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In this paper the results of the investigations of the free oscillations of the pre-stressed flexible structure elements are presented . Two cases of the central preliminary stress are investigated : without intermediate fastening of the tie to the flexible element and with the intermediate fastening in the middle of the element length. The given physical model can be applied to the flexible sloping shells and arches, membranes, large space antenna fields (besides flexible elements). The peculiarity of these systems is the possibility of the non-adjacent equilibrium form existence at the definite relations of the physical parameters . The transition from one stable equilibrium form to another, non-adjacent form, may be treated as jump. In this case they are called systems with buckling or the systems with two potential «gaps». These systems commenced the new section of the mathematical physics - the theory of chaos and strange attractors. The analysis of the solutions confirms the received for the first time by the author and given in effect of the oscillation period doubling of the system during the transition from the «small» oscillations relatively center to the >large< relatively all three equilibrium conditions. The character of the frequency (period) dependence on the free oscillation amplitudes of the non-linear system also confirms the received earlier result of the duality of the system behaviour : >small< oscillations possess the qualities of soft system; >large< oscillations possess the qualities of rigid system. The >small< oscillation natural frequency changing, depending on the oscillation amplitudes, is in the internal . Here the frequency takes zero value at the amplitude values Aa and Ad (or Aa and Ae ); the frequency takes maximum value at the amplitude value near point b .The >large< oscillation natural frequency changes in the interval . Here is also observed . The influence of the tie intermediate fastening doesn't introduce qualitative changes in the behaviour of the investigated system. It only increases ( four times ) the critical value of the preliminary tension force
Die d - Dirac - Funktion d(x-xi) und Heviside - Funktion wurden vor allem zur Beschreibung diskontinuierlicher Belastungsfunktionen von gebogenen Balken angewendet. Im Referat werden die mathematischen Operationen auf den erwähnten Funktionen dargestellt. Darüber hinaus wird die Möglichkeit eindeutiger Aufschreibung von belibigen Belestungsfunktionen vorgeschlagen, die fast alle Fälle der in der Ingenieurpraxis auftretenden Belastungen umfassen. Die vorgeschlagenen Lösungen geben die Möglichkeit leichter Aufschreibung im Form eines Algorithmus, das die Ausnutzung von Komputertechnik in statischen Berechnungen ermöglicht. Am Ende des Referates werden die Zahlebeispiele dargestellt, die die Möglichkeiten praktischer Anwendungen der besprochenen Funktionen darstellen.
Wissenschaftliches Kolloquium vom 27. bis 30. Juni 1996 in Weimar an der Bauhaus-Universität zum Thema: ‚Techno-Fiction. Zur Kritik der technologischen Utopien'
Das utopische Comic
(1997)
American images of Utopia
(1997)
Wissenschaftliches Kolloquium vom 27. - 30. Juni 1996 in Weimar an der Bauhaus-Universität zum Thema: ‚ Techno-Fiction. Zur Kritik der technologischen Utopien'
The frame of this paper is the development of methods and procedures for the description of the motion of an arbitrary shaped foundation. Since the infinite half-space cannot be properly described by a model of finite dimensions without violating the radiation condition, the basic problems are infinite dimensions of the half-space as well as its non-homogeneous nature. Consequently, an approach has been investigated to solve this problem indirectly by developing Green's function in which the non-homogeneity and the infiniteness of the half-space has been included. When the Green's function is known, the next step will be the evaluation of contact stresses acting between the foundation and the surface of the half-space through an integral equation. The equation should be solved in the area of the foundation using Green's function as the kernel. The derivation of three-dimensional Green's function for the homogeneous half-space (Kobayashi and Sasaki 1991) has been made using the potential method. Partial differential equations occurring in the problem have been made ordinary ones through the Hankel integral transform. The general idea for obtaining the three-dimensional Green's function for the layered half-space is similar. But in that case some additional phenomena may occur. One of them is the possibility of the appearance of Stonely surface waves propagating along the contact surfaces of layers. Their contribution to the final result is in most cases important enough that they should not be neglected. The main advantage of results presented in comparing to other obtained with numerical methods is their accuracy especially in the case of thin layers because all essential steps of Green's function evaluation except of the contour integration along the branch cut have been made analytically. On the other hand the disadvantage of this method is that the mathematical effort for obtaining the Green's function is increasing drastically with the increase of the number of layers. Future work will therefore be directed in simplifying of the above described process
