doi: 10.52899/24141437_2026_01_53
UDK: 629.5.015.4

Optimization of regular orthotropic plate models

Миронов М. Ю.
Article language:
Citation Link: Mironov MYu. Optimization of regular orthotropic plate models. Transactions of the Saint Petersburg State Marine Technical University. 2026;5(1):53–62. DOI: 10.52899/24141437_2026_01_53 EDN: HSHQDG

Annotation

BACKGROUND: Taking into account the expansion of technical possibilities for manufacturing plates and panels from polymer composite materials, it is relevant to mathematically substantiate their rational beam reinforcements under given quality criteria and restrictions. When using such materials in plate structures, it is important to take into account their pronounced orthotropy by applying algorithms of indirect optimization methods for finite-element models of plates. AIM: construction and application of algorithms for indirect optimization methods to finite-element models of orthotropic plates of variable thickness in order to mathematically substantiate rational beam reinforcements of plates and shells made of polymer composite materials under specified quality criteria and constraints. METHODS: The algorithm was developed based on an indirect iterative approach to satisfying the simple necessary conditions of Kuhn-Tucker optimality, considering isoperimetric restrictions. The Lagrange multiplier technique and the finite element method were employed. RESULTS: Obtaining optimal configurations of localized stiffnesses (thickenings) and the influence of elastic parameters of an orthotropic material on them is considered. CONCLUSION: The indirect method of satisfying optimality conditions of the 1st order is an effective means of controlling the properties of anisotropic plates and identifying optimal schemes of beam reinforcements (fins), while it can be no less cost-effective than the methods of homogenization in topological optimization. Consideration of transverse shifts in thickening finite elements, as well as the mutual influence of bending and longitudinal stiffness, can be carried out by constructing more efficient plate-plate finite elements based on the Reissner–Mindlin theory. Keywords: orthotropic plates; planar stress state; mass minimization under stiffness limitation; Kuhn–Tucker conditions; finite element under complex bending; regular mesh; localization of thickenings; influence of the ratio of elastic modulus.

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