scholarly journals Finite Difference Solution of Elastic-Plastic Thin Rotating Annular Disk with Exponentially Variable Thickness and Exponentially Variable Density

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Sanjeev Sharma ◽  
Yadav Sanehlata
Keyword(s):  
Finite Difference ◽  
Variable Thickness ◽  
Yield Criterion ◽  
Variable Density ◽  
Hardening Material ◽  
Annular Disk ◽  
Elastic Plastic ◽  
Flat Disk ◽  
Finite Difference Solution ◽  
Von Mises

Elastic-plastic stresses, strains, and displacements have been obtained for a thin rotating annular disk with exponentially variable thickness and exponentially variable density with nonlinear strain hardening material by finite difference method using Von-Mises' yield criterion. Results have been computed numerically and depicted graphically. From the numerical results, it can be concluded that disk whose thickness decreases radially and density increases radially is on the safer side of design as compared to the disk with exponentially varying thickness and exponentially varying density as well as to flat disk.

On the geometrically similar expansion of a hole in a thin infinite plate

1972 ◽  
Vol 326 (1566) ◽  
pp. 361-373 ◽  
Keyword(s):  
Large Deformation ◽  
Yield Criterion ◽  
Complete Solution ◽  
Infinite Plate ◽  
Iterative Solution ◽  
Matrix Formulation ◽  
Hardening Material ◽  
Elastic Plastic ◽  
Zero Radius ◽  
Von Mises

The problem is considered of expanding a central cylindrical hole from zero radius in a thin infinite plate of conical profile such that, initially, thickness is proportional to radius, chosen so that geometrical similarity is maintained. A previously incorrect theory is modified by using a matrix formulation of the equations suitable for iterative solution on the digital computer, and the predicted profile of the plate is compared with that found from an experiment performed on a finite mild steel plate of conical profile. The Prandtl-Reuss relations for the large deformation elastic-plastic flow of a work-hardening material obeying the Maxwell (von Mises) yield criterion are used. Apart from the intrinsic interest of obtaining a complete solution to a problem of this type, the solution will be used to provide a valid model against which to test solutions obtained by finite element methods for large deformation elastic-plastic analysis.

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.

Elastic-Plastic Stress Distribution in a Plastically Anisotropic Rotating Disk

2004 ◽  
Vol 71 (3) ◽  
pp. 427-429 ◽  
Author(s):  
N. Alexandrova ◽  
S. Alexandrov
Keyword(s):  
Stress Distribution ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Rotating Disk ◽  
Flow Rule ◽  
Plane State ◽  
Annular Disk ◽  
Elastic Plastic ◽  
State Of Stress ◽  
Associated Flow Rule

The plane state of stress in an elastic-plastic rotating anisotropic annular disk is studied. To incorporate the effect of anisotropy on the plastic flow, Hill’s quadratic orthotropic yield criterion and its associated flow rule are adopted. A semi-analytical solution is obtained. The solution is illustrated by numerical calculations showing various aspects of the influence of plastic anisotropy on the stress distribution in the rotating disk.

Optimal Design of a Nonhomogeneous Annular Disk Under Pressure Loadings

1994 ◽  
Vol 116 (4) ◽  
pp. 989-996
Author(s):  
Chung-Yun Gau ◽  
Souran Manoochehri
Keyword(s):  
Optimal Design ◽  
Young’S Modulus ◽  
Variable Thickness ◽  
Volume Fraction ◽  
Young's Modulus ◽  
Yield Criterion ◽  
Constant Thickness ◽  
Annular Disk ◽  
Disk Thickness ◽  
Thickness Variations

A method for the design of nonhomogeneous, variable-thickness, annular disks under internal and external pressures satisfying Tresca yield criterion is presented in this paper. The effects of varying the disk thickness and stiffness properties to achieve a fully stressed design are investigated. Analytical solutions for distributions of Young’s modulus and disk thickness variations have been developed for the case of fully stressed designs. Examples are given for three different cases, namely, constant thickness with variable Young’s modulus, variable thickness with constant Young’s modulus, and variable thickness with variable Young’s modulus. In the last case, due to the existence of many alternative solutions, optimal design techniques have been utilized. Application of the developed methodology for optimal designs of short fiber composites with random fiber orientations is discussed. The optimization results of fiber volume fraction distributions and thickness variations for a disk made of nylon 66 matrix with E glass fiber are given under specified pressure loadings.

An Analytical Elastic-Plastic Contact Model

2011 ◽  
Author(s):  
M. R. Brake
Keyword(s):  
Yield Criterion ◽  
Plastic Behavior ◽  
Elastic Plastic ◽  
Elastic Regime ◽  
Plastic Regime ◽  
Elastic Process ◽  
New Formulation ◽  
Von Mises ◽  
The Impact ◽  
Force Displacement

This paper presents a new formulation for elastic-plastic contact in the normal direction between two round surfaces that is solely based on material properties and contact geometries. The problem is formulated as three separate domains: the elastic regime, mixed elastic-plastic behavior, and unconstrained (fully plastic) flow. Solutions for the force-displacement relationship in the elastic regime follow from Hertz’s classical solution. In the fully plastic regime, two assumptions are made: that there is a uniform pressure distribution and that there is conservation of volume. The force-displacement relationship in the intermediate, mixed elastic-plastic regime is approximated by enforcing continuity between the elastic and fully plastic regimes. Transitions between the three regimes are determined based on empirical quantities: the von Mises yield criterion is used to determine the initiation of mixed elastic-plastic deformation, and Brinell’s hardness for the onset of unconstrained flow. Unloading from each of these three regimes is modeled as an elastic process with different radii of curvature based on the regime in which the maximum force occurred. Simulation results explore the relationship between the impact velocity and coefficient of restitution. Further comparisons are made between the model, experimental results found in the literature, and other existing elastic-plastic models.

