The Incremental Strain Growth of an Elastic-Plastic Body Loaded in Excess of the Shakedown Limit

1984 ◽  
Vol 51 (3) ◽  
pp. 465-469 ◽  
Author(s):  
A. R. S. Ponter ◽  
A. C. F. Cocks
Keyword(s):  
Thermal Loading ◽  
Thermoelastic Stress ◽  
Point Of View ◽  
The Body ◽  
Elastic Displacement ◽  
Perfectly Plastic ◽  
Incremental Growth ◽  
Elastic Perfectly Plastic ◽  
Shakedown Limit ◽  
Incremental Strain

This paper considers the problem of a body composed of an elastic/perfectly plastic solid that is subjected to constant applied load P and a time-varying cyclic temperature distribution, characterized by a maximum thermoelastic stress σt. For sufficiently large P and σt, in excess of the shakedown limit, the body will begin to suffer incremental growth. A linearized theory is used to obtain a relationship between the increase in displacement Δu per cycle and the increase in ΔP and Δσt, above the shakedown limit. From the result, a simple lower bound is derived for Bree-type problems, which for kinematically determinate structures shows that for moderate thermal loading the displacement increment per cycle is four times the elastic displacement of the body if it were subjected only to the increase ΔP. From a practical point of view the analysis indicates that ratchet rates are always high, in the sense that only a small increase of load above shakedown will produce substantial ratcheting within relatively few cycles.

Shakedown Limits of a 90-Degree Pipe Bend Using Small and Large Displacement Formulations

2006 ◽  
Author(s):  
Hany F. Abdalla ◽  
Mohammad M. Megahed ◽  
Maher Y. A. Younan
Keyword(s):  
Plastic Material ◽  
Limit Load ◽  
Material Model ◽  
Large Displacement ◽  
Small Displacement ◽  
Pipe Bend ◽  
Perfectly Plastic ◽  
Loading Patterns ◽  
Elastic Perfectly Plastic ◽  
Shakedown Limit

In this paper the shakedown limit load is determined for a long radius 90-degree pipe bend using two different techniques. The first technique is a simplified technique which utilizes small displacement formulation and elastic-perfectly-plastic material model. The second technique is an iterative based technique which uses the same elastic-perfectly-plastic material model, but incorporates large displacement effects accounting for geometric non-linearity. Both techniques use the finite element method for analysis. The pipe bend is subjected to constant internal pressure magnitudes and cyclic bending moments. The cyclic bending loading includes three different loading patterns namely; in-plane closing, in-plane opening, and out-of-plane bending. The simplified technique determines the shakedown limit load (moment) without the need to perform full cyclic loading simulations or conventional iterative elastic techniques. Instead, the shakedown limit moment is determined by performing two analyses namely; an elastic analysis and an elastic-plastic analysis. By extracting the results of the two analyses, the shakedown limit moment is determined through the calculation of the residual stresses developed in the pipe bend. The iterative large displacement technique determines the shakedown limit moment in an iterative manner by performing a series of full elastic-plastic cyclic loading simulations. The shakedown limit moment output by the simplified technique (small displacement) is used by the iterative large displacement technique as an initial iterative value. The iterations proceed until an applied moment guarantees a structure developed residual stress, at load removal, equals or slightly less than the material yield strength. The shakedown limit moments output by both techniques are used to generate shakedown diagrams of the pipe bend for a spectrum of constant internal pressure magnitudes for the three loading patterns stated earlier. The maximum moment carrying capacity (limit moment) the pipe bend can withstand and the elastic limit are also determined and imposed on the shakedown diagram of the pipe bend. Comparison between the shakedown diagrams generated by the two techniques, for the three loading patterns, is presented.

