TABLE OF CONTENTS Design sensitivity analysis deals with the calculation of changes in the response of the structure resulting from changes in the parameters describing the structure. The derivatives of the response vector with respect to the system parameters are usually referred to as the sensitivity coefficients. The latter are used to:
predict the changes in the system response due to changes in the parameters;
select a search direction in design optimization problems;
construct explicit approximations of the constraint functions in terms of the structural parameters (e.g. first-order Taylor series approximations);
generate approximations for the response of a modified system, including approximate reanalysis models;
assess the effects of uncertainties in the structural properties (material properties, geometric parameters and other parameters) on the system response.
Methods of design sensitivity analysis can be divided into the following classes:
Analytical methods, which are widely used and often demonstrate good performance. However, implementation of these methods is difficult in some problems, such as shape optimization, where analytical derivatives of the stiffness matrix are not easy to obtain.
"Semi-analytical", or "quasi-analytical" methods, based on finite-difference evaluation of the right-hand-side vector, the so-called "pseudo load". These methods combine ease-of-implementation and computational efficiency, and they have been implemented in several finite element programs. However, the errors associated with the finite difference approximation of the right-hand-side vector can be substantial [1] , [2].
Finite-difference methods, which are the easiest to implement and therefore they are quite popular. For a problem with n design variables, finite difference derivative calculations...
