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SUMMARYAn SQP-based reduced Hessian method for simultaneous analysis and design (SAND) of non-linearly behaving structures is presented and compared with conventional nested analysis and design (NAND) methods. It is shown that it is possible to decompose the SAND formulation to take advantage of the particular structure of the problem at hand. The resulting reduced SAND method is of the same size as the conventional NAND method but it is computationally more efficient. The presentation here builds on previous research on SAND methods generalizing the solution approach to cases with both equality and inequality constraints. The new version of the reduced SAND method is tested in the context of weight minimization of 3-D truss structures with geometrically non-linear behaviour.1997 by John Wiley & Sons, Ltd.

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.

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