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.

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.

Study on Effective Elastic Constants of Homogenization Tube Sheet

2012 ◽  
Vol 430-432 ◽  
pp. 158-163
Author(s):  
Yi Sun ◽  
Gao Ying Kang ◽  
Ding Cui ◽  
Jing Ran Ge
Keyword(s):  
Elastic Constant ◽  
Elastic Constants ◽  
Tube Sheet ◽  
Effective Elastic Constant ◽  
Effective Elastic Constants ◽  
Numerical Result ◽  
Asme Code ◽  
Cylindrical Inclusions ◽  
The Relationship ◽  
Good Agreement

The expressions of the effective elastic constants of composite material with cylindrical inclusions are derived based on M-T method, and it can be used in discussing the approximate range of effective elastic constant of air. Moreover, it is possible to homogenize tube-sheet by making use of the expression. The numerical result obtained is in good agreement with effective elastic constant adopted by the ASME code. It demonstrates that the approach is effective and accurate. At the last, the relationship between effective elastic and thickness of the tube-sheet is discussed.

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.

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.

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.

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.

Comparison of Variational and Generalized Plane Strain approaches for matrix cracking in general symmetric laminates

2017 ◽  
Vol 27 (4) ◽  
pp. 507-540 ◽  
Author(s):  
Mohammad Hajikazemi ◽  
L Neil McCartney
Keyword(s):  
Plane Strain ◽  
Elastic Constants ◽  
Variational Approach ◽  
Thermal Stresses ◽  
Research Work ◽  
Stress Transfer ◽  
Matrix Cracking ◽  
Variational Model ◽  
Numerical Comparison ◽  
Generalized Plane Strain

The current research work is aimed at comparing a stress-based variational approach with generalized plane strain (GPS) model for predicting stress transfer in cracked general symmetric laminates, subject to general in-plane loading. For each model, the fundamental assumptions made on stress and displacement fields, and also procedures for defining boundary conditions and finding solutions are detailed. Moreover, a numerical comparison has been made between the results obtained from two models with regard to stresses, displacements, and thermo-elastic constants of an unbalanced symmetric cracked laminate. Finally, the accuracy and quality of both approaches are examined by checking the satisfaction of known inter-relationships among thermo-elastic constants of cracked laminates. The paper extends an existing variational model so that the effects of residual thermal stresses can be considered. It has been also shown how the displacement field can be determined for a stress-based variational approach.

A Hybrid Membrane/Shell Method for Rapid Estimation of Springback in Anisotropic Sheet Metals

1998 ◽  
Vol 65 (3) ◽  
pp. 671-684 ◽  
Author(s):  
F. Pourboghrat ◽  
K. Chung ◽  
O. Richmond
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
Bending Moment ◽  
Isotropic Hardening ◽  
Normal Anisotropy ◽  
Bending Tests ◽  
Reverse Loading ◽  
Draw Bending ◽  
Springback Prediction ◽  
Good Agreement

A semi-analytical method to predict springback in sheet metal forming processes has been developed for the case of plane strain. In the proposed hybrid method, for each deformation increment, bending, and unbending stretches are analytically superposed on membrane stretches which are numerically obtained in advance from a membrane finite element code. Springback is then obtained by the unloading of a force and a bending moment at the boundary of each element treated as a shell. Hill’s 1948 yield criterion with normal anisotropy is used in this theory along with kinematic and isotropic hardening laws during reverse loading. The method has been applied for the springback prediction of a 2008-T4 aluminum alloy in plane-strain draw-bending tests. The results indicate the necessity of including anisotropic hardening (especially Bauschinger effects) and elastoplastic unloading in order to achieve good agreement with experimental results.

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.

Sign in / Sign up

Export Citation Format

Share Document