Ultimate Carrying Capacity of Elastic-Plastic Plates on a Pasternak Foundation

2014 ◽  
Vol 81 (5) ◽  
Author(s):  
L. Lanzoni ◽  
E. Radi ◽  
A. Nobili
Keyword(s):  
Yield Criterion ◽  
Plastic Region ◽  
Closed Form Solution ◽  
Form Solution ◽  
Flow Rule ◽  
Plastic Behavior ◽  
Elastic Plastic ◽  
Plastic Mechanism ◽  
Pasternak Elastic Foundation ◽  
Loaded Area

In the present work, the problem of an infinite elastic perfectly plastic plate under axisymmetrical loading conditions resting on a bilateral Pasternak elastic foundation is considered. The plate is assumed thin, thus making it possible to neglect the shear deformation according to the classical Kirchhoff theory. Yielding is governed by the Johansen's yield criterion with associative flow rule. A uniformly distributed load is applied on a circular area on the top of the plate. As the load is increased, a circular elastic-plastic region spreads out starting from the center of the loaded area, whereas the outer unbounded region behaves elastically. Depending on the size of the loaded area, a further increase of the load may originate two or three different elastic-plastic regions, corresponding to different yield loci. A closed form solution of the governing equations for each region is found for a special value of the ratio between Pasternak soil moduli. The performed analysis allows us to estimate the elastic-plastic behavior of the plate up to the onset of collapse, here defined by the formation of a plastic mechanism within the plate. The corresponding collapse load and the sizes of the elastic-plastic regions are thus found by imposing the boundary and continuity conditions between the different regions. The influence of the soil moduli, plate bending stiffness, and size of the loaded area on the ultimate bearing capacity of the plate is then investigated in detail.

Evaluation of Accuracy for 2D Elastic–Plastic Analysis by Embedded Force Doublet Model Combined with Automated Delaunay Tessellation

2015 ◽  
Vol 06 (04) ◽  
pp. 1550012 ◽  
Author(s):  
Takuichiro Ino ◽  
M. D. Abdul Hasib ◽  
Toru Takase ◽  
Akihide Saimoto
Keyword(s):  
Yield Criterion ◽  
Constitutive Relations ◽  
Plastic Region ◽  
Closed Form Solution ◽  
Form Solution ◽  
Delaunay Tessellation ◽  
Principle Of Superposition ◽  
Elastic Plastic ◽  
Permanent Strain ◽  
Plastic Analysis

An embedded force doublet (EFD) model is proposed to express the presence of permanent strain in body force method (BFM). BFM is known as a boundary type method for elastic stress analysis based on the principle of superposition. In EFD model, the permanent strain is replaced by distributed force doublets. In an actual elastic–plastic analysis, the plastic region whose shape is not clear a priori, have to be discretized into elements where the magnitude of embedded force doublets is unknown to be determined numerically. In general, the determination process of magnitude of EFD is considerably difficult due to nonlinear nature of yield criterion and plastic constitutive relations. In this study, by introducing the automated Delaunay tessellation scheme for discretizing the prospective plastic region, appreciable reduction in input data was realized. Adding to this, in order to improve the computational efficiency, influence coefficients used for determining the magnitude of EFD are stored in a database. The effectiveness of these two inventions was examined by computing the elastic–plastic problem of an infinite medium with circular hole subjected to uniform internal pressure. The numerical solution was compared with Nadai’s closed form solution and found a good agreement.

Failure in Mohr–Coulomb soil cavities

2001 ◽  
Vol 38 (6) ◽  
pp. 1314-1320 ◽  
Author(s):  
A Gesualdo ◽  
V Minutolo ◽  
L Nunziante
Keyword(s):  
Yield Criterion ◽  
Closed Form Solution ◽  
Soft Rock ◽  
Optimization Procedure ◽  
Form Solution ◽  
Flow Rule ◽  
Upper Bound Theorem ◽  
Theoretical Formulation ◽  
Bound Theorem ◽  
Associated Flow Rule

In many cavities, resulting from both natural excavation and anthropic action, the phenomenon of the collapse of blocks from the cavity roof presents a serious safety hazard. In a previous publication the authors proposed a method to calculate the shape and dimensions of the collapsing block by means of the upper bound theorem of the plasticity theory. The soft rock material was modelled by means of the Mohr–Coulomb yield criterion, and the associated flow rule was considered for strain plastic velocity. The linear yield criterion was suitably regularized by means of a circle in the tensile zone. The boundary of the collapsing block is described by a paraboloid surface. An optimization procedure formulated in standard Kuhn–Tucker form and an analytical solution were obtained. The above-mentioned algorithm has been successfully applied to common soils of southern Italy. To validate the theoretical formulation, several numerical tests are performed. These tests show an optimal agreement with the closed-form solution. Therefore the proposed modelling may be used as an efficient guideline for the cavity-strengthening design.Key words: roof stability, regularized Mohr–Coulomb material, limit analysis, failure mechanics.

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.

