Transactions of the Korean Society of Pressure Vessels and Piping (한국압력기기공학회 논문집)

Korean Society of Pressure Vessels and Piping (한국압력기기공학회)
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Assessment of Equivalent Elastic Modulus of Perforated Spherical Plates

  • Received : 2018.11.26
  • Accepted : 2019.06.18
  • Published : 2019.06.30
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Abstract

Perforated plates are used for the steam generator tube-sheet and the Reactor Vessel Closure Head in the Nuclear Power Plant. The ASME code, Section III Appendix A-8000, addresses the analysis of perforated plates, however, this analysis is only limited to the flat plate with a triangular perforation pattern. Based on the concept of the effective elastic constants, simulation of flat and spherical perforated plates and their equivalent solid plates were carried out using Finite Element Analysis (FEA). The isotropic material properties of the perforated plate were replaced with anisotropic material properties of the equivalent solid plate and subjected to the same loading conditions. The generated curves of effective elastic constants vs ligament efficiency for the flat perforated plate were in agreement with the design curve provided by ASME code. With this result, a plate with spherical curvature having perforations can be conveniently analyzed with equivalent elastic modulus and equivalent Poisson's ratio.

Keywords

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Fig. 1 Equivalent material properties(1)

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Fig. 2 Plane view of the triangular perforate plate.

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Fig. 3 Flat perforated plate

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Fig. 4 Perforations parallel to the plate surface.

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Fig. 5 Perforations normal to the plate surface.

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Fig. 6 Equivalent Flat Solid Plate loading and B.C.

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Fig. 7 Flat perforated plate loading and B.C.

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Fig. 8 Equivalent spherical solid plate loading and B.C.

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Fig. 9 Spherical perforated plate loading and B.C.

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Fig. 10 An example of mesh plot with quadratic elements.

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Fig. 11 Procedure to determine the equivalent material constants

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Fig. 12 Flat perforated plate equivalent material properties

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Fig. 13 Comparison of FEA result effective elastic constants and ASME design curves.

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Fig. 14 Equivalent elastic constants for a spherical plate with perforation parallel to the plane.

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Fig. 15 Equivalent elastic constants for a spherical plate with perforation normal to the surface

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Fig. 16 Comparison of the equivalent material properties of the spherical plate with perforation normal to the surface and parallel to the plane.

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Fig. 17 Comparison of the equivalent material properties of the flat and spherical plate with perforation normal to the surface and parallel to the plane.

Table 1 FEA results for equivalent material constants.

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Table 2 Equivalent elastic constants.

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Table 3 Equivalent elastic constants.

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References

  1. ASME BPVC Sec.III, 2010, "Rules for Construction of Nuclear Facility Component, Division 1, Appendix A-8000, Stresses in Perforated Flat Plates," American Society of Mechanical Engineers, New York
  2. Horvay, G, 1925, "The plane stress problem of perforated plates," Journal of. Applied Mechanics, Transactions of. ASME, Vol. 74, pp. 355-360
  3. Malkin, T., 1952, "Notes on a theoretical basis for the design of tube sheets of triangular layout," Journal of. Applied Mechanics, Transactions of. ASME, Vol. 74, pp. 389-396
  4. Slot, T., and O'Donnell, W.J., 1971, "Effective elastic constants for thick perforated plates with square and triangular penetration pattern," Journal of. Applied Mechanics, Transactions of. ASME, Vol. 93, pp. 1081-1088
  5. Bailey, R. and Hicks, R., 1960, "Behaviour of perforated plates under plane stress," Journal of. Applied Mechanics, Transactions of. ASME., Vol. 2, (2), pp. 143-161
  6. Duncan, J.P. and Upfold, R.W., 1963, "Equivalent elastic properties of perforated bars and plates," Journal of. Mechanical Engineering and Science., Vol. 15, (1), pp. 53-65 https://doi.org/10.1243/JMES_JOUR_1963_005_009_02
  7. Meijers. P., 1969, "Plate with a Doubly-Periodic Pattern of Circular Holes Loaded in Plane Stress or in Bending," ASME Publication on First International Conference on Pressure Vessel Technology, Delft, the Netherlands