Optimal Design of Trusses According to a Plastic Shakedown Criterion

2004 ◽  
Vol 71 (2) ◽  
pp. 240-246 ◽  
Author(s):  
Luigi Palizzolo
Keyword(s):  
Optimal Design ◽  
Optimization Problems ◽  
Limit Load ◽  
Truss Structures ◽  
Search Problem ◽  
Perfectly Plastic ◽  
Problem Formulations ◽  
Elastic Perfectly Plastic ◽  
Plastic Shakedown ◽  
Statical Approach

The optimal design of elastic-perfectly plastic truss structures subjected to quasi-statically loads variable within a given load domain is studied. The actions are given as the combination of fixed load and perfect cyclic load. Suitably chosen load multipliers are given. A minimum volume formulation of the design problem with assigned limit load multiplier is developed and it is provided on the grounds of a statical approach as well as of a kinematical approach. The incremental collapse (ratchetting) of the optimal structure is prevented, as long as the loads are not greater than some prescribed values, by special constraints suitably introduced in the search problem. The Kuhn-Tucker equations related to the above-described search problems are deduced and studied. The duality between the statical and the kinematical problem formulations is proved. A special iterative technique devoted to the solution of the above referred optimization problems is utilized for computational purposes. A numerical example concludes the paper. The comparison between different designs is effected.

On the Conditions to Prevent Plastic Shakedown of Structures: Part I—Theory

1993 ◽  
Vol 60 (1) ◽  
pp. 15-19 ◽  
Author(s):  
Castrenze Polizzotto
Keyword(s):  
Mechanical Load ◽  
Plastic Material ◽  
Perfectly Plastic ◽  
Shakedown Theory ◽  
Elastic Perfectly Plastic ◽  
Plastic Shakedown ◽  
Steady Load

For a structure of elastic perfectly plastic material subjected to a given cyclic (mechanical and/or kinematical) load and to a steady (mechanical) load, the conditions are established in which plastic shakedown cannot occur whatever the steady load, and thus the structure is safe against the alternating plasticity collapse. Static and kinematic theorems, analogous to those of classical shakedown theory, are presented.

A limit load solution for a thick-walled cylinder with a fully circumferential crack under axial tension

2009 ◽  
Vol 44 (6) ◽  
pp. 407-416 ◽  
Author(s):  
P J Budden ◽  
Y Lei
Keyword(s):  
Finite Element ◽  
Plastic Material ◽  
Yield Criterion ◽  
Limit Load ◽  
Cylinder Wall ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Inside Radius ◽  
Walled Cylinder

Limit loads for a thick-walled cylinder with an internal or external fully circumferential surface crack under pure axial load are derived on the basis of the von Mises yield criterion. The solutions reproduce the existing thin-walled solution when the ratio between the cylinder wall thickness and the inside radius tends to zero. The solutions are compared with published finite element limit load results for an elastic–perfectly plastic material. The comparison shows that the theoretical solutions are conservative and very close to the finite element data.

Plastic Limit Loads for Piping Branch Junctions

2007 ◽  
Vol 345-346 ◽  
pp. 1377-1380 ◽  
Author(s):  
Yun Jae Kim ◽  
Kuk Hee Lee ◽  
Chi Yong Park
Keyword(s):  
Three Dimensional ◽  
Limit Load ◽  
Plastic Limit ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Wide Range ◽  
Pipe Radius ◽  
Plastic Limit Load ◽  
The Mean ◽  
Elastic Perfectly Plastic

The present work presents plastic limit load solutions for branch junctions under internal pressure and in-plane bending, based on detailed three-dimensional (3-D) FE limit analyses using elastic-perfectly plastic materials. The proposed solutions are valid for a wide range of branch junction geometries; ratios of the branch-to-run pipe radius and thickness from 0.0 to 1.0, and the mean radius-to-thickness ratio of the run pipe from 5.0 to 20.0.

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.

Application of a Sixth Order Generalized Stress Function for Determining Limit Loads for Plates with Triangular Penetration Patterns

2002 ◽  
Author(s):  
J. L. Gordon ◽  
D. P. Jones
Keyword(s):  
Finite Element ◽  
Fourth Order ◽  
Limit Load ◽  
Sixth Order ◽  
Numerical Representation ◽  
Order Function ◽  
Practical Applications ◽  
Perfectly Plastic ◽  
Unit Cells ◽  
Elastic Perfectly Plastic

The capability to obtain limit load solutions of plates with triangular penetration patterns using fourth order functions to represent the collapse surface has been presented in previous papers. These papers describe how equivalent solid plate elastic-perfectly plastic finite element capabilities are generated and demonstrate how such capabilities can be used to great advantage in the analysis of tubesheets in large heat exchanger applications. However, these papers have pointed out that although the fourth order functions can produce sufficient accuracy for many practical applications, there are situations where improvements in the accuracy of in-plane and transverse shear are desirable. This paper investigates the use of a sixth order function to represent the collapse surface for improved accuracy of the in-plane response. Explicit elastic-perfectly plastic finite element solutions are obtained for unit cells representing an infinite array of circular penetrations arranged in an equilateral triangular array. These cells are used to create a numerical representation of the complete collapse surfaces for a number of ligament efficiencies (h/P where h is the minimum ligament width and P is the distance between hole centers). Each collapse surface is then fit to a sixth order function that satisfies the periodicity of the hole pattern. Sixth-order collapse functions were developed for h/P values between .05 and .50. Accuracy of the sixth order and the fourth order functions are compared. It was found that the sixth order function is indeed more accurate, reducing the error from 12.2% for the fourth order function to less than 3% for the sixth order function.

scholarly journals Plastic collapse load analysis for circumferential cracked cylinder under pure torsion

