Simplified determination of elastic-plastic accumulated strain for analytical life assessment of structures by means of the Simplified Theory of Plastic Zones based on Zarka's method

超出弹性极限并承受不同载荷的结构的寿命取决于在连续加载周期中导致应力和应变累积的棘轮机构是否正在发展(渐进变形)，直到这一过程可能在达到稳定时停止。此外，还应考虑疲劳问题。因此，需要确定棘轮过程结束时累积的最大弹塑性应变，以便对寿命进行分析性评估(以便与最大允许应变进行比较)，以及在后续循环中出现的有效应变范围(用于确定疲劳使用系数)。通常，这些量是通过对结构的有限元模型进行多次加载的增量弹塑性分析来获得的，直到至少达到近似稳定，这通常伴随着巨大的计算负担。与此不同的是，简化塑性区理论(STPZ)利用了Zarkas方法已知的包括硬化的弹塑性本构方程的重新表述，允许以某种适当的方式估计某些特殊的量。因此，在安定条件下，可以得到结构中每个位置的累积应变和应变范围的近似值。很少有线弹性分析是足够的，与增量弹塑性分析相比，显著减少了计算负担。尽管到目前为止，钢是开发STPZ的主要关注材料，但STPZ的基础是独立于特定材料的。因此，潜在的应用领域是广泛的，包括例如土木工程、工厂设计和机械工程。首先，人们希望STPZ，至少在确定应变范围方面，是精确但昂贵的循环增量分析和在实际结构设计中广泛使用的简单的、因此基础较弱的击倒系数(例如，系数Ke，Neuber法)之间的合理折衷。所应用的项目的目的是通过加速计算过程、扩大其适用范围和提高其性能来扩展STPZ，以便在较小的计算负担的情况下实现对累积应变的良好逼近。由于到目前为止还没有其他基于良好力学背景的量化累积应变的简化方法，因此这一目标被认为是非常有价值的。

The lifetime of a structure, operated beyond elastic limits and subjected to varying loads, is dependent on whether a ratcheting mechanism causing an accumulation of stress and strain in successive cycles of loading is developing (progressive deformation) until this process possibly ceases when shakedown is attained. In addition, fatigue is to be considered. Accordingly, the maximum elastic-plastic strain accumulated at the end of a ratcheting process needs to be determined for an analytical assessment of life (for comparison with maximum admissible strains), as well as the effective strain range occurring in subsequent cycles (for determination of fatigue usage factors). Usually, these quantities are obtained by means of incremental elastic-plastic analyses of a finite element model of the structure for many cycles of loading until shakedown is at least approximately achieved, usually associated with a huge computational burden. In contrast to this, the Simplified Theory of Plastic Zones (STPZ) makes use of a reformulation of the elastic-plastic constitutive equations including hardening known from Zarkas method, allowing for estimating some special quantities in some suitable manner. Thus, an approximation of accumulated strains and of strain ranges may be obtained at each location in the structure in the condition of shakedown. Few linear elastic analyses are sufficient, reducing the computational burden remarkably compared to incremental elastic-plastic analyses. Although steel was the material of main focus when developing the STPZ up to now, the basics of the STPZ are independent of a particular material. Accordingly, the potential field of application is widespread, including, for example, civil engineering, plant design and mechanical engineering. First applications give rise to the hope that the STPZ, at least with respect to determining the strain range, is a reasonable compromise between exact but costly cyclic incremental analyses on one hand and the simple and thus weakly based knock-down factors widely used in practical design of structures developing cyclic plasticity (e.g. factor Ke, Neuber method) on the other hand. The object of the project applied is to expand the STPZ in order to achieve a good approximation to the accumulated strains at little computational burden as well, by accelerating the calculation process, expanding its range of applicability and increasing its performance. Since no other simplified methods quantifying accumulated strains founded on sound mechanical background are known so far, this aim is considered to be of great value.