Limit analysis of reinforced masonry vaults

Reinforced brick masonry has experienced only scarce use as a fully structural material due to, among other reasons, the lack of design criteria and calculation tools allowing a scientific, but also practical, engineering approach to design and assessment. Aiming at contributing to a more widespread use of this material, a simplified method for the ultimate analysis of reinforced masonry arches and cylindrical vaults, based on the lower-bound theorem (or static approach) of plasticity, has been developed. This approach has been satisfactorily validated by comparison with experimental and numerical results obtained by more accurate numerical models

Non-Parametric Shape Design of Free-Form Shells Using Fairness Measures and Discrete Differential Geometry

A non-parametric approach is proposed for shape design of free-form shells discretized into triangular mesh. The discretized forms of curvatures are used for computing the fairness measures of the surface. The measures are defined as the area of the offset surface and the generalized form of the Gauss map. Gaussian curvature and mean curvature are computed using the angle defect and the cotangent formula, respectively, defined in the field of discrete differential geometry. Optimization problems are formulated for minimizing various fairness measures for shells with specified boundary conditions. A piecewise developable surface can be obtained without a priori assignment of the internal boundary. Effectiveness of the proposed method for generating various surface shapes is demonstrated in the numerical examples

Optimization of plastic structures

http://www.ester.ee/record=b1217974*es

Invisibility and Inverse Problems

This survey of recent developments in cloaking and transformation optics is an expanded version of the lecture by Gunther Uhlmann at the 2008 Annual Meeting of the American Mathematical Society.Comment: 68 pages, 12 figures. To appear in the Bulletin of the AM

Optimization of plastic spherical shells

http://www.ester.ee/record=b1547873~S1*es

Tile vaults as integrated formwork for reinforced concrete: Construction, experimental testing and a method for the design and analysis of two-dimensional structures

Tile vaults are traditional, unreinforced masonry structures made of thin bricks (tiles), mortar and fast-setting cement or gypsum. They can be constructed without the need for a formwork, except at the boundaries, making them inherently economic. Tile vaults have historically provided a solution for the efficient construction of vaulted structures. Today, they can be used as permanent formwork for concrete shells, allowing for a significant reduction of the construction cost and waste produced, due to the possibility of reducing or even eliminating the need for traditional formwork. The concrete can be poured directly onto a tile-vaulted formwork to form a composite structure. This paper presents a technique for the construction of single-curvature shells consisting of a composite structure combining tile vaulting and reinforced concrete. A method for the design of these composite vaults and the assessment of their strength and stability against external loading is also presented. This method is based on limit analysis but takes into account the reinforcement’s contribution to the composite cross-section’s bending capacity. The equilibrium method is implemented computationally to provide fast results for the user. It provides graphical and intuitive results and opens the possibility for the future extension to fully three-dimensional problems. The design and structural analysis method is called Extended Limit Analysis for Reinforced Masonry (ELARM). Both the proposed construction technique and the computational method have been validated through experimental research. The feasibility of the building technique has been validated by the construction of two full-scale prototypes. In addition, the prototypes have been load-tested to failure to compare the results with those predicted by ELARM.Peer ReviewedPostprint (author's final draft

