Z. Gaspar

Z. Gaspar
Budapest University of Technology and Economics · Department of Structural Mechanics

DSc

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74
Publications
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641
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September 1967 - present
Budapest University of Technology and Economics
Position
  • Professor Emeritus

Publications

Publications (74)
Article
Full-text available
Background: Some medical and technological tasks lead to the geometrical problem of how to cover the unit circle as much as possible by n congruent circles of given radius r, while r varies from the radius in the maximum packing to the radius in the minimum covering. Proven or conjectural solutions to this partial covering problem are known only fo...
Article
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? In this paper the case of n = 4 is investigated. It is known that the centres of the four equal circles form a square in both the maximum packing and the minimum covering configurations, and it is expected that for radii...
Conference Paper
Full-text available
This paper describes significant advances in the field of exact structural topology optimization, extending Michell's 110 years old theory to a number of new design conditions that are listed in the title. Exact optimal topologies serve a highly useful purpose of verifying the validity, accuracy and convergence of numerical methods in topology opti...
Article
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 n...
Article
How must n equal circles of given radius r be placed so that they cover as great a part of the area of the unit circle as possible? In this Part II of a two-part paper, a conjectured solution of this problem for n = 5 is given for r varying from the maximum packing radius to the minimum covering radius. Results are obtained by applying a mechanical...
Article
Full-text available
The problem treated here is: amongst the convex polyhedra that can be circumscribed about the unit sphere and have faces, which has the minimum surface area? A new optimization method based on mechanical analogies is worked out to solve this problem. By using this method, new computer-generated solutions are presented for and . The second of these...
Article
Full-text available
A cikk azt mutatja be, hogy hogyan lehet egy feszültség alatt lévõ rácsos tartó rúderõit (esetleg engedékenységeit, terheit) meghatározni, ha csak a csomópontok koordinátáit tudjuk megmérni, igaz, ezt akkor is, ha a terhet ismert módon megváltoztatjuk. Az ehhez szükséges terhelési esetek szá-ma és az algoritmus függ attól, hogy ismerjük-e az eredet...
Article
Full-text available
The paper deals with the determination of the state variables of generalized trusses. These trusses are composed of bars, cables and struts. Cables act only for tension, while struts only for compression. To determine displacements and inner forces a nonlinear equation system is shown, which is solved by a modified Newton-Raphson method. The sugges...
Article
The adsorption of small silica particles onto large sterically stabilized poly(2-vinylpyridine) [P2VP] latex particles in aqueous solution is assessed as a potential route to nanocomposite particles with a "core-shell" morphology. Geometric considerations allow the packing efficiency, P, to be related to the number of adsorbed silica particles per...
Article
Full-text available
The journal Epites –Epiteszettudomany and its predecessor in title have a significant place among the publications in civil engineering and architecture. To demonstrate this it should be noted that in the last 50 years 26 members of the Hungarian Academy of Sciences (or those later becoming members) had publications in the journal: Janos Bogardi, E...
Chapter
Full-text available
The aim of this paper is to discuss some issues of pivotal importance in topology optimization, which receive inadequate attention in the literature.
Article
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Different types of loss of stability of elastic structures are usually illustrated by simple models. This paper presents a family of structures which can demonstrate four cases of the double cusp catastrophe by the variation of a parameter. The path defined by this parameter is calculated in the diagram of the classes of the double cusp catastrophe...
Article
The compatibility paths of mechanisms with a single degree-of-freedom typically form sets of curves in the global representation space. We classify the different cases of compatibility by introducing an energy function. The result obtained also depends on which element of the mechanism is regarded as driven. The different singularity types are demo...
Article
The kinematic determinacy of a bar-and-joint mechanism is dependent on the topology and the metric properties of the structure. Special arrangements can result in singularities, such as bifurcation points on the compatibility paths. The analysis of a special four-bar linkage yields an infinitely degenerate bifurcation point. Modifications in plane...
