Conical Shell Inversion—An Approximate Energy Analysis

1973 ◽  
Vol 95 (1) ◽  
pp. 172-176
Author(s):  
J. W. Jones ◽  
J. G. Wagner
Keyword(s):  
Upper Bound ◽  
Conical Shell ◽  
Large Deflection ◽  
Yield Criterion ◽  
Bend Radius ◽  
Perfectly Plastic ◽  
Continuous Application ◽  
Elastic Perfectly Plastic ◽  
Load Deflection Curve

The plastic inversion of a simply supported conical shell is considered. The shell is loaded through a rigid central collar. The material is assumed to be elastic-perfectly plastic and to obey the Tresca yield criterion. Upper and lower bound calculations are presented for the collapse load of the inverted configuration. The steady state load-deflection behavior for the large deflection inversion process is determined through a continuous application of the upper bound calculation. Minimization of the upper bound serves not only to determine an accurate characterization of the load-deflection curve but also provides a realistic measure of the bend radius associated with the mode of deformation assumed. Experimental results are presented and compared with the theory.

Analytical Solutions of Crack Tip Plasticity Zone Shape for a Semi-Infinite Crack

2003 ◽  
Author(s):  
Peihua Jing ◽  
Tariq Khraishi ◽  
Larissa Gorbatikh
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Analytical Solutions ◽  
Yield Criterion ◽  
Plasticity Zone ◽  
Linear Elastic ◽  
Perfectly Plastic ◽  
Classical Plasticity ◽  
Elastic Perfectly Plastic ◽  
Von Mises

In this work, closed-form analytical solutions for the plasticity zone shape at the lip of a semi-infinite crack are developed. The material is assumed isotropic with a linear elastic-perfectly plastic constitution. The solutions have been developed for the cases of plane stress and plane strain. The three crack modes, mode I, II and III have been considered. Finally, prediction of the plasticity zone extent has been performed for both the Von Mises and Tresca yield criterion. Significant differences have been found between the plane stress and plane strain conditions, as well as between the three crack modes’ solutions. Also, significant differences have been found when compared to classical plasticity zone calculations using the Irwin approach.

A limit load solution for a thick-walled cylinder with a fully circumferential crack under axial tension

2009 ◽  
Vol 44 (6) ◽  
pp. 407-416 ◽  
Author(s):  
P J Budden ◽  
Y Lei
Keyword(s):  
Finite Element ◽  
Plastic Material ◽  
Yield Criterion ◽  
Limit Load ◽  
Cylinder Wall ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Inside Radius ◽  
Walled Cylinder

Limit loads for a thick-walled cylinder with an internal or external fully circumferential surface crack under pure axial load are derived on the basis of the von Mises yield criterion. The solutions reproduce the existing thin-walled solution when the ratio between the cylinder wall thickness and the inside radius tends to zero. The solutions are compared with published finite element limit load results for an elastic–perfectly plastic material. The comparison shows that the theoretical solutions are conservative and very close to the finite element data.

A Compressible Elastic, Perfectly Plastic Wedge

1958 ◽  
Vol 25 (2) ◽  
pp. 239-242
Author(s):  
D. R. Bland ◽  
P. M. Naghdi
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
The State ◽  
Hardening Material ◽  
Included Angle ◽  
Elastic Plastic ◽  
Numerical Example ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Abstract This paper is concerned with a compressible elastic-plastic wedge of an included angle β < π/2 in the state of plane strain. The solution, deduced for an isotropic nonwork-hardening material, employs Tresca’s yield criterion and the associated flow rules. By means of a numerical example the solution is compared with that of an incompressible elastic-plastic wedge in one case (β = π/4) for various positions of the elastic-plastic boundary.

Elasto-Plastic Asperity Contacts of Layered Media

2005 ◽  
Author(s):  
Qin Xie ◽  
Geng Liu ◽  
Tianxiang Liu ◽  
Ruiting Tong ◽  
Quanren Zeng
Keyword(s):  
Yield Criterion ◽  
Layered Media ◽  
Asperity Contact ◽  
Initial Stiffness ◽  
Programming Technique ◽  
Perfectly Plastic ◽  
Real Area Of Contact ◽  
Asperity Contacts ◽  
Elastic Perfectly Plastic ◽  
Von Mises

An elasto-plastic asperity contact model for layered media is developed in the work reported in this paper to analyze the influences of coating-substrate materials on contact when yielding and the strain-hardening properties of materials are taken into account. The finite element method, the initial stiffness method and the mathematical programming technique are employed to solve the model. The von Mises yield criterion is used to determine the inception of plastic deformation. The effects of different layer thickness and different coating-substrate materials on the contact pressure, real area of contact, average gap of rough surface, and stresses in layer and substrate under the elastic-perfectly-plastic and the elasto-plastic contact conditions are numerically investigated and discussed.

An Upper Bound on the Small Displacements of Elastic, Perfectly Plastic Structures

1972 ◽  
Vol 39 (4) ◽  
pp. 959-963 ◽  
Author(s):  
A. R. S. Ponter
Keyword(s):  
Upper Bound ◽  
Limit State ◽  
Upper Bounds ◽  
Variable Loading ◽  
Plastic Structure ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Additional Calculation

An inequality is described which allows the evaluation of upper bounds to the displacement of an elastic/perfectly plastic structure subject to variable loading. Simple examples indicate that although the bound may not be very accurate, it may well provide a useful additional calculation to the limit state and shakedown solutions.

