44 research outputs found
Ivory shells and polyhedra
p. 881-892We present a morphological survey of nested ivory shells and polyhedra made by turning,
and show examples of related objects of art of known ivory collections, that can be
interesting from geometrical and also from structural point of view.Tarnai, T. (2010). Ivory shells and polyhedra. Editorial Universitat Politècnica de València. http://hdl.handle.net/10251/695
PARTIAL COVERING OF A CIRCLE BY EQUAL CIRCLES. PART I: THE MECHANICAL MODELS
How must n equal circles of given radius be placed so that they cover as great a part of the area of the unit circle as possible? To analyse this mathematical problem, mechanical models are introduced. A generalized tensegrity structure is associated with a maximum area configuration of the n circles, whose equilibrium configuration is determined numerically with the method of dynamic relaxation, and the stability of equilibrium is investigated by means of the stiffness matrix of the tensegrity structure. In this Part I, the principles of the models are presented, while an application will be shown in the forthcoming Part II
Mechanikai problémákból származó nemlin. egyenletrendszerek elemzése és megoldása a MATHEMATICA integrált rendszer alkalmazásával. = Analysis and solving sets of nonlinear equations originated from mechanics using the integrated system MATHEMATICA.
A mĂ©rnöki gyakorlathoz kapcsolĂłdĂł mechanikai problĂ©mák sok esetben vezetnek nemlineáris numerikus feladatra. Ilyen feladatot jelent többek között a szerkezetek stabilitásvizsgálata, a nagy elmozdulásokkal kapcsolatos vizsgálatok, illetve geodĂ©ziai eredetű számĂtási problĂ©mák is. Kutatásaink során megmutattuk, hogy rugalmas szerkezetek stabilitásának (egyensĂşlyi Ăştjainak) vizsgálatakor a mĂ©rnöki intuĂciĂłval ellentĂ©tes eredmĂ©nyek is adĂłdnak. Vizsgáltuk magas rendben szimmetrikus szerkezetek kompatibilitási, valamint nagy elmozdulásokra kĂ©pes (Ă©s a DNS-molekula mechanikai modellezĂ©sĂ©re is alkalmas) hajlĂtott-csavart rudak egyensĂşlyi Ăştjait, illetve iteráciĂłs eljárást dolgoztunk ki terhelt vasbeton gerendák alakmeghatározása cĂ©ljábĂłl. ElkĂ©szĂtettĂĽk bizonyos mĂ©rnöki feladatokban használt algoritmusok Mathematica szimbolikus-numerikus integrált rendszerbeli implementáciĂłját (pl. Bairstow-mĂłdszer, illetve a geodĂ©zia mĂ©rĂ©si hibáinak kiegyenlĂtĂ©sĂ©re Ă©s GPS-rendszerekben használatos "support vector regression"-mĂłdszer), igazolva ezzel a szimbolikus-numerikus rendszerek konkrĂ©t mĂ©rnöki feladatok megoldásában valĂł hatĂ©kony alkalmazhatĂłságát. Mindezek alapján a PhD-kĂ©pzĂ©s vonatkozĂł tantárgyainak anyagát is átdolgoztuk a Mathematica által a nyĂşjtott lehetĹ‘sĂ©gek figyelembe vĂ©telĂ©vel. | Mechanical questions arising from engineering practice often lead to nonlinear numeric problems. This happens e.g. when stability or big displacements of a structure, as well as some computational problems coming from Geodesy are analysed. In the current research it has been shown that investigations on stability (equilibrium paths) of elastic structures sometimes give a result apparently opposed to the intuition of an engineer. Compatibility paths of highly symmetric structures and equilibrium paths of a twisted and bent rod (subject to big displacements) has also been investigated; this latter one is relevant by providing a possible mechanical model of the DNA molecule. An iterative method has been developed aiming the shape determination of loaded reinforced concrete beams as well. Some algorithms that are frequently used in engineering problems have been implemented in the Mathematica computer-algebraic system (CAS), e.g. the Bairstow method or the support vector regression method used in GPS navigation systems, thus proving the wide-spread applicability of CAS systems in solving given engineering problems. Accordingly, the material of related PhD subjects has been revised and synchronised with the options provided by Mathematica for engineers
Szerkezeti topolĂłgia = Structural topology
