A Simple Upper-Bound Method for Calculating Approximate Shakedown Loads

1998 ◽  
Vol 120 (2) ◽  
pp. 195-199 ◽  
Author(s):  
R. Hamilton ◽  
J. T. Boyle ◽  
J. Shi ◽  
D. Mackenzie
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Spherical Shell ◽  
Upper Bound ◽  
Pressure Vessel ◽  
Simple Approach ◽  
Finite Element Analyses ◽  
Axisymmetric Nozzle ◽  
Upper Bound Method

A simple approach for calculating upper-bound shakedown loads is described. The method is based on a series of iterative elastic finite element analyses (the elastic compensation procedure) applied to Koiter’s upper-bound shakedown theorem. The method is demonstrated for a typical pressure vessel application; an axisymmetric nozzle in a spherical shell. Several geometrical configurations are investigated. The calculated upper-bound shakedown loads are compared with lower-bound results obtained by the authors, simple shakedown criteria, and various results given in the literature.

Accelerated Limit Loads Using Repeated Elastic Finite Element Analyses

2003 ◽  
Author(s):  
Prasad Mangalaramanan
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Limit Load ◽  
Finite Element Analyses ◽  
Limit Loads ◽  
Bound Theorem

This paper demonstrates the limitations of repeated elastic finite element analyses (REFEA) based limit load determination that uses the classical lower bound theorem. The r-node method is prescribed as an alternative for obtaining better limit load estimates. Lower bound aspects pertaining to r-nodes are also discussed.

A Study of the Conservatism in ASME BPVC Section VIII Division 2 Opening Design for External Pressure

2019 ◽  
Author(s):  
Barry Millet ◽  
Kaveh Ebrahimi ◽  
James Lu ◽  
Kenneth Kirkpatrick ◽  
Bryan Mosher
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Pressure Vessel ◽  
External Pressure ◽  
The Other ◽  
Finite Element Analyses ◽  
Division 1 ◽  
Section Viii ◽  
Allowable Compressive Stress ◽  
Division 2

Abstract In the ASME Boiler and Pressure Vessel Code, nozzle reinforcement rules for nozzles attached to shells under external pressure differ from the rules for internal pressure. ASME BPVC Section I, Section VIII Division 1 and Section VIII Division 2 (Pre-2007 Edition) reinforcement rules for external pressure are less stringent than those for internal pressure. The reinforcement rules for external pressure published since the 2007 Edition of ASME BPVC Section VIII Division 2 are more stringent than those for internal pressure. The previous rule only required reinforcement for external pressure to be one-half of the reinforcement required for internal pressure. In the current BPVC Code the required reinforcement is inversely proportional to the allowable compressive stress for the shell under external pressure. Therefore as the allowable drops, the required reinforcement increases. Understandably, the rules for external pressure differ in these two Divisions, but the amount of required reinforcement can be significantly larger. This paper will examine the possible conservatism in the current Division 2 rules as compared to the other Divisions of the BPVC Code and the EN 13445-3. The paper will review the background of each method and provide finite element analyses of several selected nozzles and geometries.

On Friction of Ploughing by Rigid Asperities in the Presence of Straining—Upper Bound Method

1990 ◽  
Vol 112 (2) ◽  
pp. 324-329 ◽  
Author(s):  
A. Azarkhin ◽  
O. Richmond
Keyword(s):  
Finite Element ◽  
Friction Factor ◽  
Upper Bound ◽  
Plastic Material ◽  
High Accuracy ◽  
The Other ◽  
Periodic Array ◽  
Combined Loading ◽  
Upper Bound Method ◽  
Perfectly Plastic

Upper bound applications traditionally assume that a rigid/perfectly-plastic material moves by rigid blocks, creating discontinuities of velocity at the interfaces between the blocks. In the present version, the elements (blocks) are plastically deformable and there are no velocity discontinuities between adjacent sides. Since this modification incorporates major features of finite element representation employing arbitrary cells, it allows the use of many parameters for minimization, thus achieving high accuracy. On the other hand, it retains the advantage of upper bound techniques in that the incremental procedure for loading is not necessary, and the results for steady processes are obtained directly. Some energy statements for combined loading are derived and a technique for calculating the ploughing force is presented. Examples for a single fully embedded rigid pyramid and a periodic array of asperities ploughing through the rigid/perfectly plastic material in the presence of subsurface straining are given. The friction factor decreased as the rate of subsurface straining increased, as the pyramid angle of the asperities increased, and as the distance between asperities increased.

Probabilistic Models to Approximate Highly Repetitive Linear and Nonlinear Finite Element Analyses of Nuclear Components

2009 ◽  
Author(s):  
Dan Vlaicu ◽  
Mike Stojakovic
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Probabilistic Models ◽  
Nonlinear Material ◽  
Superposition Method ◽  
Loading Conditions ◽  
Finite Element Analyses ◽  
Axisymmetric Nozzle ◽  
Nonlinear Superposition ◽  
Pipe Bend

In the development and technical support of nuclear plants, Engineers have to deal with highly repetitive finite element analyses that involve modeling of local variations of the initial design, local flaws due to corrosion-erosion effects, material properties degradation, and modifications of the loading conditions. This paper presents the development of generic models that emulate the behavior of a complex finite element model in a simplified form, with the statistical representation based on a sampling of base-model data for a variety of test cases. An improved Latin Hypercube algorithm is employed to generate the sampling points based on the number and the range of the variables that are considered in the design space. Four filling methods of the approximation models are discussed in this study: response surface, nonlinear, neural networks, and piecewise polynomial model. Furthermore, a bootstrapping procedure is employed to improve the confidence intervals of the original coefficients, and the single-factor or double-factor analysis of variance is applied to determine whether a significant influence exists between the investigated factors. Two numerical examples highlight the accuracy and efficiency of the methods. The first example is the linear elastic analysis of a pipe bend under pressure loading. The objective of the probabilistic assessment is to determine the relation between the loading conditions as well as the geometrical aspects of this elbow (pipe wall thickness, outside diameter, elbow radius, and maximum ovality tolerance) and the maximum stress in the elbow. The second example is an axisymmetric nozzle under primary and secondary cycling loads. Variations of the geometrical dimensions, nonlinear material properties, and cycling loading are taken as the input parameters, whereas the response variable is defined in terms of Melan’s theorem translated into the Nonlinear Superposition Method.

