FG Baustatik, Stahlbau, FEM
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- 1998 (3) (remove)
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- Shakedown (3)
- Ratcheting (2)
- Zarka's method (2)
- Bree-tube (1)
- Buckling (1)
- Dehnschwingbreite (1)
- Dehnungsakkumulation (1)
- Elastic follow-up (1)
- Fließgelenktheorie (1)
- Strain range enhancement (1)
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- FG Baustatik, Stahlbau, FEM (3) (remove)
Es wird eine vereinfachte Fließzonentheorie vorgestellt, mit der das plastische Verhalten eines Tragwerks berechnet werden kann. Sie lässt sich nicht nur auf Stabwerke, sondern auch auf Flächentragwerke unter beliebiger Belastung anwenden. Das zugrunde gelegte Werkstoffgesetz ist bilinear, wodurch Verfestigung erfasst werden kann. Die Theorie beruht auf dem Konzept transformierter interner Variabler nach Zarka, mit dem das plastische Problem in ein geeignet formuliertes elastisches Problem überführt wird. Damit fällt oft nur eine weitere elastizitätstheoretische Berechnung an mit modifizierten elastischen Werkstoffparametern und mit (in Form von Anfangsdehnungen) modifizierter Belastung. Das Ergebnis kann gegebenenfalls iterativ verbessert werden, bis das "exakte" Ergebnis erreicht ist. Mehrere Beispiele erläutern die Methode.
If a mechanical structure is to be designed for operation under cyclic loading, primarily two kinds of failure must be guarded against: (1) low cycle fatigue which may occur due to strains cycling between two states (controlled by the strain range exceeding twice the yield limit);
(2) ductility exhaustion which may occur due to accumulating strain from one load cycle to another.
These two kinds of failure are local failure modes so that strains need to be calculated and then assessed by comparison with code allowables such as the 1%, 2% and 5% strain limits set by the ASME nuclear codes. Elastic-plastic strains can be calculated by incremental (or step-by-step or evolutive) analyses. Unfortunately, this can be extremely costly if thousands of cycles are required to achieve shakedown. Therefore, simplified elastic-plastic analysis methods are desired allowing to obtain specific information at reduced effort, nevertheless accounting for the main features controlling strain such as kinematic hardening. Zarka’s method, early versions of which are available since twenty years, appears promising to provide both strain ranges and accumulated strains in the saturated cycle, i.e. after shakedown has been achieved. However, several attempts to use this method in the nuclear industry failed to qualify the method as a reliable analysis tool. This was due to several reasons:
(1) the publications describing the method were written in a highly scientific language the design engineers in industry were not familiar with;
(2) in some cases Zarka’s method provided excellent results (compared with incremental analyses), but bad ones in others.
Nevertheless, there remained some interest to uncover the potential of this method. For that purpose some calculations are performed for simple configurations of structure and loading (so that the structural response can be interpreted relatively easily). More insight into the performance of the method may thus be gained in terms of computational steps to be followed, the numerical effort required, the quality of the results obtained, and the sensibility with respect to material data and load level.
The basic idea of Zarka's method is to redefine the elastic-plastic problem by an equivalent elastic problem with suitably defined modified elastic material parameters and initial strains. This requires estimating (and iteratively improving) the geometry of the plastic zone and of transformed internal variables. A particular class of material models is admitted, the simplest of which is the linear kinematic hardening model.
The European Fast Reactor (EFR) collaboration with the EFR Associates Design and Construction Rules Committee, and the R&D Agreement (AGT9B) produced significant developments in design-by-analysis procedures for high temperature plant. Many of these developments are judged to be relevant to the non-creep conditions of LWR plant, and for this reason, the CEC DGXI Working Group Codes and Standards supported this study to review and make recommendations on their potential application for improving LWR design code procedures. The topics considered are judged to be those where the most significant and relevant developments have been made and the list, although not exhaustive, is as follows:
- Negligible creep criteria
- Design-by-analysis procedures for weldments
- Shakedown design rules
- Design-by-analysis methods for tubeplates
- Buckling rules
- Interaction diagrams for assessing ratcheting
- Rules for the prevention of elastic follow-up in piping
- Strain range enhancement
- Constitutive equations for inelastic analysis
- Margins on Level D criteria
- Zarka's method