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Optimal archgrids spanning rectangular domains PDF Drukuj Email
Grzegorz Dzierżanowski, Radosław Czubacki, Optimal archgrids spanning rectangular domains, Computers and Structures, volume 242 (1 January 2021), article 106371
https://doi.org/10.1016/j.compstruc.2020.106371

Abstract
The theory of archgrids of minimal weight has been formulated in the late 1970s and recently reconsidered by means of duality theory in the calculus of variations. In the current study, we follow this approach by putting forward an efficient computational scheme. Trial functions for both primal and dual problems are decomposed in two function bases: trigonometric (Fourier) and polynomial (Legendre). Our focus is on structures composed of arches forming a rectangular grid, i.e. running in two mutually perpendicular directions and spanning a given rectangular domain. In the course of discussion, we show that the numerical algorithm is quickly convergent, CPU time efficient, and robust. In particular, it provides clear-cut solutions in which optimal parts of a structure are sharply distinguished from the non-optimal, hence redundant, ones.
 
Applications of Michell’s Theory in Design of High-Rise Buildings, Large-Scale Roofs and Long-Span Bridges PDF Drukuj Email
C. Graczykowski, T. Lewiński, Applications of Michell’s Theory in Design of High-Rise Buildings, Large-Scale Roofs and Long-Span Bridges, Computer Assisted Methods in Engineering and Science (CAMES) 27(2-3) 2020
https://cames.ippt.pan.pl/index.php/cames/article/view/288.
DOI: https://doi.org/10.24423/cames.288.

Abstract
This paper analyzes the relations between the theory of Michell structures, which is one of the most important theories in structural optimization, and some remarkable engineering structures, including selected high-rise buildings, large-scale roof coverings and long-span bridges. The first part of this study briefly presents the development of Michell’s theory, its basic concepts, assumptions, and examples and fundamental features of Michell structures. Then, several untypical engineering structures that make use of said concepts are presented, including skyscrapers proposed by the Polish structural designer W. Zalewski and the international architectural office of Skidmore, Owings and Merill (SOM). Next, large-scale roof coverings of “Spodek” arena in Poland as well as selected bridges are thoroughly analyzed in the context of similarity to Michell structures. The conducted
study reveals that considered structural forms of the analyzed structures follow some of the concepts known from Michell’s theory and thus possess many features of the optimal structural designs.
 
Optimal Form-Finding of Cable Systems PDF Drukuj Email
Dzierżanowski Grzegorz, Wójcik-Grząba Izabela, Optimal Form-Finding of Cable Systems, Archives of Civil Engineering, vol. 66, nr 3, 2020, ss. 305-321
DOI:10.24425/ace.2020.134399

online>>

Abstract
Tensile structures in general, achieve their load-carrying capability only after the process of initial form-finding. From the mechanical point of view, this process can be considered as a problem in statics. As cable systems are close siblings of trusses (cables, however, can carry tensile forces only), in our study we refer to equilibrium equation similar to those known from the theory of the latter. In particular, the paper regards designing pre-tensioned cable systems, with a goal to make them kinematically stable and such that the weight of so designed system is lowest possible. Unlike in typical topology optimization problems, our goal is not to optimize the structural layout against a particular applied load. However, our method uses much the same pattern. First, we formulate the variational problem of form-finding and next we describe the corresponding iterative numerical procedure for determining the optimum location of nodes of the cable system mesh. We base our study on the concept of force density which is a ratio of an axial force in cable segment to its length.
 
Recovery of the Auxetic Microstructures Appearing in the Least Compliant Continuum Two-Dimensional Bodies PDF Drukuj Email
Sławomir Czarnecki, Tomasz Łukasiak, Recovery of the Auxetic Microstructures Appearing in the Least Compliant Continuum Two-Dimensional Bodies, Physica Status Solidi (b) 1900676, 2020 (16 stron)

Available on line(https://doi.org/10.1002/pssb.201900676)>>

Abstract
The article discusses the 2D problem of manufacturability of the minimum compliance designs of the structural elements made of inhomogeneous materials of local isotropic or square symmetry properties. The available isotropic material design (IMD) and cubic material design (CMD) methods deliver the optimal distribution of the elastic moduli within the design domain. Within the 2D setting, the cubic symmetry reduces to the symmetry of a square. The varying underlying microstructures corresponding to the optimal designs are recovered by matching the values of the optimal moduli with the values of the effective moduli of the representative volume elements (RVEs) computed by the asymptotic homogenization method for periodic media. The shape of the RVE and its internal symmetries are properly selected providing assumed isotropy or symmetry of a square of the homogenized constitutive tensor. The microstructure topology is described by parametric description of single (or several) fibers in RVE. The periodicity of the structure and the final topology of the material within RVE is ensured by multiplication of a single fiber in accordance with the symmetries adopted for RVE. The ability to model an auxetic behavior within the subdomains where the optimal Poisson's ratio assumes negative values is shown.
 
Michell structures within L-shaped domains PDF Drukuj Email
K. Bołbotowski, T. Lewiński, T. Sokół, Michell structures within L-shaped domains, Computer Assisted Methods in Engineering and Science (CAMES),2020

on line: https://cames.ippt.pan.pl/index.php/cames/article/view/281

DOI: https://doi.org/10.24423/cames.281.
 
Abstract
By recalling the main mathematical results concerning the theory of Michell structures, the present paper puts forward an interpretation of the selected numerical methods for constructing their approximants, that is, trusses with a large number of nodes. The efficiency of one of these methods: the ground structure method in its adaptive version is shown in the context of the L-shaped design domain problem. A large family of highly accurate truss approximants corresponding to the point loads acting at selected vertices is constructed and discussed.
 
Optimal archgrids: a variational setting PDF Drukuj Email
R. Czubacki, T. Lewiński, Optimal archgrids: a variational setting, Structural and Multidisciplinary Optimization 2020,
https://doi.org/10.1007/s00158-020-02562-y

Abstract
The paper deals with the variational setting of the optimal archgrid construction. The archgrids, discovered by William Prager and George Rozvany in 1970s, are viewed here as tension-free and bending-free, uniformly stressed grid-shells forming vaults unevenly supported along the closed contour of the basis domain. The optimal archgrids are characterized by the least volume. (...)

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