Chebyshev collocation method for static intrinsic equations of geometrically exact beams

A Chebyshev collocation method is presented for the static analysis of the geometrically exact beams undergoing arbitrary large deflections using intrinsic formulation. In the intrinsic formulation of the governing equations of the spatial beams, neither displacement nor rotation variables appear. The proposed collocation technique is based on the Chebyshev points as the collocation points and the orthogonal Chebyshev polynomials as the trial functions. This method is successfully applied to the static solution of the strong form of the intrinsic governing equations of the nonlinear spatial beam and in order to show the applicability, accuracy and computational efficiency of the proposed method the numerical results are compared to the experimental, analytical and other numerical results for a number of test cases.