SUMMARYIn stress analysis procedures using the finite element method, where the results are generated through approximations using interpolation functions, there is a need to establish optimal points in a typical element that correspond to the exact values of stresses and strains. Conventionally, Gauss' points and Barlow's points are used as optimal points for stress recovery. In this paper it is shown that the justification for the existence of optimal strain/stress recovery points, referred to as Prathap points in an element, is a consequence of the best-fit paradigm, originally proposed by Prathap through the stress correspondence principle.Through the analysis of a statically indeterminate structure like a simple bar of linearly varying elastic rigidity with fixed ends, the existence of Prathap's points has been demonstrated through the best-fit paradigm that remains valid even for statically indeterminate problems in a subtle manner. The present paper reconciles the prima facie, yet misleading, violation of the best-fit rule with the fundamental theory of the finite element method, and effectively restores the validity of the best-fit paradigm even for statically indeterminate problems in a deeper sense. Furthermore, consistent modified definitions of the global and local errors from the strain point of view are prescribed here.
This paper consists of two parts. Part I presents a probabilistic based approach to determine an allowable manufacturing tolerance range on a steam turbine blade when the allowable Defects Per Million Opportunity (DPMO) are known a priori. The method allows simulating the entire row of blades with geometrical deviations by using only a few representative blade models. The proposed method takes into account the probabilistic nature of the dimensional variation within the tolerance ranges. Furthermore, the method allows the designer to understand the impact on critical blade design parameters.
Part II of this paper proposes a probabilistic evaluation of gap / interference between shrouds of two adjacent blades of a steam turbine. The method uses manufacturing process capability of the relevant design parameter: tip shroud pitch for the tip shroud gap. This method allows for a probabilistic optimization of the shroud gap between two adjacent blades in order to balance reliability and ease of assembly.
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