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

The determination of the deflected shape of a bar bent through frictionless supports using finite elements is addressed. 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, which are determined simultaneously using Newton-Raphson iteration. Linear, quadratic and cubic Lagrangian elements are considered. The method may find use in a range of applications, from pipeline analysis, curve fitting, computer aided design and wave guide optimisation. Two examples are considered.