Nonlinear adaptive analysis via quasi-Newton approach

The quasi-Newton (QN) method has proven to be the most effective optimization method. The purpose of this article is to apply this numerical procedure for optimization problems as well as large deflection nonlinear analysis. A FORTRAN program developed to calculate constrained problems is used as the basic code within an iterative nonlinear adaptive analysis. The new numerical procedure calculates the displacements of an elastic structure arising from given loading conditions. Then the displacements are added to the joint coordinates. In the deformed position the degrees of freedom of the structure are supported and the negative displacements are applied as loadings, to move the structure back to the old undeformed position. The difference of the reaction forces in both positions specifies the geometric nonlinear adaptive loading conditions. These additional forces, together with the displacement increments, form the QN vectors being applied in an iteration procedure until convergence is achieved. The new numerical procedure reduces the number of decompositions of the updated inverse stiffness matrix (solving a linear system of equations) and therefore is much more efficient than the standard QN approach. Although the word adaptive is mainly used in the sense of an "adaptive control" of a Finite Element mesh size, in this article the word is used for the calculation of the unbalanced forces applying the negative displacement increments as 'load increments". (C) 1999 Elsevier Science Ltd and Civil-Comp Ltd. All rights reserved.