Total Lagrangian perspectives on analytical sensitivities for flexible beams

This paper is set in the context of nonlinear structural optimisation. Analytical sensitivity expressions are developed from two contrasting Total Lagrangian beam formulations. Strong geometrically nonlinear structural responses are introduced through the assumption of inextensibility of the curvilinear in one case and modification of the curvature in the second. Though performing similarly in predicting structural behaviour, the two approaches are shown to require careful consideration when extended to sensitivity determination. Conditioning of the sensitivity formulation is required to avoid contamination of the solution by even a small violation of the inextensibility constraint. An arguably more robust algorithm can be developed from the modified-curvature approach at the cost of computation efficiency. Recommendations regarding application of each approach are made.