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.

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.

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.

The Contact Problem for a Rigid Inclusion Pressed Between Two Dissimilar Elastic Half Planes

1981 ◽  
Vol 48 (1) ◽  
pp. 104-108
Author(s):  
G. M. L. Gladwell
Keyword(s):  
Contact Problem ◽  
Plane Strain ◽  
Integral Equations ◽  
Elastic Constants ◽  
Contact Stress ◽  
Rigid Inclusion ◽  
Numerical Results ◽  
Stress Distributions ◽  
Plane Strain Problem

Paper concerns the plane-strain problem of a rigid, thin, rounded inclusion pressed between two isotropic elastic half planes with different elastic constants. Required to find the extents of the contact regions between each plane and the inclusion, and the contact stress distributions. The governing integral equations are solved approximately by using Chebyshev expansions. Numerical results are presented.

Cavities vis-a`-vis Rigid Inclusions and Some Related General Results in Plane Elasticity

1989 ◽  
Vol 56 (4) ◽  
pp. 786-790 ◽  
Author(s):  
John Dundurs
Keyword(s):  
Stress Field ◽  
Plane Strain ◽  
Elastic Constants ◽  
Plane Stress ◽  
Poisson Ratio ◽  
Plane Elasticity ◽  
By Products

There is a strange feature of plane elasticity that seems to have gone unnoticed: The stresses in a body that contains rigid inclusions and is loaded by specified surface tractions depend on the Poisson ratio of the material. If the Poisson ratio in this stress field is set equal to +1 for plane strain, or +∞ for plane stress, the rigid inclusions become cavities for elastic constants within the physical range. The paper pursues this circumstance, and in doing so also produces several useful by-products that are connected with the stretching and curvature change of a boundary.

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.

Three-dimensional thermo-mechanical analysis of continuous casting and comparison with two-dimensional models

2018 ◽  
Vol 53 (6) ◽  
pp. 421-434
Author(s):  
Reza Vaghefi ◽  
MR Hematiyan ◽  
Ali Nayebi
Keyword(s):  
Continuous Casting ◽  
Phase Change ◽  
Galerkin Method ◽  
Plane Strain ◽  
Plane Stress ◽  
Three Dimensional ◽  
Casting Process ◽  
Mechanical Analysis ◽  
Two Dimensional ◽  
Generalized Plane Strain

In this study, a three-dimensional thermo-elasto-plastic model is developed for simulating a continuous casting process. The obtained results are compared with those from different two-dimensional analyses, which are based on plane stress, plane strain, and generalized plane strain assumptions. All analyses are carried out using the meshless local Petrov–Galerkin method. The effective heat capacity method is employed to simulate the phase change process. The von Mises yield criterion and elastic–perfectly-plastic model are used to simulate the stress state during the casting process; while, material parameters are assumed to be temperature-dependent. Based on the three-dimensional and two-dimensional models, numerical results are provided to determine the stress, displacement, and temperature fields induced in the cast material. It is observed that the present meshless local Petrov–Galerkin method is accurate in three-dimensional thermo-mechanical analysis of highly nonlinear phase change problems. Reasonable agreements are observed between the results obtained from the three-dimensional analysis with those retrieved by the generalized plane strain assumption. However, it is observed that the results obtained under plane stress/strain conditions have some significant differences with the results obtained from three-dimensional modeling of continuous casting.

Effect of Interface Anisotropy on Elastic Wave Propagation in Particulate Composites

2008 ◽  
Vol 24 (1) ◽  
pp. 79-93 ◽  
Author(s):  
S. M. Hasheminejad ◽  
M. Maleki
Keyword(s):  
Elastic Constants ◽  
Finite Thickness ◽  
Particulate Composites ◽  
Power Series Solution ◽  
Isotropic Shell ◽  
Effective Elastic Constants ◽  
Phase Velocities ◽  
Wide Range ◽  
Interface Layers ◽  
Interface Anisotropy

ABSTRACTThe scattering of time harmonic plane longitudinal and transverse elastic waves in a composite consisting of randomly distributed identical isotropic spherical inclusions embedded in an isotropic matrix with anisotropic interface layers is examined. The interface region is modeled as a spherically isotropic shell of finite thickness with five independent elastic constants. The Frobenius power series solution method is utilized to deal with the interface anisotropy and the effect of random distribution of particulates in the composite medium is taken into account via a recently developed generalized self-consistent multiple scattering model. Numerical values of phase velocities and attenuations of coherent plane waves as well as the effective elastic constants are obtained for a moderately wide range of frequencies, particle concentrations, and interface anisotropies. The numerical results reveal the significant dependence of phase velocities and effective elastic constants on the interface properties. They show that interface anisotropy can moderately depress the effective phase velocities and the elastic moduli, but leave effective attenuation nearly unaffected, especially at low and intermediate frequencies. Limiting cases are considered and good agreements with recent solutions have been obtained.

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.

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