Alternative Formulations for Structural Optimization: An Evaluation Using Frames

Two alternative formulations based on the concept of simultaneous analysis and design are presented and evaluated for optimal design of framed structures. Different behavior variables, such as nodal displacements and member forces, are also treated as optimization variables in addition to the actual design variables for the problem. With these formulations, the equilibrium equations become equality constraints in the optimization process. The objective and all constraints become explicit functions of the optimization variables. Therefore, their derivatives can be obtained quite easily compared to those for the conventional approach where special design sensitivity analysis procedures must be used to calculate derivatives. It is also easier to use existing analysis software for optimization with the alternative formulations because the sensitivity equations are not formed or solved. A sequential quadratic programming method that exploits sparsity of problem functions is used to solve sample problems and evaluate the formulations. Implementation of the alternative formulations with an existing analysis program is explained. Advantages and disadvantages of the formulations are discussed. It is concluded that the alternative formulations work quite well for optimization of framed structures and have potential for further development.