Nonuniqueness in Contained Plastic Deformation

1980 ◽  
Vol 47 (2) ◽  
pp. 273-277 ◽  
Author(s):  
P. G. Hodge ◽  
D. L. White
Keyword(s):  
Plastic Deformation ◽  
Boundary Value Problem ◽  
Yield Point ◽  
Displacement Field ◽  
Point Load ◽  
Point Of View ◽  
Computational Point ◽  
Plastic Structure ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

It is well known that in a well-defined load-controlled boundary-value problem for an elastic/perfectly-plastic structure the displacements are unique if the structure is everywhere elastic, and they are not unique at the yield-point load when the structure becomes a mechanism. The present paper is concerned with the range of contained plastic deformation between these two extremes. Several examples are given in which more than one displacement field exists for loads less than the yield-point load. The significance of this phenomenon is commented on from a physical, mathematical, and computational point of view.

A dynamic evolution model for perfectly plastic plates

2016 ◽  
Vol 26 (10) ◽  
pp. 1825-1864 ◽  
Author(s):  
Giovanni Battista Maggiani ◽  
Maria Giovanna Mora
Keyword(s):  
Three Dimensional ◽  
Vertical Displacement ◽  
The Body ◽  
Reduced Model ◽  
Dynamic Evolution ◽  
Flow Rule ◽  
Perfectly Plastic ◽  
Body Load ◽  
Elastic Perfectly Plastic ◽  
Plastic Flow Rule

We consider the dynamic evolution of a linearly elastic-perfectly plastic thin plate subject to a purely vertical body load. As the thickness of the plate goes to zero, we prove that the three-dimensional evolutions converge to a solution of a certain reduced model. In the limiting model admissible displacements are of Kirchhoff–Love type. Moreover, the motion of the body is governed by an equilibrium equation for the stretching stress, a hyperbolic equation involving the vertical displacement and the bending stress, and a rate-independent plastic flow rule. Some further properties of the reduced model are also discussed.

scholarly journals Application of Finite Element Analysis in Modeling of Bionic Harrowing Discs

Biomimetics ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 61
Author(s):  
Benard Chirende ◽  
Jian Qiao Li ◽  
Wonder Vheremu
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Three Dimensional ◽  
Dung Beetle ◽  
The Body ◽  
Soil Deformation ◽  
Element Analysis ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Three Dimensional Finite Element

Ansys software was used to carry out three-dimensional finite element analysis (FEA) for biomimetic design of harrowing discs based on the body surface morphology of soil burrowing animals like dung beetle (Dicranocara deschodt) which have non-smooth units such as convex domes and concave dips. The main objective was to find out the effects of different biomimetic surface designs on reducing soil resistance hence the horizontal force acting on the harrowing disc during soil deformation was determined. In this FEA, soil deformation was based on the Drucker–Prager elastic–perfectly plastic model which was applied only at the lowest disc harrowing speed of 4.4 km/h which is within the limits of model. The material non-linearity of soil was addressed using an incremental technique and inside each step, the Newton–Raphson iteration method was utilized. The model results were analyzed and then summation of horizontal forces acting on the soil-disc interface was also done. An experiment was then conducted in an indoor soil bin to validate the FEA results. The FEA results are generally in agreement with those of the indoor experiment with a difference of less than or equal to the acceptable 10% with an average difference of 4%. Overall, convex bionic units gave the highest resistance reduction of 19.5% from 1526.87 N to 1228.38 N compared to concave bionic units.

scholarly journals Shakedown Analysis of “Soil-Pile Foundation-Frame” System under Seismic Action

2018 ◽  
Vol 28 (1) ◽  
pp. 100-114
Author(s):  
Piotr Alawdin ◽  
George Bulanov
Keyword(s):  
Fem Analysis ◽  
Deformation Model ◽  
Seismic Action ◽  
Elastic Halfspace ◽  
Brittle Behavior ◽  
Perfectly Plastic ◽  
Frame System ◽  
Elastic Perfectly Plastic ◽  
Pile Deformation ◽  
Shakedown Limit

Abstract In this article, the seismic shakedown FEM analysis of reinforced concrete and composite spatial frame structures on the deformable foundation, taking into account the elasticplastic and brittle behavior of structures elements, is presented. A foundation consists of group of the piles in the soil. The behavior of soil is described here using+ the elastic halfspace theory. The pile deformation model is assumed to be elastic-perfectly plastic, where the bearing capacity is determined by the results of testing the soils or the piles themselves. An example of seismic shakedown limit analysis is presented.

