Finite element response sensitivity analysis using force-based frame models

This paper presents a method to compute consistent response sensitivities of force-based finite element models of structural frame systems to both material constitutive and discrete loading parameters. It has been shown that force-based frame elements are superior to classical displacement-based elements in the sense that they enable, at no significant additional costs, a drastic reduction in the number of elements required for a given level of accuracy in the computed response of the finite element model. This advantage of force-based elements is of even more interest in structural reliability analysis, which requires accurate and efficient computation of structural response and structural response sensitivities. This paper focuses on material non-linearities in the context of both static and dynamic response analysis. The formulation presented herein assumes the use of a general-purpose non-linear finite element analysis program based on the direct stiffness method. It is based on the general so-called direct differentiation method (DDM) for computing response sensitivities. The complete analytical formulation is presented at the element level and details are provided about its implementation in a general-purpose finite element analysis program. The new formulation and its implementation are validated through some application examples, in which analytical response sensitivities are compared with their counterparts obtained using forward finite difference (FFD) analysis. The force-based finite element methodology augmented with the developed procedure for analytical response sensitivity computation offers a powerful general tool for structural response sensitivity analysis