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.

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.

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.

Mechanical Deformation Modeling of Diamond/Gaas Structures

1996 ◽  
Vol 445 ◽  
Author(s):  
Nickolaos Strifas ◽  
Aris Christou
Keyword(s):  
Finite Strain ◽  
Volume Fraction ◽  
Mechanical Deformation ◽  
Interfacial Shear ◽  
Stress And Strain ◽  
Uniform Temperature ◽  
Element Analysis ◽  
Strain Fields ◽  
Elastic Plastic ◽  
Plastic Analysis

AbstractIn this study a finite strain elastic-plastic finite element analysis is performed on diamond/GaAs structures. A series of models based upon the principal of superposition are proposed to investigate the mechanical deformation and thermal stress behavior of the diamond/gas structure due to coefficients of thermal expansions (CTE) mismatches. The interfacial shear and peeling stresses in multilayered stacks subjected to uniform temperature variation are studied. Finite strain elastic – plastic analysis is performed on a crack which lies on the interface between the diamond and gas materials. The ductile fracture from the tip of the interface crack, the stress and strain fields and distribution of microvoid volume fraction are analyzed.

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.

Experimental Solution of Elastic-Plastic Plane-Stress Problems

1962 ◽  
Vol 29 (4) ◽  
pp. 735-743 ◽  
Author(s):  
P. S. Theocaris
Keyword(s):  
Plane Stress ◽  
Yield Condition ◽  
Strain Curve ◽  
Loading Path ◽  
Flow Rule ◽  
Stress And Strain ◽  
Stress Strain ◽  
Plane State ◽  
Elastic Plastic ◽  
Principal Strains

The paper presents an experimental method for the solution of the plane state of stress of an elastic-plastic, isotropic solid that obeys the Mises yield condition and the associated flow rule. The stress-strain law is an incremental type law, determined by the Prandtl-Reuss stress-strain relations. The method consists in determining the difference of principal strains in the plane of stress by using birefringent coatings cemented on the surface of the tested solid. A determination of relative retardation using polarized light at normal incidence, complemented by a determination in two oblique incidences at 45 deg along with the tracing of isoclinics, procures enough data for obtaining the principal strains all over the field. The calculation of the elastic and plastic components of strains is obtained in a step-by-step process of loading. It is assumed that during each step the Cartesian components of stress and strain remain constant. The stress increments and the stresses can be found thereafter by using the Prandtl-Reuss stress-strain relations and used for the evaluation of the components of strains and their increments in the next step. The method can be used with any material having any arbitrary stress-strain curve, provided that convenient formulas are established relating the stress and strain components and their increments at each point of the loading path. The method is applied to an example of contained plastic flow in a notched tensile bar of an elastic, perfectly plastic material under conditions of plane stress.

Approximate Elastic-Plastic Analysis of Intersecting Equal Diameter Cylindrical Shells

1981 ◽  
Vol 103 (1) ◽  
pp. 111-115
Author(s):  
D. P. Updike
Keyword(s):  
Plastic Material ◽  
Cylindrical Shells ◽  
Yield Condition ◽  
Pressure Vessels ◽  
Ductile Materials ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Analysis ◽  
Elastic Perfectly Plastic ◽  
Von Mises

Design of connections of pipes and pressure vessels on the basis of a calculated maximum elastic stress often proves to be too conservative in the case of ductile materials. Elastic-plastic analysis by the finite element method proves to be too costly. This paper presents an alternative method which reduces the calculations to those of a rotationally symmetric shell subjected to axisymmetric loading. Using this approach approximate elastic-plastic deformations on the meridian passing through the crotch of a tee branch connection of cylindrical shells of equal diameter and thickness are determined. The method is limited to cases of the normal intersection of very thin shells of identical diameter, thickness, and material and to internal pressure loading. Numerical results for the intersection of two shells of R/t equal to 100 are given for an elastic-perfectly plastic material satisfying the von Mises yield condition.

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.

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.

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

2005 ◽  
Vol 127 (4) ◽  
pp. 443-448 ◽  
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. 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 redistribution-node (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 Solutions for Notched Shafts in Torsion

1966 ◽  
Vol 33 (1) ◽  
pp. 79-84 ◽  
Author(s):  
E. A. Davis ◽  
I. S. Tuba
Keyword(s):  
Plastic Zone ◽  
Strain Distribution ◽  
Stress And Strain ◽  
Stress Strain ◽  
Hollow Shaft ◽  
Elastic Plastic ◽  
Plastic Analysis ◽  
Strain Relationship ◽  
Stress And Strain Distribution

An elastic-plastic analysis of the stress and strain distribution in a solid or hollow shaft containing external or internal hyperbolic notches is presented. The solution can be applied for any stress-strain relationship and for various specified amounts of plastic-zone penetration.

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