Article
Full-text available
The Kirchhoff rod is a widely used model in the describing configurations of DNA chains. In the simplest case of such research the molecule-chain is represented by a twisted-bent rod. In this paper we will present an application of this rod model for describing the shapes of the DNA chain in a special configuration. Here, two finite segments of the...
Chapter
First some concepts of the structural stability and the elementary catastrophe theory are shown. A short chapter explains which types of the catastrophes are typical at elastic structures. Hence the load parameter has a special role among the parameters, a subclassification is needed in the stability analysis. The main part of the paper shows this...
Article
Full-text available
A discrete model consisting N straight links and N springs is defined. The originally straight model is bent into a discrete torus, then it is twisted. The C2 symmetric shapes can be determined by four parameters, and there are three constrains. The equilibrium paths are determined by the simplex method (piecewise linear approximation). Global bifu...
Article
Full-text available
Forcing a simpler topology than the theoretical optimum by additional constraints may have several advantages, such as ease of manufacturing, mesh independence and checkerboard control. It is shown, however, that topology simplification may result in considerable weight increases. In examining various numerical anomalies such as checkerboard patter...
Article
Full-text available
Stability analysis of an orthotropic plate is studied using the algebra system Mathematica. The critical force is computed for given material parameters, geometry and load type (direct problem). Then the critical force is assumed to be known and the material and geometric parameters are computed (inverse problem). The inverse problem can be treated...
Article
Full-text available
The problem treated here is: how must N antipodal pairs of equal circles (spherical caps) of given angular radius r be arranged on the surface of a sphere so that the area covered by the circles will be as large as possible? Conjecture solutions of this problem for N= 4,5,7 are given where r varies from the maximum antipodal packing radius to the m...
Article
Full-text available
Most existing studies of 2D problems in structural topology optimization are based on a given (limit on the) volume fraction or some equivalent formulation. The present note looks at simultaneous optimization with respect to both topology and volume fraction, termed here “extended optimality”. It is shown that the optimal volume fraction in such pr...
Article
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How must n equal non–overlapping regular spherical pentagons be packed on a sphere so that the angular radius of the circumcircles o the pentagons will be as great as possible? In this paper, locally extremal results as conjectured solutions of this proble for n = 1, 2, 3, 4, 7, 9, 11, 12 are given and locally non–extremal results for n 7equals; 10...
Article
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Comparison of the classical methods and the tools of the catastrophe theory is presented through the imperfection-sensitivity analysis of the classical stable-symmetric bifurcation problem. Generally, classical global methods are related to a large interval, while catastrophe theory concerns the neighborhood of the critical point only, being a loca...
Article
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Ha egy viszkoelasztikus szerkezetet allando teherrel megterhelunk, akkor altala- ban a terheles pillanataban letrejon egy rugalmas alakvaltozas, majd valtozatlan te- her eseten is tovabbi deformacio alakul ki. Itt, es a tovabbiakban, feltetelezzuk, hogy a terheles kvazistatikus, vagyis olyan lassan jut a teher a szerkezetre, hogy a letrejovő elmozd...
Article
Full-text available
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. Becau...
Article
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Bolker and Crapo gave a graph theoretical model of square grid frameworks with diagonal rods of certain squares. Using this model there are very fast methods for connected planar square grid frameworks to determine their (infinitesimal) rigidity when we can use diagonal rods, diagonal cables or struts, long rods, long cables or struts. But what abo...
Article
Full-text available
This paper describes a method for the analysis of prestressed tent structures. With the help of this method, it is possible to take into account the effect of the approximations, which have to be used during the cutting pattern generation. During the determination of the real shape of the tent and during the structural analysis, it is possible to t...
Chapter
Some interesting aspects of numerical computation of bar structures subject to quasi-static load are dealt with. Beyond civil engineering applications, elastic beams are used in a variety of fields as models (e.g. for DNA molecules), so the ideas presented here are addressed to all scientists applying beams as models.
