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This study focuses on the analysis of initially curved, extensible Euler-Bernoulli beams (arches) using
the Finite Element Method (FEM). A finite element formulation is developed to describe the curved element in
the at rest configuration. The formulation proposes the implementation of the extensibility of the beam axis due to
the absence of static condensation, which enhances accuracy but also adds complexity to the formulation of shape
functions and equations. The obtained FE results are compared with available analytical results and the commer-
cial software ANSYS. The distribution of natural frequencies in relation to the initial curvature is investigated.
Furthermore, the research addresses the challenges associated with the nonlinear statics and dynamics of curved
beam. The findings contribute to the understanding of the dynamic response of initially curved beams, including
the contribution of curvature effects, such as the veering of natural frequencies, nonlinear mode shapes and dynamic behavior.
