This paper describes use of equivalent solid (EQS) modeling to obtain efficient solutions to perforated material problems using three-dimensional finite element analysis (3-D-FEA) programs. It is shown that EQS modeling in 3-D-FEA requires an EQS constitutive relationship with a sufficient number of independent constants to allow the EQS material to respond according to the elastic symmetry of the penetration pattern. It is also shown that a 3-D-FEA submodel approach to calculate peak stresses and ligament stresses from EQS results is very accurate and preferred over more traditional stress multiplier approaches. The method is demonstrated on the problem of a transversely pressurized simply supported plate with a central divider lane separating two perforated regions with circular penetrations arranged in a square pattern. A 3-D-FEA solution for a model that incorporates each penetration explicitly is used for comparison with results from an EQS solution for the plate. Results for deflection and stresses from the EQS solution are within 3 percent of results from the explicit 3-D-FE model. A solution to the sample problem is also provided using the procedures in the ASME B&PV Code. The ASME B&PV Code formulas for plate deflection were shown to overestimate the stiffening effects of the divider lane and the outer stiffening ring.

Issue Section:
Research Papers
Topics:
Finite element analysis, Structural analysis, Stress, Deflection, Modeling
1.
ASME Boiler and Pressure Vessel Code, 1995, Sections III and VIII, The American Society of Mechanical Engineers, New York, NY.
2.
Singh, K. P., and Soler, A. I., 1984, Mechanical Design of Heat Exchangers and Pressure Vessel Components, ARCTURUS Publishers, First Edition.
3.
Miejers, P., 1970, “Plates With a Doubly-Periodic Pattern of Circular Holes Loaded in Plane Stress of Bending,” First International Conference on Pressure Vessel Technology, Pressure Vessels and Piping: Design and Analysis: A Decade of Progress, ASME, New York, NY, Chap. 4, pp. 1061–1079.
4.
Slot, T., and O’Donnell, W. J., 1971, “Effective Elastic Constants for Thick Perforated Plates with Square and Triangular Penetration Patterns,” ASME Journal of Engineering for Industry, Nov., pp. 935–942.
5.
O’Donnell, W. J., 1972, “Perforated Plates and Shells,” Pressure Vessels and Piping: Design and Analysis: A Decade of Progress, ASME, New York, NY, Chap. 4, pp. 1041–1101.
6.
Lempriere
B. M.
,
1968
, “
Poisson’s Ratio in Orthotropic Materials
,”
AIAA Journal
, Nov., Vol.
6
, No.
11
, pp.
2226
–
2227
.
7.
Lekhnitskii, S. G., 1963, Theory of Elasticity of an Anisotropic Elastic Body, Holden-Day, Inc., San Francisco, CA.
8.
Jones, D. P., 1979, “Axisymmetric Finite Element Analysis of Plates Containing Penetrations Arranged in a Square Pattern with Experimental Qualification,” presented at the 1979 ASME PVP Conference, Paper No. 79-PVP-79.
9.
Osweiller
F.
,
1989
, “
Evolution and Synthesis of the Effective Elastic Constants Concept for the Design of Tubesheets
,”
ASME JOURNAL OF PRESSURE VESSEL TECHNOLOGY
, Vol.
111
, Aug., pp.
209
–
217
.
10.
Paliwal
D. N.
, and
Saxena
R. M.
,
1993
, “
Design of Tubesheet for U-Tube Heat Exchangers
,”
ASME JOURNAL OF PRESSURE VESSEL TECHNOLOGY
, Feb., Vol.
115
, pp.
59
–
67
.
11.
PATRAN, 1990, Plus User Manual Volumes I & II, Release 2.5, PDA Engineering, Oct.
12.
Gardner, K. A., 1969, “Tube Sheet Design: A Basis for Standardization,” Vol. I-49, pp. 621–648, Proceedings, International Conference on Pressure Vessel Technology, ASME, New York, NY.
This content is only available via PDF.
Copyright © 1999
 by The American Society of Mechanical Engineers
You do not currently have access to this content.