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 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.

Finite Element Stress Analysis of Tubesheets Perforated by Circular Holes in Square Pitch Pattern

1998 ◽  
Vol 120 (1) ◽  
pp. 12-16 ◽  
Author(s):  
V. G. Ukadgaonker ◽  
P. A. Kale
Keyword(s):  
Finite Element ◽  
Stress Analysis ◽  
Perforated Plate ◽  
Finite Element Stress Analysis ◽  
Pitch Pattern ◽  
Circular Holes ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Bending Loading ◽  
Finite Element Stress

ASME has accepted the codes for the tubesheets with triangular pitch pattern, but the code standards for the square pitch pattern have not been accepted so far. This is the motivation behind solving the present problem. This paper deals with the finite element stress analysis of a perforated plate or tubesheets with square pitch pattern. For the stress analysis, finite number of holes and in-plane and bending loading are considered. Stress concentration factors are obtained for various ligament efficiencies. The problem of cracks emanating from holes is also considered. Stress intensity factors for various crack lengths and ligament efficiencies are obtained.

Processing-Induced Stresses and Curvature in Patterned Lines on Silicon Wafers

1996 ◽  
Vol 436 ◽  
Author(s):  
Y. -L. Shen ◽  
S. Suresh ◽  
I. A. Blech
Keyword(s):  
Finite Element ◽  
Stress Field ◽  
Plane Strain ◽  
Thermal Loading ◽  
Model Systems ◽  
Experimental Measurements ◽  
Uniform Stress ◽  
Uniform Stress Field ◽  
Induced Stresses ◽  
Generalized Plane Strain

AbstractThe evolution of stresses due to the patterning and thermal loading of thin lines on Si wafers, and the consequent changes in the overall curvature of the wafer are studied theoretically and experimentally. The analysis involves finite element simulations within the context of generalized plane strain models. The analysis is capable of predicting the wafer curvature in directions parallel and perpendicular to the lines. These predictions compare reasonably well with experimental measurements of curvature made on model systems. The thickness, width and spacing of the patterned lines have been varied systematically, and the associated changes in the evolution of stresses and curvature have been determined. The non-uniform stress field within the fine lines is also analyzed.

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.

Processing-Induced Stresses And Curvature In Patterned Lines On Silicon Wafers

1996 ◽  
Vol 428 ◽  
Author(s):  
Y-L. Shen ◽  
S. Suresh ◽  
I. A. Blech
Keyword(s):  
Finite Element ◽  
Stress Field ◽  
Plane Strain ◽  
Thermal Loading ◽  
Model Systems ◽  
Experimental Measurements ◽  
Uniform Stress ◽  
Uniform Stress Field ◽  
Induced Stresses ◽  
Generalized Plane Strain

AbstractThe evolution of stresses due to the patterning and thermal loading of thin lines on Si wafers, and the consequent changes in the overall curvature of the wafer are studied theoretically and experimentally. The analysis involves finite element simulations within the context of generalized plane strain models. The analysis is capable of predicting the wafer curvature in directions parallel and perpendicular to the lines. These predictions compare reasonably well with experimental measurements of curvature made on model systems. The thickness, width and spacing of the patterned lines have been varied systematically, and the associated changes in the evolution of stresses and curvature have been determined. The non-uniform stress field within the fine lines is also analyzed.

Thermo-Mechanical Response of Multilayered Cylinders Under Pressure and Thermal Loading With Generalized Plane Strain Condition

2019 ◽  
Vol 141 (2) ◽  
Author(s):  
Sang-Guk Kang ◽  
Kuao-John Young
Keyword(s):  
Finite Element ◽  
Plane Strain ◽  
Thermal Loading ◽  
Mechanical Response ◽  
Axial Direction ◽  
Plane Strain Condition ◽  
Strain Condition ◽  
Efficient Design ◽  
Element Analysis ◽  
Generalized Plane Strain

Multilayered cylindrical structures subject to pressure and thermal loading are commonly seen in many industries. In this study, the formulas for multilayered cylinders under pressure and thermal loading are derived with an assumption that the cylinders meet generalized plane strain condition, i.e., there is no external constraint in the axial direction and the axial growths of the cylindrical layers are the same. A numerical solution procedure for double-layered cylinders subject to both pressure and thermal load is developed and implemented in a mathcad program. To validate the solution, a finite element model for a double-layered cylinder is prepared with abaqus, and its responses under pressure and thermal loading are compared to those from the mathcad program. The algorithm of the method can be extended to three or more layered cylinders. The method developed in this study allows quick optimization and efficient design refinement for multilayered cylinders without running finite element analysis (FEA).

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.

Plastic Strength of Perforated Plates With Square Penetration Patterns

1975 ◽  
Vol 97 (3) ◽  
pp. 146-154 ◽  
Author(s):  
J. Porowski ◽  
W. J. O’Donnell
Keyword(s):  
Lower Bound ◽  
Entire Range ◽  
Solid Material ◽  
Biaxial Stress ◽  
Perforated Plates ◽  
Limit Loads ◽  
Plastic Strength ◽  
Circular Holes ◽  
Yield Surfaces

The sheet perforated with circular holes arranged in a square penetration pattern anp subjected to in-plane biaxial stress is investigated. Discontinuous fields of stress are used to obtain the lower-bound limit loads for the perforated material. The yield surfaces for the equivalent solid material are then derived and the effective plastic constants are given for the entire range of ligament efficiencies used in design.

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