Mechanical Engineering Commons^™

A Finite Element For The Three-Dimensional Deformation Of A Circular Ring Of Arbitrary Cross Section, Jeffrey Stuart Knowlton

Mechanical Engineering ETDs

A two-node finite element for relatively compact, solid curved beams is derived. A node is located at the centroid of each end of the beam, and each node has six degrees of freedom, consisting of three translations and three rotations in mutually perpendicular directions. The element stiffness matrix has dimensions 12x12. A cylindrical polar coordinate system is used to express the components of the associated displacement and load vectors. As a consequence of the assumption of a nonzero cross-section product of inertia, deflec­tions in the plane and out of the plane of beam curvature are coupled. Hence in-plane loads can …