On c⁰ beam elements with shear and their corresponding penalty function formulation

On a model of clamped beam problem we study a finite element method with approximate constraints and the corresponding penalty function approach. By a small perturbation analysis we show that the rotation is independent from the penalization. This method allows us to use simple c⁰ elements, hence we can compute approximate solutions to obstacle problems. The one dimensional nature of all the results is underlined and the extension of this FEM to flexible pipe lines is indicated.