Limit Design of a Full Reinforcement for a Circular Cutout in a Uniform Slab

1952 ◽  
Vol 19 (3) ◽  
pp. 397-401
Author(s):  
H. J. Weiss ◽  
W. Prager ◽  
P. G. Hodge
Keyword(s):  
Upper Bound ◽  
Plastic Material ◽  
Yield Criterion ◽  
Curved Beam ◽  
Shearing Stress ◽  
Concentric Ring ◽  
Perfectly Plastic ◽  
Circular Cutout

Abstract A thin square slab with a central circular cutout reinforced by a concentric ring is subjected to uniform tensions Tx and Ty on the exterior edges. It is desired to determine the dimensions of the reinforcement if the slab is not to collapse under any load which could be supported by a similar slab without any cutout or reinforcement. It is assumed that the slab and reinforcement are made of a perfectly plastic material which satisfies the Tresca yield criterion of maximum shearing stress, and that the dimensions of the reinforcement are such that it may reasonably be approximated by a curved beam. Under these assumptions, an upper bound on the necessary thickness of the reinforcement for any given radius is obtained. Certain practical limitations of the theory are discussed.

scholarly journals Influence of Material Compressibility on Displacement Solution for Structural Steel Plate Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Nelli Aleksandrova
Keyword(s):  
Structural Steel ◽  
Yield Criterion ◽  
Flow Rule ◽  
Perfectly Plastic ◽  
Open Hole ◽  
Practical Engineering ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Associated Flow Rule ◽  
Material Compressibility

Displacement field calculations are necessary for many structural steel engineering problems such as cold expansion of holes, embedment of bolts and rivets, and installation and maintenance of external devices. To this end, rigorous closed form analytical displacement solution is obtained for structural steel open-hole plates with in-plane loading. The material of the model is considered to be elastic perfectly plastic obeying the von Mises yield criterion with its associated flow rule. On the basis of this solution, two simplified engineering formulae are proposed and carefully discussed for practical engineering purposes. Graphical representations of results show validity of each formula as compared with rigorous solution and other studies.

On the stability of supported excavations

1984 ◽  
Vol 21 (2) ◽  
pp. 338-348 ◽  
Author(s):  
A. M. Britto ◽  
O. Kusakabe
Keyword(s):  
Plane Strain ◽  
Upper Bound ◽  
Plastic Material ◽  
Cohesive Soil ◽  
Perfectly Plastic ◽  
Centrifuge Tests ◽  
Bentonite Slurry ◽  
Undrained Conditions ◽  
Elastic Perfectly Plastic ◽  
The Stability

Unsupported plane strain trenches and axisymmetric shafts cannot be excavated to great depths in a purely cohesive soil. Therefore, it is standard practice to provide some form of support. Timber supports with struts are conventional and quite common. Bentonite slurry support has become more popular in recent years especially in the construction of diaphragm walls. In this paper the effect of rigid lateral support and slurry support on the stability (mode of failure) for both plane strain and axisymmetric excavations are investigated under undrained conditions. When immediate failure is of interest in saturated clays the changes in the water content can be neglected and the soil can be treated as a [Formula: see text] material. For the purposes of the analyses presented here the lateral support is assumed to be rigid and the soil is idealized as an elastic perfectly plastic material with cohesion Cu. The results from upper bound calculations, finite element collapse analyses, and centrifuge tests are presented. The analogy between deep footing failure and base failure of excavation allows the solutions for the footing problem to be interpreted for trench excavations. It is found that slurry support is more effective than rigid lateral support for axisymmetric excavations. The slurry support reduces the amount of surface settlement and also stabilises the trench against base failure. For excavations with rigid lateral support the possibility of base failure is greatly increased. The results are presented in the form of stability charts. Keywords: limit analysis, slurry support, stability number, supported excavation, upper bound solution.

The Application of Limit Analysis to Punch-Indentation Problems

1953 ◽  
Vol 20 (4) ◽  
pp. 453-460
Author(s):  
R. T. Shield ◽  
D. C. Drucker
Keyword(s):  
Limit Analysis ◽  
Plane Surface ◽  
Plastic Material ◽  
Yield Criterion ◽  
Three Dimensional ◽  
Upper And Lower Bounds ◽  
Two Dimensional ◽  
Flat Punch ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Abstract Limit analysis is applied to obtain upper and lower bounds for the punch pressure in the indentation of the plane surface of an elastic-perfectly plastic material by a flat rigid punch. The two-dimensional flat punch and the three-dimensional flat square and rectangular punch problems are considered. The analysis assumes Tresca’s yield criterion of constant maximum shearing stress k, during plastic deformation. It is shown that the pressure required to produce indentation in the two-dimensional problem lies between 5k and (2 + π)k. The lower bound obtained for any rectangular punch is again 5k while the upper bound for a smooth punch lies between 5.71k for a square and (2 + π)k for a very long rectangle. A value of 5.36k is found for a ratio of length to breadth of 3. The limit pressure for a uniformly loaded area, as distinguished from an area loaded by a punch, is bracketed by 5k and (2 + π)k when the area is convex.

scholarly journals Analysis of stress and strain in a rotating disk mounted on a rigid shaft

2006 ◽  
Vol 33 (1) ◽  
pp. 65-90 ◽  
Author(s):  
Nelli Alexandrova ◽  
Sergei Alexandrov ◽  
Real Vila
Keyword(s):  
Yield Criterion ◽  
Strain Analysis ◽  
Rotating Disk ◽  
Outer Radius ◽  
Constant Thickness ◽  
Flow Rule ◽  
Plane State ◽  
Annular Disk ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

The plane state of stress in an elastic-perfectly plastic isotropic rotating annular disk mounted on a rigid shaft is studied. The analysis of stresses, strains and displacements within the disk of constant thickness and density is based on the Mises yield criterion and its associated flow rule. It is observed that the plastic deformation is localized in the vicinity of the inner radius of the disk, and the disk of a sufficiently large outer radius never becomes fully plastic. The semi-analytical method of stress-strain analysis developed is illustrated by some numerical examples. .

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