Stresses of Thick Perforated Plates With Reinforcement of Tubes and Their Effective Elastic Constants

1992 ◽  
Vol 114 (3) ◽  
pp. 271-279 ◽  
Author(s):  
K. C. Hwang ◽  
M. D. Xue ◽  
X. F. Wen ◽  
G. Chen
Keyword(s):  
Elastic Constants ◽  
Experimental Results ◽  
Design Codes ◽  
Perforated Plates ◽  
Effective Elastic Constants ◽  
Solid Plate ◽  
Current Design ◽  
Stiffening Effect

Based on the concept of equivalent solid plate, this paper deals with thick perforated plates with triangular or square patterns of holes reinforced by tubes. The results obtained show that the tubes connected (by welding or expanding) to the perforated plates lead to a noticeable stiffening effect which is neglected or considerably underestimated by current design codes. The stresses of tubesheets calculated based on the effective elastic constants given by this method are in better agreement with the experimental results than those based on the effective elastic constants given by current codes.

Effective Elastic Constants for the Bending of Thin Perforated Plates With Triangular and Square Penetration Patterns

1973 ◽  
Vol 95 (1) ◽  
pp. 121-128 ◽  
Author(s):  
W. J. O’Donnell
Keyword(s):  
Plane Strain ◽  
Elastic Constants ◽  
Thin Plates ◽  
Perforated Plates ◽  
Bending Tests ◽  
Effective Elastic Constants ◽  
Asme Code ◽  
Aluminum Beam ◽  
Generalized Plane Strain ◽  
Good Agreement

Bending tests were run on a series of aluminum beam specimens perforated in triangular and square arrays. Progressively thinner specimens were tested down to 1/8 the thickness covered by the ASME Code. The results for the thick specimens show good agreement with the theoretical generalized plane strain values. The trend of the results with decreasing thickness agrees with the theoretical values for the bending of very thin plates. The applicability of the results is generalized using dimensionless parameters.

Design of Perforated Plates

1962 ◽  
Vol 84 (3) ◽  
pp. 307-319 ◽  
Author(s):  
W. J. O’Donnell ◽  
B. F. Langer
Keyword(s):  
Heat Exchanger ◽  
Elastic Constants ◽  
Thermal Stresses ◽  
Heat Exchanger Tube ◽  
Perforated Plates ◽  
Strain Measurements ◽  
Effective Elastic Constants ◽  
Theoretical Considerations ◽  
Exchanger Tube

This paper describes a method for calculating stresses and deflections in perforated plates with a triangular penetration pattern. The method is based partly on theory and partly on experiment. Average ligament stresses are obtained from purely theoretical considerations but effective elastic constants and peak stresses are derived from strain measurements and photoelastic tests. Acceptable limits for pressure stresses and thermal stresses in heat exchanger tube sheets are also proposed.

Simple estimation of effective elastic constants for thin plates with regular perforations and an application to the vibration of distillation column trays

2016 ◽  
Vol 52 (1) ◽  
pp. 57-66
Author(s):  
Wensong Zhang ◽  
Paul H Taylor ◽  
Richard C Darton
Keyword(s):  
Finite Element ◽  
Elastic Constants ◽  
Analytical Method ◽  
Distillation Column ◽  
Fatigue Cracking ◽  
Thin Plates ◽  
Element Analysis ◽  
Process Industries ◽  
Perforated Plates ◽  
Effective Elastic Constants

The horizontal perforated sheet metal plates are commonly used in the process industries as trays in distillation columns, important internal parts for fractionating the input liquid mixture. Normally, the operating performance of such trays is satisfactory. However, cases have been reported of abnormally high levels of tray vibration during operation at particular conditions. The trays then experienced fatigue cracking accompanied by the loosening of bolts and fixings, which led to expensive failures. The excitation of structural resonance was suspected as a component in flow-induced vibration. Using linear stress superposition, a simple but robust analytical method is developed to provide high-quality predictions for the stress and strain distributions for in-plane loaded thin perforated plates with periodic hole arrangements. This approach is built on the classical solution for the elastic stress field around a single circular hole in a large plate. The perforated plates with square penetration patterns are investigated in this article, although the same approach is applicable to any regular penetration pattern. Stress concentration factors as well as the effective elastic constants, which can be used to describe the bending properties of the perforated plates, are then verified against both the established theoretical solutions and the results from finite element simulations. Excellent agreement to both previously published physical experiments and complex modelling is observed in all cases, with small-to-medium (up to 40%) hole-area fraction. The proposed analytical method is much simpler and computationally efficient than finite element analysis. The computed effective elastic constants are used in a finite element modal analysis to estimate the free vibration frequencies of a stiffened distillation column tray example; the first 30 vibration modes are found to be almost uniformly distributed between 25 and 70 Hz, which matches the vibration frequency range reported from plant operations.

