NONLINEAR INCREMENTAL-ANALYSIS OF LOADING AND DESIGN SENSITIVITY PROBLEMS

In this paper, it is demonstrated that incremental problems of nonline ar potential and nonpotential systems, including sensitivity problems, can be uniformly treated within the analysis of a homogeneous set of equations. Regular and critical states are considered. It is shown tha t rank analysis of a rectangular matrix of a homogeneous set of increm ental equations reveals all possible problems associated with singular ity conditions. When considering nonlinear design modification problem s, it is necessary to use derivatives of the secant and tangent stiffn ess matrices. A direct approach to differentiation of stiffness matric es on a finite element level in sensitivity problems is also presented . Simple illustrative examples are discussed.