Article
E. D. Bolker and H. Crapo [SIAM J. Appl. Math. 36, 473-490 (1979; Zbl 0416.70009)] gave a graph theoretical model of square grid frameworks with diagonal rods of certain squares. J. A. Baglivo and J. E. Graver [Incidence and symmetry in designs and architecture (Cambridge Urban & Architectural Studies 7, Cambridge University Press, Cambridge and Ne...
Article
Full-text available
We discuss a global, iteration-free numerical scheme (based on the Piecewise Linear algorithm), with special respect to the computation of elasto-plastic frames. The plastic deformations are concentrated in plastic hinges which may appear at both ends of the bars, while the inner parts of the bars can have only elastic deformations but without lima...
Article
Full-text available
Tent structures are an interesting field of civil engineering, There exist special methods for their computation. There are only a few companies which are specialized in the design and constructing of tent structures in Europe. This paper compares the basic ideas of two working groups, each of which developed its own methods of calculation from the...
Article
Full-text available
This paper presents an algorithm for parallel computers, which is suitable for the global (arbitrary displacements) computation of elastic bar structures subject to quasi-static loads. Our method is also capable to determine equilibria which are not connected to the initial, trivial configuration. The paper discusses the gains and the disadvantages...
Article
Full-text available
A method is presented by means of which the equilibrium path of any elastic bar structure may be traced globally, without applying iteration techniques. The basic idea is that the bar structure is reduced to a set of Initial Value Problems (IVPs) with parameters, and the equilibrium path is piecewise linearly interpolated in the parameter space. Th...
Article
A connection is made between 1) the observed structures of virus capsids whose capsomers are all pentamers and 2) the mathematical problem of determination of the largest size of a given number of equal regular spherical pentagons that can be packed on the surface of the unit sphere without overlapping. It is found that papillomaviruses provide the...
Article
Full-text available
R. Connelly and H. Servatius [Discrete Comput. Geom. 11, No. 2, 193-200 (1994; Zbl 0793.52005)] showed an example of a nonrigid bar-and-joint assembly which was third-order rigid by their definition. Seeing this obvious contradiction, they concluded that the whole notion of higher-order rigidity is questionable. In this paper, using a definition of...
Article
Full-text available
How must a sphere be covered by n equal circles so that the angular radius of the circles will be as small as possible? In this paper, conjectured solutions of this problem for n = 15 to 20 are given and some sporadic results for n > 20 (n = 22, 26, 38, 42, 50) are presented. The local optima are obtained by using a ‘cooling technique’ based on the...
Article
Full-text available
The problem of determining the largest angular diameter dn of n equal circles which can be packed on the surface of a sphere without overlapping is investigated. It is known that the best packing of 5 (11) circles on a sphere is obtained if one circle is removed from the best packing of 6 (12) circles. Robinson has suggested that perhaps there are...
Article
Full-text available
Mathematical tools for the global description of discretized line continua are presented. These tools are applied to the analysis of the planar buckling of elastic bars under static loading. The results of the computer experiments display an essential difference between discrete models consisting of even and odd number of rigid bars. Propositions a...
Article
Full-text available
An analysis is presented for the Tammes problem: how must n points be distributed on the surface of a sphere in order that the minimum angular distance between any two of the points be a maximum? With the analogy of the capsid structure of small 'spherical' viruses, locally extremal arrangements are constructed in tetrahedral, octahedral and icosah...
Article
Full-text available
Elastic stability of structures with finite degrees of freedom is analyzed. The two smallest critical values of the load parameter are supposed to be equal or nearly equal. The effect of imperfections on the distance between critical values is considered. Using the results of catastrophe theory, imperfections are determined at which the structure l...
Article
Full-text available
How must n equal non-overlapping circles be packed on a sphere so that the angular diameter of the circles will be as great as possible? In the paper, the conjectured solutions of this problem for n = 18, 27, 34, 35, 40 are improved on the basis of an idea of Danzer. Using the theory of bar structures it is ascertained that, in these cases, the edg...
