A sparse approach to simultaneous analysis and design of geometrically nonlinear structures

Abstract: "The problem of increasing the efficiency of the optimization process for nonlinear structures has been examined by several authors in the last ten years. One of the methods that has been proposed to improve the efficiency of this process considers the equilibrium equations as equality constraints of the nonlinear mathematical programming problem. The efficiency of this method, commonly called simultaneous, as compared to the more traditional approach of nesting the analysis and design phases, is reexamined in this paper. It is shown that, when projected Lagrangian methods are used, the simultaneous method is computationally more efficient than the nested provided the sparsity of at least the Jacobian matrix is exploited.The basic structure of the Hessian and Jacobian matrices for geometrically nonlinear behavior of truss structures is given and numerical results are presented for a series of large problems using both dense and sparse projected Lagrangian methods."