DYNA JOURNAL ENGINEERING

Key words:

optimización, carga crítica y modo de pandeo, inercia variable, optimization, critical load and buckling mode, variable cross-section.

Article type:

ARTICULO DE INVESTIGACION / RESEARCH ARTICLE

Section:

VARIOUS

ABSTRACT
The structural design has been one of the first fields of engineering in needing powerful tools for analysis. The methods to asses that the structure agrees with any of the design criteria (strength, stability, vibrations, etc. ) are usually implemented in numerical applications that, even under usual simplifications such as constant cross-section or linearization, are computationally very demanding. Nevertheless, with the current capacities both of analysis and of manufacturing and the use of new materials, it is possible to propose problems like the ones shown in this work, where the variation of the dimensions of the cross-section of the beams of any 2D frame is determined so that its strength to buckle is maximum. Classic solutions exist for isolated beams, in some cases even analytical solutions. But for structures built of several beams, the problem is more complex and numerical solutions are compulsory. The new formulation presented in this work can deal with the optimization problem of frames in which the geometrical shape of the profile is found under restrictions such as stability (no buckling), elastic behaviour (equivalent von Mises stress below the yield stress), limited displacements, etc. With these aim, equilibrium equations for each beam are established in its deformed configuration, and using the hypothesis of small displacements and small deformations (Second Order Theory) a system of differential equations of variable coeficients is set. For its solution, numerical techniques as quadratic sequential programming are employed.
KEYWORDS: optimization, critical load and buckling mode, variable cross-section.