Effect of Plane Strain, Plane Stress and Bending on Equivalent Solid Collapse Predictions for Perforated Plates

2002 ◽  
Author(s):  
Wolf Reinhardt
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Finite Thickness ◽  
Collapse Load ◽  
Element Analysis ◽  
Perforated Plates ◽  
Periodic Cell ◽  
State Of Stress ◽  
Symmetry Properties ◽  
A Cell

An equivalent solid based method of predicting the plastic (limit) collapse of perforated plates has been developed in the recent literature. Higher order collapse surfaces with suitable symmetry properties are used for the analysis. The equation for the collapse surface contains a number of constants that are determined by comparison to a Finite Element analysis of an actual perforated periodic cell subject to selected membrane states of stress. Using a typical triangular perforation pattern, the present paper investigates the effect of simplifying assumptions that were made during the periodic cell analysis on the predicted collapse load of the actual cell geometry. For a finite thickness cell subjected to a membrane state of stress, the collapse load is expected to lie between that of the bounding cases of plane stress and generalised plane strain, which are compared here. The connection between the collapse of a cell subjected to a membrane state of stress and a cell of large thickness in bending is established.

scholarly journals Elastic soil

1971 ◽  
Vol 4 (2) ◽  
pp. 258-269
Author(s):  
A. J. Carr ◽  
P. J. Moss
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Soil Structure ◽  
Soil Structure Interaction ◽  
Mode Shapes ◽  
Element Analysis ◽  
Structure Interaction ◽  
Stiffness Properties ◽  
Acceleration History ◽  
Elastic Soil

This paper presents a refined finite element analysis for the analysis of two-dimensional plane stress and plane strain structures with particular emphasis being placed on the ability to solve problems of soil-structure interaction under earthquake loadings. The structure and
the soil are idealized as an assemblage of quadrilateral plane stress and plane strain elements having a cubic variation in displacement enabling a more accurate representation of the stiffness properties of the system than that previously available. The response of the system to the earthquake acceleration history is achieved by a superposition of normal mode responses and the methods of obtaining the mode shapes and frequencies are outlined. Examples are presented to illustrate the capability of this approach.

Three-Dimensional Elastic Stress Fields of Finite Thickness Plates with Elliptical Hole

2007 ◽  
Vol 353-358 ◽  
pp. 74-77
Author(s):  
Zheng Yang ◽  
Chong Du Cho ◽  
Ting Ya Su ◽  
Chang Boo Kim ◽  
Hyeon Gyu Beom
Keyword(s):  
Stress Concentration ◽  
Plane Strain ◽  
Plane Stress ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Maximum Stress ◽  
Elastic Stress ◽  
Finite Thickness ◽  
Plate Thickness ◽  
Three Dimensional

Based on detailed three-dimensional finite element analyses, elastic stress and strain field of ellipse major axis end in plates with different thickness and ellipse configurations subjected to uniaxial tension have been investigated. The plate thickness and ellipse configuration have obvious effects on the stress concentration factor, which is higher in finite thickness plates than in plane stress and plane strain cases. The out-of-plane stress constraint factor tends the maximum on the mid-plane and approaches to zero on the free plane. Stress concentration factors distribute ununiformly through the plate thickness, the value and location of maximum stress concentration factor depend on the plate thickness and the ellipse configurations. Both stress concentration factor in the middle plane and the maximum stress concentration factor are greater than that under plane stress or plane strain states, so it is unsafe to suppose a tensioned plate with finite thickness as one undergone plane stress or plane strain. For the sharper notch, the influence of three-dimensional stress state on the SCF must be considered.

On the Plane Stress to Plane Strain Transition Across the Shear Zone in Metal Cutting

1988 ◽  
Vol 110 (4) ◽  
pp. 322-325 ◽  
Author(s):  
B. E. Klamecki ◽  
S. Kim
Keyword(s):  
Plane Strain ◽  
Shear Zone ◽  
Plane Stress ◽  
Central Region ◽  
Chip Formation ◽  
Metal Cutting ◽  
High Strain ◽  
Surface Characteristics ◽  
Workpiece Material ◽  
Element Analysis

The effects of the stress state transition from plane stress at the workpiece surface to plane strain in the central region of the chip formation zone were studied. A finite element analysis of the incipient chip formation process was performed. The model included heat generation and temperature induced workpiece material property changes. The primary result is that the unique high strain, high strain rate, large free surface characteristics of the metal cutting process can result in qualitatively different deformation behavior across the shear zone. Temperatures are higher in the regions near the surface of the workpiece than in the central region. In extreme cases, this will result in strain hardening behavior in the plain strain regions and thermal softening of the work material near the surface.

scholarly journals Comparison of theoretical approaches to determine the stresses in surface mounted permanent magnet rotors for high speed electric machines