Pragudega elastsete astmeliste talade stabiilsus

Väitekirja elektrooniline versioon ei sisalda publikatsiooneKäesolevas väitekirjas vaadeldakse elastsete astmeliste talade stabiilsust. Töö aluseks on autori kuus teaduslikku publikatsiooni, millest kolm on avaldatud viimase kolme aasta jooksul. Väitekiri koosneb neljast osast: kokkuvõtvast osast ehk kokkuvõtteartiklist, publikatsioonide koopiatest, kirjanduse ülevaatest ja autori elulookirjeldusest. Antud töös uuritakse elastseid talasid, millele mõjub teljesuunaline koormus. Talad on astmelised ning astme kohtades asuvad defektid ehk praod, mis antud uurimuses on stabiilsed. Pragude sügavus ja asukoht mõjutab talade stabiilsust ning stabiilsuse tundlikkust antud parameetrite suhtes on analüüsitud kombineerides elastsusteooria ja lineaarse purunemismehaanika meetodeid. Esimeses peatükis tuuakse ajalooline ülevaade kirjandusest. Teises peatükis esitatakse uurimuse põhialused prao mõju analüüsiks. Praoga tala uurimiseks kasutatakse nn. kaalutu väändevedru mudelit. Selle mudeli kohaselt asendatakse praoga tala konstruktsiooniga, mis koosneb kahest tala tükist (elemendist). Need elemendid on omavahel ühendatud kaalutu väändevedruga, mille jäikus on võrdeline pinge intensiivsuse koefitsendiga prao tipu juures. Järgnevas neljas peatükis uuritakse kriitilise koormuse sõltuvust prao parameetritest erinevate talade ja kinnitustingimuste korral. Esimesel juhul on vaatluse all konsooltala, teisel juhul on vabale otsale lisatud elastne kinnitus. Kolmandaks uuritakse konsooltala, mis asub elastsel alusel ning lõpetuseks tala, mis on seest õõnes (nelinurkne toru).In the present thesis critical buckling loads of stepped beams are studied and the sensitivity of the critical load on the parameters of stable cracks as location and depth is analysed. Combining the methods of the elastic beam theory and of the linear elastic fracture mechanics an approximate method for the stability analysis of beams and columns subjected to the axial pressure is developed. Introducing the additional compliance matrix the flexibility of the beam in the vicinity of a crack is prescribed by means of the compliance of the structure. This, in turn, is coupled with the stress intensity factor which can be calculated by methods of the linear elastic fracture mechanics. Critical buckling loads of stepped columns subjected to the axial pressure and weakened with cracks emanating from re-entrant corners of steps are established. Numerical results are presented for uniform and hollow beams with single step of the cross section, also for two-stepped beams. The beams under consideration are simply supported or clamped at the ends, also cantilevers, elastically fixed. The case of beams resting on elastic foundation is studied separately. The dissertation is based on the six papers of the author (two of these are published during the last two years). The dissertation consists of the review of the obtained results, the copies of the papers, the list of literature and CV of the author. The dissertation is organized as follows. Section 1 contains historic background of the stability analysis, the aim and the structure of the dissertation. In section 2 the concept of local flexibility is described in detail. In sections 3, 4, 5 and 6 the method is applied to partcular cases of beams. The first case concerns elastic beams that are clamped at one end and free at another end. Secondly elastically fixed beams are studied in greater detail. In section 5 beams resting on elastic foundation are considered. Finally, in section 6 beams with hollow cross sections are studied. The influence of crack length and step location on the stability of the beams has been analyzed

Differentiable Stripe Patterns for Inverse Design of Structured Surfaces

Stripe patterns are ubiquitous in nature and everyday life. While the synthesis of these patterns has been thoroughly studied in the literature, their potential to control the mechanics of structured materials remains largely unexplored. In this work, we introduce Differentiable Stripe Patterns -- a computational approach for automated design of physical surfaces structured with stripe-shaped bi-material distributions. Our method builds on the work by Knoppel and colleagues for generating globally-continuous and equally-spaced stripe patterns. To unlock the full potential of this design space, we propose a gradient-based optimization tool to automatically compute stripe patterns that best approximate macromechanical performance goals. Specifically, we propose a computational model that combines solid shell finite elements with XFEM for accurate and fully-differentiable modeling of elastic bi-material surfaces. To resolve non-uniqueness problems in the original method, we furthermore propose a robust formulation that yields unique and differentiable stripe patterns. %Finally, we introduce design space regularizers to avoid numerical singularities and improve stripe neatness We combine these components with equilibrium state derivatives into an end-to-end differentiable pipeline that enables inverse design of mechanical stripe patterns. We demonstrate our method on a diverse set of examples that illustrate the potential of stripe patterns as a design space for structured materials. Our simulation results are experimentally validated on physical prototypes.Comment: 14 page

Piezo-electromechanical smart materials with distributed arrays of piezoelectric transducers: Current and upcoming applications

This review paper intends to gather and organize a series of works which discuss the possibility of exploiting the mechanical properties of distributed arrays of piezoelectric transducers. The concept can be described as follows: on every structural member one can uniformly distribute an array of piezoelectric transducers whose electric terminals are to be connected to a suitably optimized electric waveguide. If the aim of such a modification is identified to be the suppression of mechanical vibrations then the optimal electric waveguide is identified to be the 'electric analog' of the considered structural member. The obtained electromechanical systems were called PEM (PiezoElectroMechanical) structures. The authors especially focus on the role played by Lagrange methods in the design of these analog circuits and in the study of PEM structures and we suggest some possible research developments in the conception of new devices, in their study and in their technological application. Other potential uses of PEMs, such as Structural Health Monitoring and Energy Harvesting, are described as well. PEM structures can be regarded as a particular kind of smart materials, i.e. materials especially designed and engineered to show a specific andwell-defined response to external excitations: for this reason, the authors try to find connection between PEM beams and plates and some micromorphic materials whose properties as carriers of waves have been studied recently. Finally, this paper aims to establish some links among some concepts which are used in different cultural groups, as smart structure, metamaterial and functional structural modifications, showing how appropriate would be to avoid the use of different names for similar concepts. © 2015 - IOS Press and the authors