A set of design sensitivity formulas for nonlinear structures is derived in connection with the arc-length method. The structural analysis formulation considering proportional loading is based on the total Lagrangian method. Sensitivity formulas for both load factor and displacement at an arbitrary equilibrium are obtained, and can be applied not only to a prebuckling but also to a postbuckling state.
Several typical examples of truss, beam and shallow arch, from the literature are taken to test the analysis results. Sensitivity values obtained are compared with those by finite differencing. The predicted displacement trajectory near limit points are also compared with the perturbed. It is shown that the formulas are applicable to all through the trajectory. The choice and effect of the size of an arc-length is yet to be studied further.