Evolution and Synthesis of the Effective Elastic Constants Concept for the Design of Tubesheets

1989 ◽  
Vol 111 (3) ◽  
pp. 209-217 ◽  
Author(s):  
F. Osweiller
Keyword(s):  
Elastic Constants ◽  
Pressure Vessel ◽  
Perforated Plates ◽  
Effective Elastic Constants ◽  
Pattern Problem

The simplest way to take into account the weakening effect of holes in a multiperforated plate is to replace it by an equivalent solid one with adjusted “effective elastic constants.” This paper intends to show how this concept has evolved since 1948 to the present by providing a thorough review and comparison of papers dealing with this subject. A special item is devoted to square pattern problem. Curves for calculating effective elastic constants E* and ν* are proposed which enable treatment of even perforated plates, circular or not, as solid ones for which the classical equations of elasticity apply. These curves have been adopted in the French Pressure Vessel Code (CODAP) for the design of tubesheets.

Effective Elastic Constants for Thick Perforated Plates With Square and Triangular Penetration Patterns

1971 ◽  
Vol 93 (4) ◽  
pp. 935-942 ◽  
Author(s):  
T. Slot ◽  
W. J. O’Donnell
Keyword(s):  
Plane Strain ◽  
Elastic Constants ◽  
Plane Stress ◽  
Numerical Results ◽  
Exact Formulation ◽  
Perforated Plates ◽  
Effective Elastic Constants ◽  
Wide Range ◽  
The Relationship ◽  
Generalized Plane Strain

An exact formulation is presented of the relationship between the effective elastic constants for thick perforated plates (generalized plane strain) and thin perforated plates (plane stress). Extensive numerical results covering a wide range of ligament efficiencies and Poisson’s ratios are given for plates with square and triangular penetration patterns.

Elastic Design Methods for Perforated Plates

1978 ◽  
Vol 100 (2) ◽  
pp. 356-362 ◽  
Author(s):  
J. S. Porowski ◽  
W. J. O’Donnell
Keyword(s):  
Finite Element ◽  
Thermal Loading ◽  
Solid Material ◽  
Perforated Plates ◽  
Finite Element Stress Analysis ◽  
Effective Elastic Constants ◽  
New Methods ◽  
Circular Holes ◽  
Elastic Design ◽  
Generalized Plane Strain

Methods for performing finite element stress analysis of perforated plates under pressure and complex thermal loading conditions are described. The concept of the equivalent solid material of anisotropic properties is employed to define the elasticity matrices to be used for axisymmetric analysis of plates containing triangular and square patterns of circular holes. Generalized plane strain effective elastic constants are used for better approximation of the overall plate behavior. New methods and curves for obtaining local ligament stresses from the nominal stresses in the equivalent solid material are given.

Effective Elastic Constants of Fiber-Eutectics and Transformation Particles Composite Ceramic

2010 ◽  
Vol 177 ◽  
pp. 182-185 ◽  
Author(s):  
Bao Feng Li ◽  
Jian Zheng ◽  
Xin Hua Ni ◽  
Ying Chen Ma ◽  
Jing Zhang
Keyword(s):  
Elastic Modulus ◽  
Elastic Constant ◽  
Effective Stress ◽  
Elastic Constants ◽  
Transverse Isotropy ◽  
Analytical Formula ◽  
Composite Ceramic ◽  
Phase Model ◽  
Composite Ceramics ◽  
Effective Elastic Constants

The composite ceramics is composed of fiber-eutectics, transformation particles and matrix particles. First, the recessive expression between the effective stress in fiber-eutectic and the flexibility increment tensor is obtained according to the four-phase model. Second, the analytical formula which contains elastic constant of the fiber-eutectic is obtained applying Taylor’s formula. The eutectic is transverse isotropy, so there are five elastic constants. Third, the effective elastic constants of composite ceramics are predicted. The result shows that the elastic modulus of composite ceramic is reduced with the increase of fibers fraction and fibers diameter.

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