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.

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.

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 A Simple Model for Elastic-Plastic Contact of Granular Geomaterials

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Jian Wang ◽  
Qimin Li ◽  
Changwei Yang ◽  
Yidan Huang ◽  
Caizhi Zhou
Keyword(s):  
Material Properties ◽  
Yield Criterion ◽  
Contact Process ◽  
Confining Pressure ◽  
Elastic Plastic ◽  
Nonlinear Fitting ◽  
Von Mises ◽  
Stress And Strain Rate ◽  
The Given ◽  
Element Method

We propose a simple elastic-plastic contact model by considering the interaction of two spheres in the normal direction, for use in discrete element method (DEM) simulations of geomaterials. This model has been developed by using the finite element method (FEM) and nonlinear fitting methods, in the form of power-law relation of the dimensionless normal force and displacement. Only four parameters are needed for each loading-unloading contact process between two spheres, which are relevant to material properties evaluated by FEM simulations. Within the given range of material properties, those four parameters can be quickly accessed by interpolating the data appended or by regression functions supplied. Instead of the Von Mises (V-M) yield criterion, the Drucker–Prager (D-P) criterion is used to describe the yield behavior of contacting spheres in this model. The D-P criterion takes the effects of confining pressure, the intermediate principal stress, and strain rate into consideration; thus, this model can be used for DEM simulation of geomaterials as well as other granular materials with pressure sensitivity.

A Three-Dimensional Friction Model for Elastic-Plastic Contact With Tangential Loading: Application to Dented Surfaces

2004 ◽  
Author(s):  
Eduard Antaluca ◽  
Daniel Ne´lias ◽  
Spiridon Cretu
Keyword(s):  
Stress State ◽  
Pressure Distribution ◽  
Contact Pressure ◽  
Yield Criterion ◽  
Three Dimensional ◽  
Friction Model ◽  
Reciprocal Theorem ◽  
Elastic Plastic ◽  
Fine Mesh ◽  
Von Mises

A three-dimensional numerical model based on a semi-analytical method in the framework of small strains and small displacements with respect of Hertz’s hypotheses is presented for solving an elastic-plastic dented contact with friction. The calculation of surface deformations and pressure distribution, which is the most time consuming step during the elastic-plastic algorithm, is obtained using a method based on a variational principle with a Fast Fourier Transform (FFT) and a Conjugate Gradient Method (CGM). The method is fast enough to allow investigating the effect of a small size surface defect, here a debris denting, on the subsurface elastic-plastic stress state, requiring a fine mesh with around 106 surface grid points. Further, the FFT approach is also involved in the calculation of internal stress state. The plasticity model is based on an incremental load and Von Mises yield criterion. The effects of the contact pressure distribution and residual strain on the geometry of the contacting surfaces yield from the Betti’s reciprocal theorem with initial strain. The code is used to compute a few smooth and dented contacts, with several types of contact interfaces conditions, including frictionless and Coulomb friction. The effects of surface dents and friction on the contact pressure and subsurface stress field are presented and discussed.

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.

Element Bearing Ratio Based Shakedown Analysis for Branch Pipe

2013 ◽  
Vol 842 ◽  
pp. 586-590
Author(s):  
Yang Zhang ◽  
Wei Zhang ◽  
Yi He Qi ◽  
Jian Wang
Keyword(s):  
Optimization Problem ◽  
Yield Criterion ◽  
Water Pressure ◽  
Branch Pipe ◽  
Analysis Method ◽  
Shakedown Analysis ◽  
Elastic Plastic ◽  
Element Bearing ◽  
Stress Term ◽  
Incremental Loading

Shakedown analysis is important for branch pipe because it is often damaged under various water pressure. In this paper, an element bearing ratio (EBR) based shakedown analysis method is employed for shakedown analysis of branch pipe. The EBR is used to replace the stress term in classical optimization problem in the procedure, and series of residual EBR fields can be generated by the D-value of the elastic-plastic EBR fields and the elastic EBR fields at every incremental loading step. The shakedown load is determined by performing an incremental non-linear static analysis when the yield criterion is arrived either by the elastic-plastic EBR fields or residual EBR fields. By introducing the EBR, the proposed procedure can be easily used to shakedown analysis of branch pipe with multi-material and complicated configuration. Numerical examples validate the method and demonstrate its performance.

Fatigue Analysis of Notched Shafts under Multiaxial Synchronous Cyclic Loading

2007 ◽  
Vol 348-349 ◽  
pp. 233-236
Author(s):  
N. Pitatzis ◽  
G. Savaidis ◽  
A. Savaidis ◽  
Chuan Zeng Zhang
Keyword(s):  
Plastic Material ◽  
Yield Criterion ◽  
Notch Root ◽  
Strain Curve ◽  
Local Stress ◽  
Fatigue Loading ◽  
Material Behavior ◽  
Stress Strain ◽  
Elastic Plastic ◽  
Von Mises

Parametrical elastic-plastic finite element analyses of a circumferentially notched shaft subjected to multiaxial synchronous fatigue loading are performed considering two load combinations: (1) constant tension with cyclic torsion and (2) constant torsion with cyclic tensioncompression. The load amplitudes and the mean loads are varied to investigate their influences on the local stress-strain responses. The Multilayer Plasticity Model of Besseling in conjunction with the von Mises yield criterion is applied to describe the elastic-plastic material behavior. Coarse and fine meshes as well as three different types of multilinear approximations (twenty-, five- and threesegments) of the material stress-strain curve are used. Numerical results are presented to reveal the mutual interactions between the applied normal and torsional loads and the stress-strain response at the notch-root.

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