Enriched finite element modeling in the dynamic analysis of plane frame subject to random loads

Abstract

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.