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Optimal design of a beam subject to bending: a basic application. (English) Zbl 1383.49053

Summary: The minimization of both the mass and deflection of a beam in bending is addressed in the paper. To solve the minimization problem, a multi-objective approach is adopted by imposing the Fritz John conditions for Pareto-optimality. Constraints on the maximum stress and elastic stability (buckling) of the structure are taken into account. Additional constraints are set on the beam cross section dimensions. Three different cross sections of the beam are analyzed and compared, namely the hollow square, the I-shaped and the hollow rectangular cross sections. The analytical expressions of the Pareto-optimal sets are derived. As expected, the I-shaped beam exhibits the best compromise in structural performance, which is related on the particular loading considered.

MSC:

49S05 Variational principles of physics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74P05 Compliance or weight optimization in solid mechanics
49M30 Other numerical methods in calculus of variations (MSC2010)
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