Optimization of Flat Ends in Pressure Vessels.

Bogdan Szybiński,Paweł J Romanowicz

doi:10.3390/ma12244194

Bogdan Szybiński, Paweł J Romanowicz

Open Access

https://doi.org/10.3390/ma12244194

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Abstract

The application of flat ends in pressure boilers is inevitably associated with the presence of stress concentration, which is observed in the vicinity of the junction of the cylinder and the closing flat plate. The analyzed flat end plates with stress relief grooves fall into the group of solutions recognized by the respective Standards of Calculations of Pressure Vessels. Unfortunately, no clear evidence is given in the Standards on how to choose the best groove parameters. This opens up the problem of the optimal choice of the groove parameters providing a minimum stress level. Even for the optimal values defining the stress relief groove geometry, certain plastic deformations are observed in the groove area for materials which exhibit elastic-plastic properties. Such a situation is completely unacceptable during exploitation, and a suitable reduction of the operating pressure is necessary. This paper discusses the effectiveness of other designs for flat ends used in pressure vessels. The proposed modifications took the form of external ribs applied around the top of the endplate circumference. The dimensions of these ribs were set using parametric optimization. The results of the study encouraged the authors to perform a more general analysis with the use of topology optimization. The results of all performed studies proved that the reduction of stress concentration and the full elimination of plastic deformation are possible. All numerical calculations were made using the finite element code (FEM), Ansys.

Highlights

In standard applications, commonly-used pressure vessels are closed by ellipsoidal or hemispherical heads
It was observed that significant plastic deformations may occur in the boundary area of the stress relief groove if nonoptimal values for the groove parameters are used in the design
The performed numerical investigations confirmed the presence of strong stress concentrations in the area of the groove

Summary

Introduction

Commonly-used pressure vessels are closed by ellipsoidal or hemispherical heads. In order to reduce the notch effect, a stress relief groove can be applied, which provides a smoother shape transition in the shell-endplate junction and releases the stress concentration Even in this case, due to the lack of continuity of the curvature along the contour in the area where the inner edge of the cylindrical wall transforms to the curved one, a certain stress concentration is still observed [5,6,7,8]. The minimization of the stress peak is achieved by the introduction of respective functions approximating the curved shape of the shell, which provides continuity of the curvature on the inner skin of the vessel This approach is still not commonly applied in the construction of flat heads of boilers due to manufacturing problems

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