Chebyshev collocation method for static intrinsic equations of geometrically exact beams

Chebyshev collocation method for the free vibration analysis of geometrically exact beams with fully intrinsic formulation

“…The 1D generalized strain measures for an initially curved and twisted beam can be expressed as (Khaneh Masjedi and Ovesy (2015)):…”

“…In order to avoid the difficulties associated with the interpolation of finite rotations, the formulations with no rotational degrees of freedom have been emerged. For a more thorough review of various approaches with rotation free formulation the readers are referred to Khaneh Masjedi and Ovesy (2015).…”

“…Schillinger et al (2013) have shown that the collocation method significantly reduces the computational cost in comparison to Galerkin's and finite element methods and also can be orders of magnitude faster than these methods to achieve a specified level of accuracy. Khaneh Masjedi and Ovesy (2015) have introduced the Chebyshev collocation method to the static analysis of geometrically exact beams with intrinsic formulation and have shown that this scheme while computationally efficient exhibits comparable accuracy as distinct from other numerical schemes such as finite element method.…”

“…The main objectives of the current work have been to extend the approach presented by Khaneh Masjedi and Ovesy (2015) for the first time to the free vibration analysis of geometrically exact beams with intrinsic formulation and to show the accuracy and applicability of this scheme for the proper treatment of eigenvalue analysis of geometrically exact beams with fully intrinsic formulation. Additionally the free vibration problem for various boundary conditions in the context of geometrically exact beams with intrinsic formulation is considered which is addressed very rarely in the literature.…”

“…These equations will be linearized about a steady state position using perturbation method. It should be noted that for the current work in order to be self-sufficient some parts in theoretical developments are borrowed from Khaneh Masjedi and Ovesy (2015). In Section 3 the Chebyshev collocation method is introduced into the linearized intrinsic formulation of the beam and a general eigenvalue problem is constructed.…”