Global optimization of 2D frames with variable cross-section beams

The structural design was one of the first engineering fields in needing powerful tools for analysis. The methods to check design criteria (strength, stability, vibrations, etc.) are very demanding on a computationally point of view and they usually assume usual simplifications, such as constant cross-section or linearization... However, with current capabilities - both of analysis and manufacturing - and the use of new materials togethet with certain aesthetic constraints, it is possible dealing with problems like the one presented in this paper, which try to determinate the optimal variation of the dimensions of the cross-section of the beams of any 2D frame is determined in order to fulfill all the criteria required, including stability, ie buckling phenomena don't appear/its strength to buckle is maximum. But for beams structure. The problem is more complex and must be solved numerically. The new/novel formulation presented in this paper can solve the optimization problem, considering/taking into account frames not only buckling conditions, but any other, such as allowable stresses, restricted movement and so on. Certain design parameters are selected and the optimizacion problem is mathematically formulated in order to determine what values maximize buckling load, under design restrictions (material, stresses, displacement). With these aim, equilibrium equations for each beam are established/considered in its deformed configuration, under the hypothesis of small displacements and small deformations (Second Order Theory), resulting in a system of differential equations of variable coefficients, which is numerically solved thorugh sequential quadratic programming.