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.

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.

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.

Plane-Strain Bending With Isotropic Strain Hardening at Large Strains

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
Sergei Alexandrov ◽  
Yeong-Maw Hwang
Keyword(s):  
Strain Hardening ◽  
Plane Strain ◽  
Closed Form Solution ◽  
Bending Moment ◽  
Form Solution ◽  
Isotropic Hardening ◽  
Large Strains ◽  
Rigid Plastic ◽  
Elastic Plastic ◽  
Hardening Law

Finite deformation elastic-plastic analysis of plane-strain pure bending of a strain hardening sheet is presented. The general closed-form solution is proposed for an arbitrary isotropic hardening law assuming that the material is incompressible. Explicit relations are given for most popular conventional laws. The stage of unloading is included in the analysis to investigate the distribution of residual stresses and springback. The paper emphasizes the method of solution and the general qualitative features of elastic-plastic solutions rather than the study of the bending process for a specific material. In particular, it is shown that rigid-plastic solutions can be used to predict the bending moment at sufficiently large strains.

Effective Yield Criterion Accounting for Microvoid Coalescence

2013 ◽  
Vol 81 (3) ◽  
Author(s):  
A. Amine Benzerga ◽  
Jean-Baptiste Leblond
Keyword(s):  
Boundary Conditions ◽  
Limit Analysis ◽  
Yield Criterion ◽  
Closed Form Solution ◽  
Yield Function ◽  
Form Solution ◽  
Homogenization Theory ◽  
Porous Solids ◽  
Microvoid Coalescence ◽  
Effective Yield

An effective yield function is derived for a porous ductile solid near a state of failure by microvoid coalescence. Homogenization theory combined with limit analysis are used to that end. A cylindrical cell is taken to contain a coaxial cylindrical void of finite height. Plastic flow in the intervoid matrix is described by J2 theory while regions above and below the void remain rigid. Velocity boundary conditions are employed which are compatible with an overall uniaxial straining for the cell, a postlocalization kinematics that is ubiquitous during the coalescence of neighboring microvoids in rate-independent solids. Such boundary conditions are not of the uniform strain rate kind, as is the case for Gursonlike models. A similar limit analysis problem for a square-prismatic cell containing a square-prismatic void was posed long ago (Thomason, P. F., 1985, “Three-Dimensional Models for the Plastic Limit–Loads at Incipient Failure of the Intervoid Matrix in Ductile Porous Solids,” Acta Metallurgica, 33, pp. 1079–1085). However, to date a closed-form solution to this problem has been lacking. Instead, an empirical expression of the yield function proposed therein has been widely used in the literature. The fully analytical expression derived here is intended to be used concurrently with a Gursonlike yield function in numerical simulations of ductile fracture.

Limit Load Analysis of Pipe Bend Using the R-Node Method

2005 ◽  
Author(s):  
Ihab F. Z. Fanous ◽  
R. Adibi-Asl ◽  
R. Seshadri
Keyword(s):  
Closed Form Solution ◽  
Limit Load ◽  
Form Solution ◽  
Collapse Load ◽  
Pipe Bend ◽  
Bending Force ◽  
Multiple Loads ◽  
Plastic Analysis ◽  
Out Of Plane ◽  
Load Analysis

The R-Node method has been developed earlier as a technique to find the limit load using the Elastic Modulus Adjustment Procedures (EMAP). It utilizes the systematic redistribution of the stress to find the load controlled locations in a component to estimate the collapse load. In this paper, the method is shown to be applicable for multiple loads. A simple cantilever beam is analyzed using the R-Node method subjected to both bending force and moment. The results compare well with the closed form solution of the problem. The method is then used to estimate the limit load for an elbow subjected to in-plane and out-of-plane moment. The results compare well with the elastic-plastic analysis.

Elastic-Plastic Stress Field in a Coated Continuous Fibrous Composite Subjected to Thermomechanical Loading

1999 ◽  
Vol 66 (3) ◽  
pp. 750-757 ◽  
Author(s):  
L. You ◽  
S. Long ◽  
L. Rohr
Keyword(s):  
Stress Field ◽  
Governing Equation ◽  
Yield Criterion ◽  
Fibrous Composite ◽  
Closed Form Solution ◽  
Metallic Matrix ◽  
Form Solution ◽  
Concentric Cylinders ◽  
The Matrix ◽  
Strain Relationship

A micromechanics investigation was performed in the present work to analyze the stress field in a coated continuous fibrous composite subjected to thermal and mechanical loading based on a four-concentric-cylinders model. A temperature-independent stress-plastic strain relationship for the metallic matrix and coating layer with linear strain-hardening behaviour were introduced. Tresca’s yield criterion and the associated flow law were employed to derive the governing equation of the coating and matrix. The closed-form solution of the governing equation was obtained. Some numerical examples were given. The numerical results indicate that the plasticity of the coating greatly decreases the circumferential and axial stresses in the coating itself, but has very limited influence on the stresses in other constituents of the composite. The plasticity of the matrix imposes no significant influence on all the stresses in the composite.

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.

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