Linear Curved Beam Finite Element with Exact Rigid Body Displacements

Abstract

Finite element models of curved beams using polynomial interpolation functions for discretization of radial and tangential displacement fields show ill-conditioning problems and shear locking. Polynomial and Fourier trigonometric-function elements for in-plane vibration of thin and thick curved beams have been proposed by different authors as enriching functions to avoid the illconditioning problem mentioned, avoiding membrane and shear locking. The research presented in this paper focuses on the development of finite elements for linear analysis of thin and thick beams that include exact rigid body motion interpolating functions. The dynamic behavior of thin and thick beams is analyzed using the proposed finite-element discretization. Modal analysis of clampedclampled circular arches is carried out as numerical examples. Precision obtained with the proposed finite element is compared with traditional finite elements and other numerical results published on these models.