Curved, linear Kirchhoff beams formulated using tangential differential calculus and Lagrange multipliers

Linear Kirchhoff beams, also known as curved Euler-Bernoulli beams, are reformulated using tangential differential calculus (TDC). The model is formulated in a two dimensional Cartesian coordinate system. Isogeometric analysis (IGA) is employed, hence, NURBS are used for the geometry definition and generation of sufficiently smooth shape functions. Dirichlet boundary conditions are enforced weakly using Lagrange multipliers. As a post-processing step, the obtained FE solution is inserted into the strong form of the governing equations and this residual error is integrated over the domain in an L2-sense. For sufficiently smooth physical fields, higher-order convergence rates are achieved in the residual errors. For classical benchmark test cases with known analytical solutions, we also confirm optimal convergence rates in the displacements.