The elastica problem using moving mesh and isoparametric Hermitian elements (Q1262166)

The elastica problem is solved iteratively using Hermitian isoparametric beam elements. When the geometric mapping is linear - the element used corresponds to the usual beam element with explicit Hermitian polynomials as shape functions - the tip displacement is larger than the exact one. This is in controversy with the commonly known fact that the Rayleigh- Ritz solution is either exact or too stiff. However, when proper nonlinear geometric mapping is chosen the tip deflection obtained differs less than \(10^{-6}\) per cent from the analytical result. In this case the deflection curve is a parametric spline instead of an explicit polynomial.