Article
There is a degenerate critical point (usually elliptic or hyperbolic umbilic) of the potential function of semisymmetric conservative systems in the case of a two-fold branching point. The bifurcation set of a standard form is known in both cases in a parametrized form. In an imperfection-sensitivity examination the relevant critical point is regar...
Article
Full-text available
The critical limit load of elastic structures can decrease due to the effect of unavoidable imperfections. The “critical imperfection territory” covers all imperfections resulting in a value of the critical load that is smaller than a prescribed value. These territories are determined with the help of a potential function and by using results of ca...
Article
Full-text available
The present paper deals with a numerically efficient iteration method for computing the n smallest generalized eigenvalues in magnitude and the corresponding generalized eigenvectors of lambda -matrices of degree m and order n. The conditions of convergence are given in the theorem. The method can be considered as an extension of the Bernoulli's me...
Article
Full-text available
Zeeman has drawn attention to the sequences in which catastrophes, or modes of instability, can be linked, and it is a common observation that sequences of catastrophes of low order are always found in the environment of catastrophes of higher order. In this paper, a simple buckling model is presented that generates in an elegant manner a complete...
Article
Full-text available
An illustrative study of higher order catastrophes (elliptic umbilic and two kinds of double cusp) is presented on a simple elastic structure using polar co-ordinates. The bifurcation paths are analyzed for both perfect and imperfect structures.
Article
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The paper shows simple two-degrees-of-freedom mechanical models to illustrate the unstable-X point of bifurcation, the stable-X point of bifurcation and the point-like instability. Using the total potential energy function we determine: the critical loads of the perfect structures, the transformations which separate the active and passive parts of...
Article
Recently developed were a general stability theory in terms of the elastic continuum, and a discrete coordinate theory. Both theories apply gradient potential functions to define equilibrium states, critical load parameters, equilibrium paths in the neighbourhood of critical points and imperfection-sensitivity surfaces (curves). Elementary catastro...
Article
A mérnöki gyakorlathoz kapcsolódó mechanikai problémák sok esetben vezetnek nemlineáris numerikus feladatra. Ilyen feladatot jelent többek között a szerkezetek stabilitásvizsgálata, a nagy elmozdulásokkal kapcsolatos vizsgálatok, illetve geodéziai eredetű számítási problémák is. Kutatásaink során megmutattuk, hogy rugalmas szerkezetek stabilitásána...
Article
Numerikus megoldásokat állítottunk elő a körpárok és körhármasok gömbön való legsűrűbb elhelyezésének problémájára, és szimmetria alapú vizsgálatokat végeztünk a gömbi körelhelyezés gráfjának Danzer-féle merevségére vonatkozóan. Egy általunk bevezetett gömbölyűségi kritérium alapján optimális, gömböt közelítő poliédereket konstruáltunk. A szakrális...

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Projects (3)
Archived project
Structures made of membranes, cables and rigid frames are systems where the stability is strongly dependent on an initial stress field. Their mechanical behavior is nonlinear and design and analysis needs following steps : form finding analysis to determine an initial equilibrium shape; analysis of the mechanical behavior in response to external loads; cutting pattern step which consists of cutting and flattening three-dimensional shapes. These steps are strongly dependent to each others and needs some repeated analysis to perform the optimal design. This project deals with the above steps. Computational, optimisation and sensitivity analysis tools have been developped in order to improve the design process.
Project
An important problem in discrete geometry is addressed in this study: amongst the 1 convex polyhedra circumscribed about the unit sphere and have n faces, which has the minimum 2 surface area? The solution of this problem represents the closest approximation of the sphere, i.e. the 3 roundest polyhedra. A new numerical optimization method developed previously by the authors 4 has been applied to find optimal polyhedra if tetrahedral, octahedral, or icosahedral symmetry 5 constraints are applied. Conjectured solutions are shown for various cases with face numbers up 6 to 132.