Complex-shaped beam finite element

Two approaches to derive two-dimensional beam finite-element matrices to map the structural behavior of complex-shaped beams are studied. The beams have varying thickness and the centerline may be strongly curved. The beam-theory approach combined with the Castigliano theorem explicitly includes thickness and curvature effects. The other approach evaluates the response of a Lagrangian-type higher-order solid finite element where all mechanical effects are naturally included. Both methods are explained and their accuracy levels as well as the numerical costs are assessed. Possible application fields for the complex-shaped beam finite element are ground-structure approaches to compliant-mechanism design where it can be used for finding the topology as well as refining the shape in a numerically efficient manner.