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The elliptic curved beam finite element for static and dynamic analysis of arches

Litewka P.

Foundations of Civil and Environmental Engineering

2011

No. 14

73--109

In this paper the physical curved beam finite element of elliptic shape was derived. Unlike for the typically used beam elements the shape functions derived here are not of constant coefficients but rather depend on physical and geometrical parameters of the element. To avoid elliptic integrals in the derivation the basic functions for the ellipse were replaced with their expansions into polynomial series. Thus, the shape functions obtained are quasi-exact solutions of differential equations for the deformed shape of the curved beam. The quasi-exact stiffness matrix was also derived as well as the consistent mass matrix. The derivations were carried out using the symbolic algebra program Maple. The performance of the element featuring no locking was checked in several numerical examples.