The Elastic-Plastic Analysis of Tubes—II: Variable Loading

1992 ◽  
Vol 114 (2) ◽  
pp. 222-228 ◽  
Author(s):  
W. Jiang
Keyword(s):  
Closed Form Solution ◽  
Yield Condition ◽  
Complex Loading ◽  
Form Solution ◽  
Stress And Strain ◽  
Variable Loading ◽  
Elastic Plastic ◽  
Incremental Method ◽  
Plastic Analysis ◽  
General Program

This paper is concerned with the elastic-plastic analysis of tubes subjected to variable loads. The yield condition for a material having residual stress and strain is first derived. Then by incremental method, the stresses and strains of the tube at any loading stage can be found. A closed-form solution is achieved as an example of tubes incurring ratchetting, and a general program is developed to make the theory applicable to complex loading situations.

scholarly journals A Novel Closed-Form Solution for Circular Openings in Generalized Hoek-Brown Media

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Qing Xiang Meng ◽  
Wei Wang
Keyword(s):  
Rock Mass ◽  
Closed Form ◽  
Hydrostatic Stress ◽  
Yield Criterion ◽  
Closed Form Solution ◽  
Form Solution ◽  
Preliminary Design ◽  
Exact Integration ◽  
Sensitive Factor ◽  
Brittle Rock Mass

A novel closed-form solution is presented in this paper for the estimation of displacements around circular openings in a brittle rock mass subject to a hydrostatic stress field. The rock mass is assumed to be elastic-brittle-plastic media governed by the generalized Hoek-Brown yield criterion. The present closed-form solution was validated by employing the existing analytical solutions. Results of several example cases are analyzed to show that, with the simplified assumption, a novel closed-form solution is derived and found to be in an excellent agreement with those obtained by using the exact integration method with mathematical software. Parametric sensitivity analysis is carried out and the parameterartends to be the sensitive factor. As a closed-form solution that does not require transformation technique and the use of any numerical method, this work can provide a better choice in the preliminary design for circular opening.

Negative skin friction and the neutral plane

1994 ◽  
Vol 31 (4) ◽  
pp. 591-597 ◽  
Author(s):  
Elmer L. Matyas ◽  
J. Carlos Santamarina
Keyword(s):  
Closed Form ◽  
Key Words ◽  
Skin Friction ◽  
Closed Form Solution ◽  
Form Solution ◽  
Neutral Plane ◽  
Rigid Plastic ◽  
Negative Skin Friction ◽  
Elastic Plastic ◽  
Drag Forces

Current views indicate that negative skin friction on piles can be mobilized at small relative deformations and should be considered in all designs, primarily for serviceability conditions. An elastic-plastic closed-form solution is presented that permits an estimate of down-drag forces and the location of the neutral plane. It is shown that the conventional rigid-plastic solution may overestimate down-drag forces by as much as 50% and may also overestimate the depth of the neutral plane. Key words : piles, negative skin friction, neutral plane, capacity.

Elastic-plastic stress distributions and limit angular velocities in rotating hyperbolic annular discs

2007 ◽  
Vol 221 (2) ◽  
pp. 137-142 ◽  
Author(s):  
N N Alexandrova ◽  
P M M Vila Real
Keyword(s):  
Rotational Speed ◽  
Yield Criterion ◽  
Circumferential Stress ◽  
Radial Pressure ◽  
Thickness Variation ◽  
Flow Rule ◽  
Stress Distributions ◽  
Elastic Plastic ◽  
Angular Velocities ◽  
Hyperbolic Form

Plastic analytical stress analysis of a rotating annular disc with its contours being free from the radial pressure and with specifically variable thickness is presented in terms of the Mises-yield criterion and its associated flow rule. The hyperbolic form of thickness variation is considered and optimized towards the maximum rotational speed and favourable stress combinations. Radial and circumferential stress distributions in the disc both in the intermediate elastic-plastic and in the limit plastic states are obtained. As a particular case, limit elastic angular velocity parameter is derived. The influences of rotational speed as well as the disc's thickness profile on the plastic solution and size of elastic-plastic zone are demonstrated and discussed. The results obtained may be used for the correct implementation of numerical codes and preliminary engineering design.

Axially Symmetric Radial Flow of Rigid/Linear-Hardening Materials

1979 ◽  
Vol 46 (2) ◽  
pp. 322-328 ◽  
Author(s):  
D. Durban
Keyword(s):  
Radial Flow ◽  
Closed Form Solution ◽  
Wire Drawing ◽  
Form Solution ◽  
Flow Rule ◽  
Axially Symmetric ◽  
Linear Hardening ◽  
Stress Components ◽  
Von Mises ◽  
Good Agreement

A closed-form solution has been discovered for axially symmetric radial flow of rigid/linear-hardening materials. It is assumed that the materials obey the von Mises flow rule and that the flow field is in steady state. Explicit expressions for the stress components and the radial velocity are given. The applicability of the solution to wire drawing or extrusion is discussed. Some approximate formulas are derived and shown to be in good agreement, within their range of validity, with experimental results for drawing.

An Analytical Solution for Three-Dimensional Elliptical Elastic-Plastic Rolling Contact

2014 ◽  
Vol 658 ◽  
pp. 207-212
Author(s):  
Gabriel Popescu
Keyword(s):  
Residual Stresses ◽  
Yield Criterion ◽  
Tangential Force ◽  
Rolling Direction ◽  
Three Dimensional ◽  
Rolling Contact ◽  
Material Behavior ◽  
Hertzian Contact ◽  
Plastic Behavior ◽  
Elastic Plastic

An analytical three-dimensional elastic-plastic over-rolling solution is used to evaluate the plastic strains and residual stresses. Central to this plastic contact formulation is the incremental approach to deal with non-linear material behavior. The Prandtl-Reuss constitutive equations in conjunction with Huber-Mises-Hencky yield criterion and Ramberg-Osgood strain-hardening relationships are applied to describe the plastic behavior of common hardened bearing steel. The model was extended to include the tangential force in the rolling direction, assumed to be proportional to the hertzian contact pressure. Comparisons of three-dimensional pure rolling and rolling/sliding contact results were provided to elucidate the differences in residual stresses and residual profiles in case of kinematic and work-hardening materials.

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