by a 2D or 3D finite element model according to the defect profile. In this work, a semicircular defect and a rectangular defect are considered. The stress concentration factor is inserted into the beampipe element elastoplastic formulation, and several applications are presented to show the applicability of the proposed method.
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