The paper analyses the influence of the effect of inertia on the reliability of production systems. Systems inertia represents the phenomenon of continuing work for some time after the breakdown of one of the former phases. In our considerations, inertia is treated as the time elapsed from the onset of breakdown till the system's inability to work. A special method had to be devised to investigate the effect of inertia in order to evaluate the reliability of production systems and to attempt algorithmization to control the reliability of production system by means of inertia or reserving. The method of reliability analysis is presented only in an inform aspect. The possibilities of increasing reliability of production systems are listed. A comparison of the redundancy method and inertia method is presented. The results of this comparison and simulated investigations of influence of inertia on reliability of system are essential scope of the paper. Selected conclusions are as follows: when inertia approaches the last phase in the system, its influence on the shape of the distribution of the system's ability increases; an increase in inertia causes an increase in the availability of the system which approaches a certain border value; dependence of the average of a system's disability on inertia has a saddle-like character whereas dependence of the number of breakdowns (stoppages) in the system has the nature of an S-curve.
Thin elastic plates are the basic constructional elements and are very often subjected to dynamic effects especially in the machine-building structures. Their saving design of resonance conditions of operation is an extremely complicated task which cannot be solved analytically. In the present report an efficient and sufficiently general method for optimal design of thin plates is worked out on the basis of energy resonance method of Wilder, the method of the finite elements for dynamic research and the methods of parameter optimization. By means of these methods various limitations and requirements put by the designer to the plates can be taken into account. A programme module for numerical investigation of the weight variation of the plate depending on the taken variable of the designed thickness at different supporting conditions is developed. The reasons for the considerable quantity and quality difference between the obtained optimal designs are also analysed.
The problem of the computation of stresses and settlements in the half-space under various types of loads is often presented in geotechnical engineering. In 1885 Boussinesq advanced theoretical expressions to determine stresses at a point within an ideal mass. His equation considers a point load on the surface of a semi-infinite, homogeneous, isotropic, weightless, elastic half-space. Newmark in 1942 performed the integration of Boussinesq's equations for the vertical stress under a corner of a rectangular area loaded with a uniform load. The problem of the determination of vertical stresses under a rectangular shaped footing has been satisfactorily solved with renewal integration of the Boussinesq's equation over the arbitrary rectangle on surface of the half-space, with a non-uniform load represented with piecewise linear interpolation functions. The problem of the determination of stresses in the case when the footing shape is an arbitrary quadrilateral however remains unsolved. The paper discusses an approach to the computation of vertical stresses and settlements in an arbitrary point of the half-space, loaded with a uniform load, which shape in the ground plan can be a general four noded form with straight edges. Since the form is transformed into a biunit square and all integrations are performed over this area, all solutions are valid also for an arbitrary triangle by the implementation of the degeneration rule.
Wissenschaftliches Kolloquium vom 27. bis 30. Juni 1996 in Weimar an der Bauhaus-Universität zum Thema: ‚Techno-Fiction. Zur Kritik der technologischen Utopien'
Der Funktionsumfang von 3D-Modellierern und die Leistung allgemein zur Verfügung stehender Rechnersysteme gestatten die Modellierung beliebiger Objekte in jeder nur denkbaren Fachdisziplin. Das potentielle Leistungsvermögen von 3D-Modellierern sollte Anreiz sein, sie so alltäglich einzusetzen, wie die etablierten Standardapplikationen. Die im Vortrag gezeigten Modelle umfassen ein kleines Spektrum der möglichen Anwendungsgebiete. Weder vom (Daten)Umfang noch von ihrem Kompliziertheitsgrad stellen sie etwas Besonderes dar. Sie sollen nur das Interesse für einen alltäglichen Einsatz von 3D-Modellierern wecken und eventuell vorhandenen Einsatzschwellen abbauen helfen. Die im Vortrag gezeigten Bildfolgen sind unter http://www.uni-weimar.de/animationen zu finden.