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The propagation of mechanical waves in plates of isotropic elastic material is investigated. After a short introduction to the understanding of focussing of stress waves in a plate with a curved boundary the method of characteristics is applied to a plate of hyperelastic material. Using this method the propagation of acceleration waves is discussed. Based on this a numerical difference scheme is developed for solving initial-boundary-value problems and applied to two examples: propagation of a point disturbance in a homogeneously finitely strained non-linear elastic plate and geometrical focussing in al linear elastic plate.
Shock waves, explosions, impacts or cavitation bubble collapses may generate stress waves in solids causing cracks or unexpected dammage due to focussing, physical nonlinearity or interaction with existing cracks. There is a growing interest in wave propagation, which poses many novel problems to experimentalists and theorists.
The nonlinear scalar constitutive equations of gases lead to a change in sound speed from point to point as would be found in linear inhomogeneous (and time dependent) media. The nonlinear tensor constitutive equations of solids introduce the additional local effect of solution dependent anisotropy. The speed of a wave passing through a point changes with propagation direction and its rays are inclined to the front. It is an open question whether the widely used operator splitting techniques achieve a dimensional splitting with physically reasonable results for these multi-dimensional problems. May be this is the main reason why the theoretical and numerical investigations of multi-dimensional wave propagation in nonlinear solids are so far behind gas dynamics. We hope to promote the subject a little by a discussion of some fundamental aspects of the solution of the equations of nonlinear elastodynamics. We use methods of characteristics because they only integrate mathematically exact equations which have a direct physical interpretation.
Limit and shakedown theorems are exact theories of classical plasticity for the direct computation of safety factors or of the load carrying capacity under constant and varying loads. Simple versions of limit and shakedown analysis are the basis of all design codes for pressure vessels and pipings. Using Finite Element Methods more realistic modeling can be used for a more rational design. The methods can be extended to yield optimum plastic design. In this paper we present a first implementation in FE of limit and shakedown analyses for perfectly plastic material. Limit and shakedown analyses are done of a pipe–junction and a interaction diagram is calculated. The results are in good correspondence with the analytic solution we give in the appendix.
Abstracts of the ACHEMA 2000 - International Meeting on Chemical Engineering, Environmental Protection and Biotechnology, May 22 - 27, 2000. Frankfurt am Main. Achema 2000 : special edition / Linde. [Ed.: Linde AG. Red.: Volker R. Leski]. - Wiesbaden : Linde AG, 2000. - 56 p. : Ill., . - pp: 79 - 81
Safety and reliability of structures may be assessed indirectly by stress distributions. Limit and shakedown theorems are simplified but exact methods of plasticity that provide safety factors directly in the loading space. These theorems may be used for a direct definition of the limit state function for failure by plastic collapse or by inadaptation. In a FEM formulation the limit state function is obtained from a nonlinear optimization problem. This direct approach reduces considerably the necessary knowledge of uncertain technological input data, the computing time, and the numerical error. Moreover, the direct way leads to highly effective and precise reliability analyses. The theorems are implemented into a general purpose FEM program in a way capable of large-scale analysis.
Limit and shakedown analysis are effective methods for assessing the load carrying capacity of a given structure. The elasto–plastic behavior of the structure subjected to loads varying in a given load domain is characterized by the shakedown load factor, defined as the maximum factor which satisfies the sufficient conditions stated in the corresponding static shakedown theorem. The finite element dicretization of the problem may lead to very large convex optimization. For the effective solution a basis reduction method has been developed that makes use of the special problem structure for perfectly plastic material. The paper proposes a modified basis reduction method for direct application to the two-surface plasticity model of bounded kinematic hardening material. The considered numerical examples show an enlargement of the load carrying capacity due to bounded hardening.
The structural reliability with respect to plastic collapse or to inadaptation is formulated on the basis of the lower bound limit and shakedown theorems. A direct definition of the limit state function is achieved which permits the use of the highly effective first order reliability methods (FORM) is achieved. The theorems are implemented into a general purpose FEM program in a way capable of large-scale analysis. The limit state function and its gradient are obtained from a mathematical optimization problem. This direct approach reduces considerably the necessary knowledge of uncertain technological input data, the computing time, and the numerical error, leading to highly effective and precise reliability analyses.
Fatigue analyses are conducted with the aim of verifying that thermal ratcheting is limited. To this end it is important to make a clear distintion between the shakedown range and the ratcheting range (continuing deformation). As part of an EU-supported research project, experiments were carried out using a 4-bar model. The experiment comprised a water-cooled internal tube, and three insulated heatable outer test bars. The system was subjected to alternating axial forces, superimposed with alternating temperatures at the outer bars. The test parameters were partly selected on the basis of previous shakedown analyses. During the test, temperatures and strains were measured as a function of time. The loads and the resulting stresses were confirmed on an ongoing basis during performance of the test, and after it. Different material models were applied for this incremental elasto-plastic analysis using the ANSYS program. The results of the simulation are used to verify the FEM-based shakedown analysis.
The load-carrying capacity or the safety against plastic limit states are the central questions in the design of structures and passive components in the apparatus engineering. A precise answer is most simply given by limit and shakedown analysis. These methods can be based on static and kinematic theorems for lower and upper bound analysis. Both may be formulated as optimization problems for finite element discretizations of structures. The problems of large-scale analysis and the extension towards realistic material modelling will be solved in a European research project. Limit and shakedown analyses are briefly demonstrated with illustrative examples.
