NTH-ORDER STIFFNESS SENSITIVITIES IN STRUCTURAL-ANALYSIS

This paper presents a general expression for the Nth-order stiffness s ensitivities in linear elastic frames. It is based on modelling the st ructure as being composed of unimodal elements. It is shown that the s ensitivity of the structural response to the variation of the stiffnes s of an arbitrary component depends only on the corresponding elementa l displacements. These are the nodal displacements due to nodal elemen t loads applied to the structure at the end nodes of the considered el ement. Therefore, on the basis of one structural analysis we obtain th e sensitivity of the structure to the variation of a given stiffness, to any order and for all loading conditions. Partial derivatives with respect to several element stiffnesses are obtained from the elemental displacements of the considered elements. The method is equally appli cable to more general finite element models. It requires, however, the preliminary decomposition of the finite elements into their unimodal components.