Elasto-plastic analysis and finite element simulation of thick-walled functionally graded cylinder subjected to combined pressure and thermal loading

2017 ◽  
Vol 24 (4) ◽  
pp. 609-620 ◽  
Author(s):  
Shahryar Alikarami ◽  
Ali Parvizi
Keyword(s):  
Finite Element ◽  
Finite Element Simulation ◽  
Thermal Loading ◽  
Functionally Graded ◽  
Combined Loading ◽  
Plastic Behavior ◽  
Graded Materials ◽  
Perfectly Plastic ◽  
Element Simulation ◽  
Elastic Perfectly Plastic

AbstractAn exact analytical elasto-plastic solution for thick-walled cylinder made of functionally graded materials (FGMs) subjected to combined pressure and thermal loading is presented in this paper. It is assumed that the cylinder is bonded at both ends, the material is radially graded and complies with the elastic perfectly plastic behavior. The relations in determining the plastic zone radius as well as the radial, circumferential, longitudinal and effective stresses in both elastic and plastic zones are obtained for any combined loading condition. Moreover, using ABAQUS/Explicit software, the functionally graded (FG) cylinder is simulated in every respect. Comparison of the present theoretical results with those from a finite element simulation illustrates the accuracy of the present analysis.

Shakedown Limits of a 90-Degree Pipe Bend Using Small and Large Displacement Formulations

2006 ◽  
Vol 129 (2) ◽  
pp. 287-295 ◽  
Author(s):  
Hany F. Abdalla ◽  
Mohammad M. Megahed ◽  
Maher Y. A. Younan
Keyword(s):  
Plastic Material ◽  
Limit Load ◽  
Material Model ◽  
Large Displacement ◽  
Small Displacement ◽  
Pipe Bend ◽  
Perfectly Plastic ◽  
Loading Patterns ◽  
Elastic Perfectly Plastic ◽  
Shakedown Limit

In this paper the shakedown limit load is determined for a long radius 90-deg pipe bend using two different techniques. The first technique is a simplified technique which utilizes small displacement formulation and elastic–perfectly plastic material model. The second technique is an iterative based technique which uses the same elastic–perfectly plastic material model, but incorporates large displacement effects accounting for geometric nonlinearity. Both techniques use the finite element method for analysis. The pipe bend is subjected to constant internal pressure magnitudes and cyclic bending moments. The cyclic bending loading includes three different loading patterns, namely, in-plane closing, in-plane opening, and out-of-plane bending. The simplified technique determines the shakedown limit load (moment) without the need to perform full cyclic loading simulations or conventional iterative elastic techniques. Instead, the shakedown limit moment is determined by performing two analyses, namely, an elastic analysis and an elastic–plastic analysis. By extracting the results of the two analyses, the shakedown limit moment is determined through the calculation of the residual stresses developed in the pipe bend. The iterative large displacement technique determines the shakedown limit moment in an iterative manner by performing a series of full elastic–plastic cyclic loading simulations. The shakedown limit moment output by the simplified technique (small displacement) is used by the iterative large displacement technique as an initial iterative value. The iterations proceed until an applied moment guarantees a structure developed residual stress, at load removal, equal to or slightly less than the material yield strength. The shakedown limit moments output by both techniques are used to generate shakedown diagrams of the pipe bend for a spectrum of constant internal pressure magnitudes for the three loading patterns stated earlier. The maximum moment carrying capacity (limit moment) the pipe bend can withstand and the elastic limit are also determined and imposed on the shakedown diagram of the pipe bend. Comparison between the shakedown diagrams generated by the two techniques, for the three loading patterns, is presented.

