Geometry optimization of a slender cantilever beam subjected to lateral buckling

Authors:
Miha Polajnar;Radovan Drazumeric;Franc Kosel
Affiliations:
Cimos d.d., Koper, Slovenia 6000;Faculty of Mechanical Engineering, University of Ljubljana, Ljubljana, Slovenia 1000;Faculty of Mechanical Engineering, University of Ljubljana, Ljubljana, Slovenia 1000
Venue:
Structural and Multidisciplinary Optimization
Year:
2013

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Abstract

The paper deals with the geometry optimization of a slender cantilever beam subjected to a concentrated force acting at the free end. The two-parametric mathematical model of lateral torsional buckling is based on the Bernoulli---Euler beam theory and is given in dimensionless form. The optimization procedure is performed using the optimal control theory and the relation between state and adjoint variables is presented. The boundary value problem derived from the optimization procedure is solved numerically and compared to solutions obtained via an alternative optimization approach called sequential approximate optimization.