A plane circular ring is modeled by various elements, some straight and others curved. All formulations have two translations and one rotation as nodal dof. We consider static deflection, under point loading, and bifurcation buckling, under constant-direction loading and fluid pressure loading. Matrices that account for fluid pressure loading are derived. Numerical examples show that excellent results aregiven by a standard straight beam element whose length is that ofthe arc itsubtends,
Arch element
[12], matrix [kMl This element, Fig. l(a), is based on the displacement field where U and V are tangential and normal displacements. Generalized coordinates a o are replaced by nodal dof during element formulation. Equation (1) satisfies the inextensibility condition, (dU/dO) + V=: O. Rotation if; is taken as dof, then transformed to global dof before assembly. Local dof u and v are along and normal to straight elements. Global dof U and V are tangent and normal to the arc of the ring. Nodal rotational dof, defined below, are taken as lj!\ and if;2 for curved elements and 4JI and 4J2 for straightelements. (2) (I) 6 V = -? alU -1)8 i -2 1=2 Linear straight element [13], matrix [kJ Linear interpolation is used for axial displacement u, transverse displacement v, and the rotation of crosssections 4J. u = [N] {~J v=: [N] {~J 4J =: [N] {:~} (3) STIFFNESS MATRICES The following conventional stiffness matrices are used. Straight elements, Fig. l(b), are formulated with local