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T. LEWIŃSKI, On Cherkaev–Lurie–Milton theorem in the plane problems of linear elasticity PDF Print E-mail
T. Lewiński, On Cherkaev–Lurie–Milton theorem in the plane problems of linear elasticity, Arch. Mech. 74 (4), 319–339, 2022,
DOI: 10.24423/aom.4083

Abstract
The paper delivers a full justification of the Cherkaev–Lurie–Milton theorem in application to the elasticity problem of in-plane loaded plates, 2D periodic
elastic composites, elasticity of thin plates subjected to transverse loads as well as in-plane periodic thin plates in bending. The theorem is treated as natural extension
of Michell’s result on 2D elasticity and the Gauss–Bonnet formula applied to the deflection surface of a thin plate subject to bending.
 
Korekta do książki PDF Print E-mail
Korekta do książki: T. Sokół, C. Graczykowski, T. Lewiński, Michell Structures,  Springer 2019.

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Enhanced growth method for topology and geometry optimization of truss structures PDF Print E-mail
Kozłowski, G., Sokół, T. Enhanced growth method for topology and geometry optimization of truss structures. Struct Multidisc Optim 65, 220 (2022).
https://doi.org/10.1007/s00158-022-03317-7

Abstract
In this paper, we present an enhanced growth method based on virtual displacements and strains fields for generating optimal design in terms of topology and geometry of plane trusses without the need of a generation of so-called ground structure. The method has been applied to the single load case problem with stress and size constraints in plastic design. In order to demonstrate the reliability and accuracy of the proposed method, three examples are carried out: Hemp cantilever, Chan cantilever and McConnel structure.
 
Setting the Free Material Design problem through the methods of optimal mass distribution PDF Print E-mail
Bołbotowski, K., Lewiński, T. Setting the Free Material Design problem through the methods of optimal mass distribution. Calc. Var. 61, 76 (2022).
https://doi.org/10.1007/s00526-022-02186-8

Abstract
The paper deals with the Free Material Design (FMD) problem aimed at constructing the least compliant structures from an elastic material, the constitutive field of which plays the role of design variable in the form of a tensor valued measure λ supported in the design domain. (...)
 
Optimal design of archgrids: the second-order cone programming perspective PDF Print E-mail
Grzegorz Dzierzanowski, Krzysztof Hetmanski, Optimal design of archgrids: the second-order cone programming perspective, Archives of Civil Engineering, 2021, 67(4), pp. 469-486,

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Abstract
This paper regards the minimum weight problem of spatial systems, known in the literature as Rozvany–Prager archgrids. Their architectural role is to transmit a load of fixed intensity to the line of supports located at the boundary of a given plane domain. The system consists of arches spaced apart from one another, hence the mechanics of such a system is that of a gridwork shell and not a shell continuum.
Mathematically, description of an archgrid falls into the class of Michell frames. (...)
 
Optimal vault problem – form finding through 2D convex program PDF Print E-mail
Bołbotowski, K. Optimal vault problem – form finding through 2D convex program. Computers & Mathematics with Applications, Elsevier (2022), t. 109, str. 280–324.
Abstract
This work puts forward a form finding problem of designing a least-volume vault that is a surface structure spanning over a plane region, which via pure compression transfers a vertically tracking load to the supporting boundary. Through a duality scheme, developed recently for the design of pre-stressed membranes, the optimal vault problem is reduced to a pair of mutually dual convex problems formulated on the 2D reference region. (...)
 
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