Shakedown at Thermal Discontinuities Involving Thermal Membrane and Thermal Bending Stress

2012 ◽  
Author(s):  
Ali Asadkarami ◽  
Wolf Reinhardt
Keyword(s):  
Thermal Stress ◽  
Stress Gradient ◽  
Axial Direction ◽  
Bending Stress ◽  
Primary Stress ◽  
Perfectly Plastic ◽  
Thermal Bending ◽  
Asme Code ◽  
Elastic Perfectly Plastic ◽  
Shakedown Limit

The current ASME Code Section III NB-3200 rules on thermal stress ratchet require that the thermal stress must be less than the ratchet condition that Bree established for a cyclic pure thermal bending stress as a function of the level of primary membrane stress. It has been shown that this method can predict shakedown when elastic-perfectly plastic analysis shows ratcheting. However, there is also conservatism in the Code rules because the highest stresses that dominate the evaluation of a component are typically found at discontinuities, where there is a stress gradient at least in the axial direction. The stress limits, on the other hand, are based on stress distributions that are constant in the axial (and circumferential) direction. This paper investigates the effect of thermal discontinuities on the shakedown limit in the presence of a thermal through-wall gradient and a pressure-induced primary stress. The investigation is based on the simple model of a cylinder with an isolated thermal discontinuity. The effect of proximity to another discontinuity is explored, to obtain the minimum distance between two discontinuities that would allow them to be considered separately. Simple rules are developed and proposed to take potentially advantage of higher stress limits at an isolated discontinuity.

Integrating Focusing and Differentiation: A Therapeutic Path for Couples in Intimate Relationships

2018 ◽  
Vol 3 ◽  
Author(s):  
Evi Zohar
Keyword(s):  
Couples Therapy ◽  
Therapeutic Potential ◽  
Well Being ◽  
Point Of View ◽  
The Body ◽  
Self Awareness ◽  
Emotional Healing ◽  
Felt Sense ◽  
Inner World

Continuing the workshop I've given in the WPC Paris (2017), this article elaborates my discussion of the way I interlace Focusing with Differentiation Based Couples Therapy (Megged, 2017) under the systemic view, in order to facilitate processes of change and healing in working with intimate couples. This article presents the theory and rationale of integrating Differentiation (Bowen, 1978; Schnarch, 2009; Megged, 2017) and Focusing (Gendlin, 1981) approaches, and its therapeutic potential in couple's therapy. It is written from the point of view of a practicing professional in order to illustrate the experiential nature and dynamics of the suggested therapeutic path. Differentiation is a key to mutuality. It offers a solution to the central struggle of any long term intimate relationship: balancing two basic life forces - the drive for individuality and the drive for togetherness (Schnarch, 2009). Focusing is a body-oriented process of self-awareness and emotional healing, in which one learns to pay attention to the body and the ‘Felt Sense’, in order to unfold the implicit, keep it in motion at the precise pace it needs for carrying the next step forward (Gendlin, 1996). Combining Focusing and Differentiation perspectives can cultivate the kind of relationship where a conflict can be constructively and successfully held in the inner world of each partner, while taking into consideration the others' well-being. This creates the possibility for two people to build a mutual emotional field, open to changes, permeable and resilient.

Presentation

2014 ◽  
Vol 2 (3) ◽  
Author(s):  
Redacción CEIICH
Keyword(s):  
Cultural History ◽  
Social Reality ◽  
Point Of View ◽  
The Body ◽  
Literary Studies ◽  
The Third ◽  
The Social ◽  
Feminist Theories ◽  
History Of

<p class="p1">The third number of <span class="s1"><strong>INTER</strong></span><span class="s2"><strong>disciplina </strong></span>underscores this generic reference of <em>Bodies </em>as an approach to a key issue in the understanding of social reality from a humanistic perspective, and to understand, from the social point of view, the contributions of the research in philosophy of the body, cultural history of the anatomy, as well as the approximations queer, feminist theories and the psychoanalytical, and literary studies.</p>

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