A Multi-Surface Plasticity Method for Lower Bound Shakedown Load

2019 ◽  
Vol 795 ◽  
pp. 458-465
Author(s):  
Alan Jappy ◽  
Donald Mackenzie ◽  
Hao Feng Chen
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Finite Number ◽  
Upper Bound ◽  
Direct Method ◽  
Extreme Points ◽  
Residual Stress Field ◽  
Periodic Load ◽  
Surface Plasticity ◽  
Elastic Shakedown

A new direct method for calculation of lower bound shakedown limits based on Melan’s theorem and a novel, non-smooth multi-surface plasticity model is proposed and implemented in a Finite Element environment. The load history is defined by a finite number of extreme points defining the load-envelope of a periodic load set. The shakedown problem is stated as a plasticity problem in terms of a finite number of independent yield conditions, solved for a residual stress field that satisfies a piecewise, non-smooth yield surface defined by the intersection of multiple yield surfaces. The implemented Finite Element procedure is applied to two shakedown problems and the results compared with lower and upper bound elastic shakedown solutions given by the Linear Matching Method, LMM. The example analyses show that the proposed Elastic-Shakedown Multi Surface Plasticity (EMSP) method defines robust lower bound shakedown limits between the LMM lower and upper bound limits, close to the LMM upper bound.

Bounded Elastic Moduli Multiplier Technique for Limit Loads: Part 1 - Theory

2022 ◽  
Author(s):  
Sathya Prasad Mangalaramanan
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Lower Bound ◽  
Power Law ◽  
Elastic Moduli ◽  
Stress Distributions ◽  
Finite Element Analyses ◽  
Element Analysis ◽  
Limit Loads ◽  
Reduced Modulus

Abstract Statically admissible stress distributions are necessary to evaluate lower bound limit loads. Over the last three decades, several methods have been postulated to obtain these distributions using iterative elastic finite element analyses. Some of the pioneering techniques are the reduced modulus, r-node, elastic compensation, and linear matching methods, to mention a few. A new method, called the Bounded Elastic Moduli Multiplier Technique (BEMMT), is proposed and the theoretical underpinnings thereof are explained in this paper. BEMMT demonstrates greater robustness, more generality, and better stress distributions, consistently leading to lower-bound limit loads that are closer to elastoplastic finite element analysis estimates. BEMMT also questions the validity of the prevailing power law based stationary stress distributions. An accompanying research offers several case studies to validate this claim.

Limit Load Estimation Using Plastic Flow Parameter in Repeated Elastic Finite Element Analyses

2002 ◽  
Vol 124 (4) ◽  
pp. 433-439 ◽  
Author(s):  
L. Pan ◽  
R. Seshadri
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Plastic Flow ◽  
Flow Parameter ◽  
Limit State ◽  
Limit Load ◽  
Finite Element Analyses ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
Linear Elastic

The procedures described in this paper for determining a limit load is based on Mura’s extended variational formulation. Used in conjunction with linear elastic finite element analyses, the approach provides a robust method to estimate limit loads of mechanical components and structures. The secant modulus of the various elements in a finite element discretization scheme is prescribed in order to simulate the distributed effect of the plastic flow parameter, μ0. The upper and lower-bound multipliers m0 and m′ obtained using this formulation converge to near exact values. By using the notion of “leap-frogging” to limit state, an improved lower-bound multiplier, mα, can be obtained. The condition for which mα is a reasonable lower bound is discussed in this paper. The method is applied to component configurations such as cylinder, torispherical head, indeterminate beam, and a cracked specimen.

Assessment of Overlapped Internal and External Volumetric Flaws in p-M Diagram

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Shinji Konosu ◽  
Hikaru Miyata
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Pressure Vessel ◽  
Effective Cross Section ◽  
Finite Element Analyses ◽  
Diagram Method ◽  
Reference Stress ◽  
Common Problems ◽  
Good Agreement

Assessment of overlapped internal and external volumetric flaws is one of the most common problems related to pressure vessel and piping components. Under the current fitness for service rules, such as those provided in ASME, BS, and so on, the procedures for the assessment of these flaws have not yet been defined. In this paper, a reference stress, incorporating the decrease in the effective cross section as a function of flaw depth and flaw angle in a cylinder, has been proposed in order to assess the flaws using the simple p-M (pressure-moment) diagram method. Numerous finite element analyses for a cylinder with overlapped internal and external flaws were conducted to verify the proposed procedure. There is good agreement among them.

Upper-bound and finite-element analyses of non-isothermal ECAP

2012 ◽  
Vol 546 ◽  
pp. 180-188 ◽  
Author(s):  
F.R.F. Silva ◽  
N. Medeiros ◽  
L.P. Moreira ◽  
J.F.C. Lins ◽  
J.P. Gouvêa
Keyword(s):  
Finite Element ◽  
Upper Bound ◽  
Finite Element Analyses
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