Optimal design of a beam subjected to compression forces in the framework of different structural models

The optimal design of a vertical cantilever beam is presented in this paper. The beam is assumed immersed in an elastic Winkler soil and subjected to several loads: a point force at the tip section, its self weight and a uniform distributed load along its length. lbe optimal design problem is to find the beam of a given length and minimum volume, such that the resultant compressive stresses are admisible. This prohlem is analyzed according to linear elasticity theory and within different alternative structural models: column, Navier-Bernoulli beam-column, Timoshenko beamcolumn (i.e. with shear strain) under conservative loads, typically, constant direction loads. Results obtained in each case are compared, in order to evaluate the sensitivity of model on the numerical results. The beam optimal design is described by the section distribution layout (area, second moment, shear area etc.) along the beam span and the corresponding beam total volume. Other situations, some of them very interesting from a theoretical point of view, with follower loads (Beck and Leipholz problems) are also discussed, leaving for future work numerical details and results.