Large deflection analysis of geometrically exact spatial beams under conservative and nonconservative loads using intrinsic equations

Abstract

Large deflection analysis of geometrically exact beams under conservative and nonconservative loads is considered. A Chebyshev collocation method is used for the discretization of the governing equations of the spatial beam with intrinsic formulation. In the case of nonconservative (follower) loads, since the formulation is expressed in a deformed frame, the formulation is fully free from any displacement or rotational variables, and a direct solution can be achieved. In the case of conservative loads, the applied loads are functions of beam rotations, and in order to retain the intrinsic nature of the formulation, a direct integration of rotations is avoided and an iterative solution of the governing equations in addition to an update on the beam rotations as a post-processing step has been employed. A number of test cases have been considered and are compared to the existing experimental as well as numerical results in the literature. A very good agreement has been observed in the comparison cases, and it is shown that the intrinsic formulation in conjunction with a Chebyshev collocation method while exhibiting advantages in ease of implementation, computational cost and convergence characteristics over other methods can effectively capture the large deflection behavior of spatial beams under various load conditions.

Differential Quadrature Method for Fully Intrinsic Equations of Geometrically Exact Beams

“…They [13] also extended the application of fully intrinsic theory to more general configurations by establishing different types of fully intrinsic boundary conditions. Khaneh, Masjedi, and Ovesy [14,15] investigated the static analysis method by discretizing the fully intrinsic equations using the Chebyshev collocation method. Tashaorian et al [16] established non-local, fully intrinsic equations for non-beam-like structures whose one-dimensional structure length is close to the two-dimensional cross-section size, which breaks through the limitation that the fully intrinsic equations can only be used for modeling slender structures.…”

“…The third method is the Chebyshev collocation method. Khaneh, Masjedi, and Ovesy [14,15] used this method to discretize static intrinsic equations. The last method is the differential quadrature (DQ) method that has been used more recently.…”