The solution of open and closed elasticas using intrinsic coordinate finite elements (Q1376628)

We determine the deflected shape of a bar bent through frictionless supports using finite elements. The finite element procedure uses intrinsic coordinates, which are computationally efficient and produce solutions in a convenient form. Variables include node rotations. Lagrange multipliers and bar lengths between supports are determined simultaneously using Newton-Raphson iteration. Linear, quadratic and cubic Lagrangian elements are considered. Two examples illustrate the method.