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.