Dynamic analysis of Euler–Bernoulli beam problems using the Generalized Finite Element Method

•GFEM approximations are proposed for the dynamic analysis of Euler–Bernoulli beams and bars.•Different levels of enrichment monomials are investigated systematically.•The application of GFEM to elastoplastic dynamic analysis is original.•The proposed GFEM is more accurate than the standard FEM and HFEM.•GFEM associated with HHT method is more stable than FEM and HFEM associated with HHT.

This work presents dynamic analyses of one-dimensional bar and Euler–Bernoulli beam problems with Generalized Finite Element Method (GFEM). Enrichment monomials are trigonometric and exponential functions. A beam free vibration problem is analyzed to assess the element’s robustness and efficiency. Next, an elastodynamic analysis of a bar is performed using several enrichment levels. Finally, a dynamic elastoplastic analysis of a beam problem is carried out. Error measures and nonlinear strains are estimated. Results from GFEM are compared to results from a conventional FE formulation to show GFEM’s level of efficiency in solving Euler–Bernoulli beam elastic as well as elastoplastic dynamic problems.