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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.
In the presented paper data collected from the field related to damage statistics of electrical and electronic apparatus in household are reported and investigated. These damages (total number approx. 74000 cases), registered by five German insurance companies in 2005 and 2006, were adviced by customers as caused by lightning overvoltages. With the use of stochastical methods it is possible, to reasses the collected data and to distinguish between cases, which are with high probability caused by lightning overvoltages, and those, which are not. If there was an indication for a direct strike, this case was excluded, so the focus was only on indirect lightning flashes, i.e. only flashes to ground near the structure and flashes to or nearby an incoming service line were investigated. The data from the field contain the location of damaged apparatus (residence of the policy holder) and the distances of the nearest cloud-to-ground stroke to the location of the damage registered by the German lightning location network BLIDS at the date of damage. The statistical data along with some complementary numerical simulations allow to verify the correspondence of the Standards rules used for IEC 62305-2 with the field data and to define some correction needs. The results could lead to a better understanding whether a damage reported to an insurance company is really caused by indirect lightning, or not.
7th International Conference on Reliability of Materials and Structures (RELMAS 2008). June 17 - 20, 2008 ; Saint Petersburg, Russia. pp 354-358. Reprint with corrections in red Introduction Analysis of advanced structures working under extreme heavy loading such as nuclear power plants and piping system should take into account the randomness of loading, geometrical and material parameters. The existing reliability are restricted mostly to the elastic working regime, e.g. allowable local stresses. Development of the limit and shakedown reliability-based analysis and design methods, exploiting potential of the shakedown working regime, is highly needed. In this paper the application of a new algorithm of probabilistic limit and shakedown analysis for shell structures is presented, in which the loading and strength of the material as well as the thickness of the shell are considered as random variables. The reliability analysis problems may be efficiently solved by using a system combining the available FE codes, a deterministic limit and shakedown analysis, and the First and Second Order Reliability Methods (FORM/SORM). Non-linear sensitivity analyses are obtained directly from the solution of the deterministic problem without extra computational costs.
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
A procedure for the evaluation of the failure probability of elastic-plastic thin shell structures is presented. The procedure involves a deterministic limit and shakedown analysis for each probabilistic iteration which is based on the kinematical approach and the use the exact Ilyushin yield surface. Based on a direct definition of the limit state function, the non-linear problems may be efficiently solved by using the First and Second Order Reliabiblity Methods (Form/SORM). This direct approach reduces considerably the necessary knowledge of uncertain technological input data, computing costs and the numerical error. In: Computational plasticity / ed. by Eugenio Onate. Dordrecht: Springer 2007. VII, 265 S. (Computational Methods in Applied Sciences ; 7) (COMPLAS IX. Part 1 . International Center for Numerical Methods in Engineering (CIMNE)). ISBN 978-1-402-06576-7 S. 186-189
Proceedings of the International Conference on Material Theory and Nonlinear Dynamics. MatDyn. Hanoi, Vietnam, Sept. 24-26, 2007, 8 p. In this paper, a method is introduced to determine the limit load of general shells using the finite element method. The method is based on an upper bound limit and shakedown analysis with elastic-perfectly plastic material model. A non-linear constrained optimisation problem is solved by using Newton’s method in conjunction with a penalty method and the Lagrangean dual method. Numerical investigation of a pipe bend subjected to bending moments proves the effectiveness of the algorithm.
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.
In: Technical feasibility and reliability of passive safety systems for nuclear power plants. Proceedings of an Advisory Group Meeting held in Jülich, 21-24 November 1994. - Vienna , 1996. - Seite: 43 - 55 IAEA-TECDOC-920 Abstract: It is shown that the difficulty for probabilistic fracture mechanics (PFM) is the general problem of the high reliability of a small population. There is no way around the problem as yet. Therefore what PFM can contribute to the reliability of steel pressure boundaries is demonstrated with the example of a typical reactor pressure vessel and critically discussed. Although no method is distinguishable that could give exact failure probabilities, PFM has several additional chances. Upper limits for failure probability may be obtained together with trends for design and operating conditions. Further, PFM can identify the most sensitive parameters, improved control of which would increase reliability. Thus PFM should play a vital role in the analysis of steel pressure boundaries despite all shortcomings.