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Weight Minimization of an Elastic Beam with Classical and Non‐Classical Boundary Conditions
Author(s) -
Hlaváček I.
Publication year - 1987
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19870670804
Subject(s) - mathematics , piecewise , beam (structure) , convergence (economics) , minification , mathematical analysis , boundary value problem , homogeneous , piecewise linear function , variable (mathematics) , minimum weight , bending , dual (grammatical number) , duality (order theory) , elastic energy , mathematical optimization , physics , combinatorics , optics , art , literature , quantum mechanics , economics , thermodynamics , economic growth
A minimum weight optimal design problem for an elastic homogeneous beam is studied. The existence of an optimal solution – i.e. of an optimal variable height of the rectangular cross‐section of the beam – is proven. To this end, a dual variational formulation in terms of the bending moments (generalized principle of minimum complementary energy) is employed. We propose piecewise linear approximations and present a convergence analysis.
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