2021 ◽  
pp. 030932472110076
Author(s):  
Levi Mallin ◽  
Simon Barrans
Keyword(s):  
Permanent Magnet ◽  
Plane Strain ◽  
Plane Stress ◽  
High Speed ◽  
Electric Machines ◽  
Mechanical Transmission ◽  
Element Analysis ◽  
Theoretical Approaches ◽  
Rotor Design ◽  
Stress Plane

High-speed electrical machines (HSEMs) are becoming more popular in applications such as air handling devices. Using surface-mounted permanent magnet (PM) rotors manufactured from rare earth metals, they provide benefits over their mechanical transmission counterparts. However, these PMs have low tensile strength and are prone to failure under large centrifugal loads when rotating. Therefore, retaining sleeves are used to hold the PMs in compression to eliminate tensile stress and reduce failure risk. The magnets are also often held on a back iron or carrier, forming an assembly of three cylinders. The ability to predict these stresses is extremely important to rotor design. Current published work shows a lack of exploration of analytical methods of calculating these stresses for three-cylinder assemblies. This paper shows the development of plane stress, plane strain and generalised plane strain (GPS) theories for three cylinders. For a range of rotor designs, these theories are compared with finite element analysis (FEA). GPS is shown to be more accurate than plane stress or plane strain for the central region of long cylinders. For short cylinders and for the ends of cylinders, all three theories give poor results.

ASME 1993 Nadai Lecture—Elastoplastic Stress and Strain Concentrations

1995 ◽  
Vol 117 (1) ◽  
pp. 1-7 ◽  
Author(s):  
William N. Sharpe
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Stress And Strain ◽  
Predictive Capability ◽  
Element Analysis ◽  
Elastoplastic Behavior ◽  
Local Stresses ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Elastic Constraint

Elastic stress concentration factors are familiar and easily incorporated into the design of components or structures through charts or finite element analysis. However when the material at the most concentrated location no longer behaves elastically, computation of the local stresses and strains is not so easy. Local elastoplastic behavior is an especially important consideration when the loading is cyclic. This paper summarizes the predictive capability of the Neuber and the Glinka models that relate gross loading to the local stresses and strains. The author and his students have used a unique laser-based technique capable of measuring biaxial strains over very short gage lengths to evaluate the two models. Their results, as well as those from earlier studies by other researchers using foil gages, lead to the general conclusion that the Neuber model works best when the local region is in a state of plane stress and the Glinka model is best for plane strain. There are intermediate levels of constraint that are neither plane stress nor plane strain. This paper presents a recommended practice for predicting the local elastoplastic stresses and strains for any constraint. First, one computes or estimates the initial elastic strains. Then, based on the amount of elastic constraint, one selects the appropriate model to compute the local elastoplastic stresses and strains.

Effect of State-of-Stress and Yield Criterion on the Bauschinger Effect

1968 ◽  
Vol 90 (3) ◽  
pp. 403-408 ◽  
Author(s):  
S. T. Rolfe ◽  
R. P. Haak ◽  
J. H. Gross
Keyword(s):  
Yield Strength ◽  
Plane Strain ◽  
Plane Stress ◽  
Bauschinger Effect ◽  
Yield Criterion ◽  
Cold Deformation ◽  
Stress Relief ◽  
Cold Forming ◽  
State Of Stress ◽  
Direction Opposite

During fabrication, the cold forming of structural components may reduce the yield strength of a component if it is loaded in a direction opposite to that of the cold forming. This reduction in yield strength, referred to as the Bauschinger effect, is influenced by the state-of-stress under which the cold forming is performed, by the criterion used to determine the yield strength, and by the use of post-forming stress relief. To establish the importance and magnitude of these effects, specimens from 2 1/2-in-thick plates of HY-80 steel, cold-formed by plane strain bending, were tested along with specimens that were cold-formed by plane-stress axial straining. For material tested in a direction opposite to that of cold forming, the Bauschinger effect was observed both in tension and compression, whereas for material tested at 90 deg to the direction of cold forming in plane strain, both the tensile and compressive yield strengths increased and no Bauschinger effect was observed. Because of the difference in restraint, the Bauschinger effect was greater for plane-stress axial deformation than for plane-strain bending deformation. The Bauschinger effect was greater when the yield strength was determined at small offsets and was essentially eliminated at an offset greater than 0.5 percent. In addition, the Bauschinger effect was greatest for small amounts of cold deformation and was progressively decreased by strain hardening at large amounts of cold deformation. The reduction in secant modulus and in yield strength (Bauschinger effect) in cold-formed material was essentially eliminated by stress-relief treatment at 1025 deg. F. The results indicate the importance of knowing the cold-forming state-of-stress, the criterion used in determining yield strength, and the effects of stress relief when assessing the effects of cold deformation on mechanical properties.

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.

Sign in / Sign up

Export Citation Format

Share Document