A Galerkin approximation for curved beams
We apply a Galerkin method to the equations of linearized three- dimensional elasticity for a curved beam. We explicitly construct an approximate solution of the three-dimensional elasticity problem as a minimizer of the \(H^ 1\) norm with respect to a geometric parameter. This is done by replacing the three-dimensional elasticity problem by a series of two- and one-dimensional problems, which are easier to solve. We prove that the approximation error in the \(H^ 1\) norm is a function of the loading, the geometry, the order of approximation and the curvature and torsion tensors associated with the definition of the beam axis.
scientific article; zbMATH DE number 219613
scientific article