In: Advances in intelligent computing in engineering : proceedings of the 9.International EG-ICE Workshop ; Darmstadt, (01 - 03 August) 2002 / Martina Schnellenbach-Held ... (eds.) . - Düsseldorf: VDI-Verl., 2002 .- Fortschritt-Berichte VDI, Reihe 4, Bauingenieurwesen ; 180 ; S. 1-35 The paper describes a novel way to support conceptual design in civil engineering. The designer uses semantical tools guaranteeing certain internal structures of the design result but also the fulfillment of various constraints. Two different approaches and corresponding tools are discussed: (a) Visually specified tools with automatic code generation to determine a design structure as well as fixing various constraints a design has to obey. These tools are also valuable for design knowledge specialist. (b) Extensions of existing CAD tools to provide semantical knowledge to be used by an architect. It is sketched how these different tools can be combined in the future. The main part of the paper discusses the concepts and realization of two prototypes following the two above approaches. The paper especially discusses that specific graphs and the specification of their structure are useful for both tool realization projects.
Structural design analyses are conducted with the aim of verifying the exclusion of ratcheting. To this end it is important to make a clear distinction between the shakedown range and the ratcheting range. In cyclic plasticity more sophisticated hardening models have been suggested in order to model the strain evolution observed in ratcheting experiments. The hardening models used in shakedown analysis are comparatively simple. It is shown that shakedown analysis can make quite stable predictions of admissible load ranges despite the simplicity of the underlying hardening models. A linear and a nonlinear kinematic hardening model of two-surface plasticity are compared in material shakedown analysis. Both give identical or similar shakedown ranges. Structural shakedown analyses show that the loading may have a more pronounced effect than the hardening model.
ITCE-2003 - 4th Joint Symposium on Information Technology in Civil Engineering ed Flood, I., Seite 1-12, ASCE (CD-ROM), Nashville, USA In this paper we discussed graph based tools to support architects during the conceptual design phase. Conceptual Design is defined before constructive design; the used concepts are more abstract. We develop two graph based approaches, a topdown using the graph rewriting system PROGRES and a more industrially oriented approach, where we extend the CAD system ArchiCAD. In both approaches, knowledge can be defined by a knowledge engineer, in the top-down approach in the domain model graph, in the bottom-up approach in the in an XML file. The defined knowledge is used to incrementally check the sketch and to inform the architect about violations of the defined knowledge. Our goal is to discover design error as soon as possible and to support the architect to design buildings with consideration of conceptual knowledge.
Recently, SHARP corporation has developed the world’s first “Plasma Cluster Ions (PCI)” air purification technology, which uses plasma discharge to generate cluster ions. The new plasma cluster device releases into the air positive and negative ions, which are harmless to humans and are able to decompose and deactivate airborne substances by chemical reactions. A lot of phenomenological tests of the PCI air purification technology on microbial cells have been conducted. And, in most cases, it has been shown that PCI demonstrate strongly pronounced killing effect. Although, the particular mechanisms of PCI action are still not evident. We studied variations in resistance to PCI among gram-positive airborne microorganisms, as well as some dose-dependent, spatial, cultural and biochemical properties of PCI action in respect of Staphylococcus spp, Enterococcus spp, Micrococcus spp.
Summary and Conclusions PCIs were clearly effective in terms of their antibacterial effects with the strains tested. This efficacy increased with the time the bacteries were exposed to PCIs. The bactericidal action has proved to be irreversible. PCIs were significantly less effective in shadowed areas. PCI exposure caused multiple protein damages as observed in SDS PAGE studies. There was no single but multiple molecular mechanism causing the bacterial death.
Recently, the SHARP Corporation, Japan, has developed the world’s first "Plasma Cluster Ions (PCI)" air purification technology using plasma discharge to generate cluster ions. The new plasma cluster device releases positive and negative ions into the air, which are able to decompose and deactivate harmful airborne substances by chemical reactions. Because cluster ions consist of positive and negative ions that normally exist in the natural world, they are completely harmless and safe to humans. The amount of ozone generated by cluster ions is less than 0.01 ppm, which is significantly less than the 0.05-ppm standard for industrial operations and consumer electronics. This amount, thus, has no harming effects whatsoever on the human body. But particular properties and chemical processes in PCI treatment are still under study. It has been shown that PCI in most cases show strongly pronounced irreversible killing effects in respect of airborne microflora due to free-radical induced reactions and can be considered as a potent technology to disinfect both home, medical and industrial appliances.
Recently, SHARP corporation has developed the world’s first "Plasma Cluster Ions® (PCI)" air purification technology, which uses plasma discharge to generate cluster ions. The new Plasma Cluster Device releases positive and negative ions into the air, which are harmless to humans and are able to decompose and deactivate airborne substances by chemical reactions. In the past, phenomenological tests on the efficacy of the PCI air purification technology on microbial cells have been conducted. In most cases, it has been shown that PCI demonstrated strongly pronounced killing effects on microorganisms. However, the particular mechanisms of PCI action still have to be uncovered.