Range and Null Space Decomposition applied to analysis of slender concrete columns

Abstract

The strength analysis of a simply supported slender concrete column subject to biaxial bending is formulated as a nonlinear programming problem. Geometrical imperfections as well as two types of concrete constitutive equations, for local and global verifications, are taken into account. The algorithm of choice is the Sequential Quadratic Programming method (SQP). Large numbers of state variables and equilibrium equality constraints appear in the formulation, which is a characteristic of the optimization of nonlinear structures in general. This considerably hinders the efficiency and robustness of the SQP algorithm. Therefore the Range and Null Space Decomposition (RND) is employed in order to decrease the size of the quadratic programming subproblem that must be solved in each iteration, as well as the size of the approximating Hessian that must be updated. An example is presented to illustrate the efficiency of the proposed approach which took almost one-third of the CPU time required by the standard SQP algorithm to converge to a solution.