Contact Analysis of Multilayered Elastic/Plastic Solids With Rough Surfaces for Decreasing Friction and Wear

2005 ◽  
Author(s):  
Shaobiao Cai ◽  
Bharat Bhushan
Keyword(s):  
Surface Roughness ◽  
Contact Area ◽  
Yield Criterion ◽  
Rough Surfaces ◽  
Three Dimensional ◽  
Surface Displacement ◽  
Maximum Displacement ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Von Mises

A numerical three-dimensional contact model is presented to investigate the contact behavior of multilayered elastic-perfectly plastic solids with rough surfaces. The surface displacement and contact pressure distributions are obtained based on the variational principle with fast Fourier transform (FFT)-based scheme. Von Mises yield criterion is used to determine the onset of yield. The effective hardness is modeled and plays role when the local displacement meet the maximum displacement criterion. Simulations are performed to obtain the contact pressures, fractional total contact area, fractional plastic contact area, and surface/subsurface stresses. These contact statistics are analyzed to study the effects of the layer-to-substrate ratios of stiffness and hardness, surface roughness, and layers thickness of rough, two-layered elastic/plastic solids. The results yield insight into the effects of stiffness and hardness of layers and substrates, surface roughness, and applied load on the contact performance. The layer parameters leading to low friction, stiction, and wear are investigated and identified.

Analytical Solution for Strain Gradient Plasticity of Rotating Functionally Graded Thick Cylinders

2020 ◽  
Vol 12 (07) ◽  
pp. 2050082
Author(s):  
Saeid Varmazyari ◽  
Hassan Shokrollahi
Keyword(s):  
Analytical Solution ◽  
Strain Gradient ◽  
Yield Criterion ◽  
External Pressure ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Gradient Plasticity ◽  
Elastic Plastic ◽  
Von Mises

The elastic-plastic deformation of rotating functionally graded (FG) cylinders is investigated based on strain gradient theory. The governing equations are obtained based on the modified von Mises yield criterion, linear work hardening and plane strain assumptions. An analytical solution for the obtained equations is presented by which the deformation, strain and stress components for any point of the cylinder can be obtained. After verification of the formulation by comparing the obtained results with the reported results in the literature, some studies are presented to investigate the effects of cylinder size on the stress distribution and elastic-plastic interface radius of the rotating FG cylinder under internal and external pressure. The effects of the strain gradient coefficient, angular velocity, and the heterogeneity constant of the material are investigated. The results show that increasing the heterogeneity constant of the material and decreasing the cylinder radius lead to increasing the strength of material and decreasing the elastic-plastic interface radius. Moreover, classical theory is compared with this study and the range of the sizes in which both the theories leading to the same results, are defined.

scholarly journals INTEGRATED LOAD OPTIMIZATION OF ELASTIC‐PLASTIC AXISYMMETRIC PLATES AT SHAKEDOWN

2010 ◽  
Vol 16 (2) ◽  
pp. 203-208 ◽  
Author(s):  
Artūras Venskus ◽  
Stanislovas Kalanta ◽  
Juozas Atkočiūnas ◽  
Tomas Ulitinas
Keyword(s):  
Gradient Method ◽  
Strain State ◽  
Optimization Problem ◽  
Yield Criterion ◽  
Dissipative Systems ◽  
Variable Load ◽  
Loading History ◽  
Load Optimization ◽  
Elastic Plastic ◽  
Von Mises

An elastic‐plastic axisymmetric steel bending plate subjected to a repeated variable load (RVL) is considered. The solution to the load optimization problem at shakedown is complicated because the stress‐strain state of the dissipative systems (e.g. the plate plastic deforming) depends on their loading history. A new algorithm for the load optimization problem combining von Mises and Tresca yield criterion based on the Rosen project gradient method is proposed. The optimization results are obtained by integrating the existing software and that created by the authors. Santrauka Nagrinejama tampriai plastine simetrine lenkiama plokšte, veikiama kintamosios kartotines apkrovos. Prisitaikančiu konstrukciju itempiu ir deformaciju būvis priklauso nuo apkrovimo istorijos. Plokštes apkrovos optimizavimo uždavinio matematiniame modelyje naudojamos stiprumo ir standumo salygos. I apkrovimo istorija atsižvelgiama, pasitelkiant ekst‐remines iražu ir ilinkius ribojančias ju normines reikšmes. Remiantis Rozeno projektuojamuju gradientu metodu sukurtas naujas apkrovos optimizavimo algoritmas, derinantis Mizeso ir Treska takumo salygas. Skaitinio pavyzdžio rezultatai gauti originalia autoriu kompiuterine programa.

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