Assessment of Equivalent Elastic Modulus of Perforated Spherical Plates

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.

Fig. 1 Equivalent material properties⁽¹⁾

Fig. 2 Plane view of the triangular perforate plate.

Fig. 3 Flat perforated plate

Fig. 4 Perforations parallel to the plate surface.

Fig. 5 Perforations normal to the plate surface.

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

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

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

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

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

Fig. 11 Procedure to determine the equivalent material constants

Fig. 12 Flat perforated plate equivalent material properties

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

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

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

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

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.

Table 2 Equivalent elastic constants.

Table 3 Equivalent elastic constants.