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Optimization of Axially Compressed Rods with Mixed Boundary Conditions

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Fundamentals of Structural Optimization

Part of the book series: Mathematical Engineering ((MATHENGIN))

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Abstract

The optimization problem for a column with arbitrary clamped ends, loaded by compression forces is studied in this chapter. The closed-form solutions for boundary conditions of mixed type are derived. The solutions are expressed in terms of the higher transcendental functions. The principal results are the closed form solution in terms of the elliptic functions, the analysis of bimodal regimes, and the exact bounds for the masses of the optimal columns. The isoperimetric inequality was formulated as the strict inequality sign, because the optimal solution could not be attained for any finite setting of the design parameter. The additional restriction on the minimal area of the cross-section regularizes the optimization problem and leads to the definite attainable shape of the optimal column.

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  1. Department of Natural Sciences, University of Siegen, Paul-Bonatz-Str. 9-11, 57068, Siegen, Germany

    Vladimir Kobelev

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  1. Vladimir Kobelev
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Kobelev, V. (2023). Optimization of Axially Compressed Rods with Mixed Boundary Conditions. In: Fundamentals of Structural Optimization. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-34632-3_6

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