2018 ◽  
Vol 192 ◽  
pp. 02023
Author(s):  
Sutham Arun ◽  
Thongchai Fongsamootr
Keyword(s):  
Limit Load ◽  
Fe Model ◽  
Plastic Collapse ◽  
Collapse Load ◽  
Pure Torsion ◽  
Perfectly Plastic ◽  
Torsion Moment ◽  
Elastic Perfectly Plastic ◽  
Distribution Of Stress ◽  
Cracked Cylinder

This paper aims to analyze the plastic collapse moment of circumferential cracked cylinder under pure torsion using the NSC approach and 3D FE model. The material considered in this work is assumed to be elastic-perfectly plastic. The influences of geometric parameters of crack and cylinder, such as Rm/t, a/t and θ/π on solution of plastic collapse load are also investigated. The analysis shows that for the case of a/t < 0.75, the values of limit torsion moment can be estimated by NSC analysis which provides conservative results. However, for the case of deeper crack, a/t ≥ 0.75, the limit load solution predicted by NSC approach may not be safe, because the distribution of stress at yielding state does not correspond to the NSC assumption. Therefore, the approximated solution of collapse torsion moment for the case of deeper crack with a/t ≥ 0.75 is proposed based on FE analysis.

Effects of Torsion on Equivalent Bending Moment for Limit Load and EPFM Circumferential Pipe Flaw Evaluations

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Phuong H. Hoang ◽  
Kunio Hasegawa ◽  
Bostjan Bezensek ◽  
Yinsheng Li
Keyword(s):  
Finite Element ◽  
Pressure Vessel ◽  
Large Strain ◽  
Bending Moment ◽  
Limit Load ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Weighted Factor ◽  
Elastic Perfectly Plastic

The circumferential flaw evaluation procedures in ASME Boiler and Pressure Vessel Code Section XI nonmandatory Appendix C are currently limited to straight pipes under pressure and bending loads without consideration of torsion loading. The Working Group on Pipe Flaw Evaluation of the ASME Boiler and Pressure Vessel Code is developing guidance for considering the effects of torsion by a mean of an equivalent bending moment, which is a square root of sum square combination of bending moment and torsion load with a weighted factor for torsion moment. A torsion weighted factor, Ce, is established in this paper using large strain finite element limit load analysis with elastic perfectly plastic materials. Planar flaws and nonplanar flaws in a 10.75 in. (273 mm) OD pipe are investigated. Additionally, a finite element J-integral calculation is performed for a planar through wall circumferential flaw with elastic plastic materials subjected to bending and torsion load combinations. The proposed Ce factor for planar flaws is intended for use with the ASME B&PV Code Section XI, Appendix C for limit load and Elastic Plastic Fracture Mechanics (EPFM) circumferential planar flaw evaluations.

Plastic Limit Loads for Through-Wall Cracked Pipes Using Finite Element Limit Analysis

2006 ◽  
Vol 321-323 ◽  
pp. 724-728
Author(s):  
Nam Su Huh ◽  
Yoon Suk Chang ◽  
Young Jin Kim
Keyword(s):  
Finite Element ◽  
Limit Analysis ◽  
Structural Integrity ◽  
Three Dimensional ◽  
Limit Load ◽  
Plastic Behavior ◽  
Plastic Limit ◽  
Integrity Assessment ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

The present paper provides plastic limit load solutions for axial and circumferential through-wall cracked pipes based on detailed three-dimensional (3-D) finite element (FE) limit analysis using elastic-perfectly plastic behavior. As a loading condition, both single and combined loadings are considered. Being based on detailed 3-D FE limit analysis, the present solutions are believed to be valuable information for structural integrity assessment of cracked pipes.

Incorporation of Strain Hardening Effect Into Simplified Limit Analysis

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
P. S. Reddy Gudimetla ◽  
R. Adibi-Asl ◽  
R. Seshadri
Keyword(s):  
Lower Bound ◽  
Strain Hardening ◽  
Limit Load ◽  
Element Analysis ◽  
Active Volume ◽  
Limit Loads ◽  
Reference Volume ◽  
Perfectly Plastic ◽  
Tangent Method ◽  
Elastic Perfectly Plastic

In this paper, a method for determining limit loads in the components or structures by incorporating strain hardening effects is presented. This has been done by including a certain amount of the strain hardening into limit load analysis, which normally idealizes the material to be elastic perfectly plastic. Typical strain hardening curves such as bilinear hardening and Ramberg–Osgood material models are investigated. This paper also focuses on the plastic reference volume correction concept to determine the active volume participating in plastic collapse. The reference volume concept in combination with mα-tangent method is used to estimate lower-bound limit loads of different components. Lower-bound limit loads obtained compare well with the nonlinear finite element analysis results for several typical configurations with/without crack.

On the Conditions to Prevent Plastic Shakedown of Structures: Part II—The Plastic Shakedown Limit Load

1993 ◽  
Vol 60 (1) ◽  
pp. 20-25 ◽  
Author(s):  
Castrenze Polizzotto
Keyword(s):  
Mechanical Load ◽  
Plastic Material ◽  
Limit State ◽  
Limit Load ◽  
Companion Paper ◽  
Material Structure ◽  
Perfectly Plastic ◽  
Shakedown Limit ◽  
Elastic Shakedown ◽  
Plastic Shakedown

Following the results of a companion paper, the concept of plastic shakedown limit load is introduced for an elastic-perfectly plastic material structure subjected to combined cyclic (mechanical and/or kinematical) loads and steady (mechanical) load. Static and kinematic approaches are available for the computation of this load, in perfect analogy with the classic (elastic) shakedown limit load. The plastic shakedown limit state of the structure being in an impending alternating plasticity collapse is studied and a number of interesting features of it are pointed out.

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