Numerikus megoldásokat állĂtottunk elĹ‘ a körpárok Ă©s körhármasok gömbön valĂł legsűrűbb elhelyezĂ©sĂ©nek problĂ©májára, Ă©s szimmetria alapĂş vizsgálatokat vĂ©geztĂĽnk a gömbi körelhelyezĂ©s gráfjának Danzer-fĂ©le merevsĂ©gĂ©re vonatkozĂłan. Egy általunk bevezetett gömbölyűsĂ©gi kritĂ©rium alapján optimális, gömböt közelĂtĹ‘ poliĂ©dereket konstruáltunk. A szakrális Ă©pĂĽleteken elĹ‘fordulĂł csillagpoliĂ©derekre alakmeghatározást Ă©s számĂtĂłgĂ©pes rekonstrukciĂłt hajtottunk vĂ©gre. Konvex testekre vonatkozĂłan több tĂ©telt bizonyĂtottunk. Meghatároztuk a gömbi Ă©s tĂ©rbeli trivalens szálhálĂłzatok megfeszĂthetĹ‘sĂ©gĂ©nek feltĂ©teleit. Gömbi koordinátákban Ărtuk fel a gömbfelszĂnre illeszkedĹ‘ csuklĂłs rĂşdszerkezetek egyensĂşlyi Ă©s kompatibilitási egyenleteit, Ă©s állĂtottuk elĹ‘ a szerkezet potenciálfĂĽggvĂ©nyĂ©t. BebizonyĂtottuk, hogy egy tĂşlhatározott, háromszorosan szimmetrikus Bricard-mechanizmus esetĂ©ben bizonyos paramĂ©ter Ă©rtĂ©keknĂ©l elĹ‘fordulhat a kompatibilitási Ăşt elágazása. A katasztrĂłfaelmĂ©letet kompatibilitási utak elágazásának vizsgálatára alkalmaztuk. Az itt elĹ‘fordulĂł kettĹ‘scsĂşcs-katasztrĂłfával kapcsolatban egy olyan modellcsaládot elemeztĂĽnk, amely a kettĹ‘scsĂşcs-katasztrĂłfa nĂ©gy alosztályán is keresztĂĽlhalad. | Numerical solutions are established to the problem of the densest packing of pairs and triplets of circles on a sphere, and symmetry extended analysis of the Danzerian rigidity of the packing graphs is executed. On the basis of a sphericity criterion introduced by us, polyhedra approximating the sphere are constructed. Shape determination and computer aided reconstruction is done for star polyhedra occurring on sacred buildings. A number of theorems are proved for convex bodies. Criteria of stressability of spherical and spatial trivalent fibre nets are determined. Equilibrium and compatibility equations as well as potential function of bar-and-joint assemblies lying on the surface of a sphere are written with spherical co-ordinates. It is proved that, for certain parameter values, there exists bifurcation of the compatibility path of an overconstrained, threefold symmetric Bricard linkage. Catastrophe theory is applied for investigation of bifurcation of compatibility paths. Concerning double cusp catastrophe, a family of models is analysed, which goes through four subclasses of the double cusp catastrophe
The systematic development and optimization of large-scale sperm cryopreservation in northern pike (Esox lucius)
UPPER BOUND OF DENSITY FOR PACKING OF EQUAL CIRCLES IN SPECIAL DOMAINS IN THE PLANE
In the paper we will give heuristic upper bounds for the density of packings
of non-overlapping equal circles in a square, an equilateral triangle, and a
circle. The area of interstices at the boundary of these domains is
calculated with greater precision than by other authors, so the obtained
upper bounds are sharper than those known before. Because the function
int(x) appears in the relationships, the upper
bounds are not monotonous functions of the circle number. Not only the
formulae of upper bounds of the maximum packing density are given, but their
numerical values are listed up to 30 circles
Les Mécanismes Finis et la Charpente Octogonale de la Cathédral d'Ely
Cet article utilise I’exemple de la charpente octogonale de la cathédrale d’Ely pour montrer qu’une structure en anneau, topologiquement équivalente au réseau d’arêtes d’un antiprisrne n-gonal où n est pair, constitue un mécanisme fini si elle est symétrique par rapport à un plan passant par un sommet du n-gone supérieur de la structure en anneau. Dans I’appendice de J. Eddie Baker (p. 17), on montre que I’existence d’un plan de symétrie est, en général, non seulement suffisante mais aussi necessaire à la mobilité.Using the example of the timber octagon of Ely Cathedral this paper shows that a ring structure, topologically equivalent to the edge network of an n-gonal antiprism where n is even, constitutes a finite mechanism if it is symmetric with respect to a plane passing through a vertex of the upper n-gon of the ring structure. In the Appendix by J. Eddie Baker (p. 17) it is proved that the existence of a plane of symmetry is, in general, not only sufficient but also
necessary for mobility.Peer Reviewe