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.

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.

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.

Estimation of the Stresses in Rotational Autofrettage of Thick-Walled Pressure Vessels Using von Mises Yield Criterion

2021 ◽  
Author(s):  
S. M. Kamal ◽  
Faruque Aziz
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
Pressure Vessels ◽  
Flow Rule ◽  
Stress Distributions ◽  
Von Mises Yield Criterion ◽  
Potential Methods ◽  
Von Mises ◽  
Associated Flow Rule ◽  
Theoretical Analyses

Abstract Rotational autofrettage is one of the recently proposed potential methods for eliminating the in-service yielding of thick-walled cylindrical pressure vessels. A few researchers have studied the feasibility of the process theoretically, and asserted certain advantages over the practicing hydraulic and swage autofrettage processes. In the literature, all theoretical analyses on the rotational autofrettage are based on the Tresca yield criterion and its associated flow rule, along with the assumption of different plane end conditions (plane strain and generalized plane strain). In this paper, an analysis of the rotational autofrettage of cylindrical vessel is attempted incorporating von Mises yield criterion. The plane strain condition is used for the analysis. A numerical shooting method is used to solve the governing differential equations providing the elastic-plastic stress distributions in the cylinder during loading. The present procedure is numerically experimented for a typical AH36 pressure vessel. It is found that the achievable level of the maximum stress pressure of the rotationally autofrettaged vessel is 74.46% higher than that of its non-autofrettaged counterpart for an overstrain level of 46.7%.

The Elastic, Plastic Bending of a Simply Supported Plate

1961 ◽  
Vol 28 (3) ◽  
pp. 395-401 ◽  
Author(s):  
G. Eason
Keyword(s):  
Yield Condition ◽  
Constant Load ◽  
Flow Rule ◽  
Plastic Bending ◽  
Simply Supported ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises

In this paper the problem of the elastic, plastic bending of a circular plate which is simply supported at its edge and carries a constant load over a central circular area is considered. The von Mises yield condition and the associated flow rule are assumed and the material of the plate is assumed to be nonhardening, elastic, perfectly plastic, and compressible. Stress fields are obtained in all cases and a velocity field is presented for the case of point loading. Some numerical results are given comparing the results obtained here with those obtained when the Tresca yield condition is assumed.

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. .

scholarly journals INCREMENTAL METHOD FOR UNLOADING PHENOMENON FIXATION AT SHAKEDOWN

2003 ◽  
Vol 9 (3) ◽  
pp. 178-191
Author(s):  
Dovilė Merkevičiūtė ◽  
Juozas Atkočiūnas
Keyword(s):  
Deformation Energy ◽  
Programming Approach ◽  
Problem Solution ◽  
Energy Principle ◽  
Incremental Method ◽  
Perfectly Plastic ◽  
Residual Strains ◽  
Residual Force ◽  
Elastic Perfectly Plastic ◽  
Von Mises

Incremental method for shakedown analysis of the elastic perfectly plastic structures is based on the extremum energy principles and non-linear mathematical programming approach. Residual force increment calculation problem is developed applying minimum complementary deformation energy principle. The Rozen project gradient and equilibrium finite element methods were applied for solution. The Rozen optimality criterion (Kuhn-Tucker conditions) ensures compatibility of residual strains and allows plastic strain and residual displacement increment calculation without dual problem solution. The possibility to fix the structure cross-section unloading phenomenon during shakedown process was developed. The proposed technique is illustrated by annular bending plate residual force and deflection calculation examples, when the von Mises criterion is taken into account.

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.

Descriptions of Reversed Yielding in Internally Pressurized Tubes

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Sergei Alexandrov ◽  
Woncheol Jeong ◽  
Kwansoo Chung
Keyword(s):  
Yield Criterion ◽  
Numerical Technique ◽  
Kinematic Hardening ◽  
Material Model ◽  
Flow Rule ◽  
Hardening Material ◽  
Hardening Law ◽  
Solving Equations ◽  
Associated Flow Rule ◽  
Reversed Deformation

Using Tresca's yield criterion and its associated flow rule, solutions are obtained for the stresses and strains when a thick-walled tube is subject to internal pressure and subsequent unloading. A bilinear hardening material model in which allowances are made for a Bauschinger effect is adopted. A variable elastic range and different rates under forward and reversed deformation are assumed. Prager's translation law is obtained as a particular case. The solutions are practically analytic. However, a numerical technique is necessary to solve transcendental equations. Conditions are expressed for which the release is purely elastic and elastic–plastic. The importance of verifying conditions under which the Tresca theory is valid is emphasized. Possible numerical difficulties with solving equations that express these conditions are highlighted. The effect of kinematic hardening law on the validity of the solutions found is demonstrated.

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