Lower Bound Limit Load Estimation Using a Linear Elastic Analysis

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
C. Hari Manoj Simha ◽  
R. Adibi-Asl
Keyword(s):  
Lower Bound ◽  
Deformation Theory ◽  
Elastic Stress ◽  
Limit Load ◽  
Load Estimation ◽  
Elastic Analysis ◽  
Numerical Examples ◽  
Linear Elastic ◽  
Plastic Localization ◽  
Appl Math

We present a scheme that utilizes one elastic stress field (no iterations) to compute lower bound limit load multipliers of structures that collapse through gross (or localized) plasticity. A criterion to distinguish between these collapse modes is presented. For structures that collapse through gross plasticity, we demonstrate that the m′ multiplier proposed by Mura et al. (1965, Extended Theorems of Limit Analysis,” Q. Appl. Math., 23(2), pp. 171–179) is a lower bound in the context of deformation theory. For structures that undergo plastic localization at collapse, we present a criterion that identifies (approximately) the subvolumes of the structure that participate in the collapse. Multiplier m′ is computed over the selected subvolumes, denoted as m'S, and demonstrated to be a lower bound multiplier in the context of deformation theory. We consider numerical examples of structures that collapse by localized or gross plasticity and show that our proposed multiplier is lower than the corresponding multiplier obtained through elastic–plastic analysis and the proposed multiplier is not overly conservative.

Estimating Lower Bound Limit Loads for Structures Subjected to Multiple Loads

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
C. Hari Manoj Simha ◽  
Reza Adibi-Asl
Keyword(s):  
Lower Bound ◽  
Elastic Stress ◽  
Limit Load ◽  
Selection Method ◽  
Elastic Analysis ◽  
Limit Loads ◽  
Linear Elastic ◽  
Multiple Loads ◽  
Cracked Structures ◽  
Appl Math

It is shown that the extended variational theorem of Mura et al. (1965, “Extended Theorems of Limit Analysis,” Q. Appl. Math., 23(2), pp. 171–179) can be applied to structures subjected to more than one load and be used to compute lower bound limit load multipliers. In particular, the multiplier proposed by Simha and Adibi-Asl (2011, “Lower Bound Limit Load Estimation Using a Linear Elastic Analysis,” ASME J. Pressure Vessel Technol., 134(2), p. 021207), which can be computed using an elastic stress field, is shown to be a lower bound. Furthermore, it is demonstrated that lower bound limit load for cracked structures may also be computed using a subvolume selection method. No iterations or elastic modulus adjustment are required. Several analytical and numerical examples that illustrate the procedure are presented.

Analytical Methods for Preliminary Design of Anchor Flanges for Subsea Structures

2019 ◽  
Author(s):  
Sabesan Rajaratnam ◽  
T. Sriskandarajah ◽  
Daryl Clayton ◽  
Graeme Roberts ◽  
Vincent Loentgen ◽  
...  
Keyword(s):  
Stress Concentration ◽  
Plastic Strain ◽  
Elastic Stress ◽  
Limit Load ◽  
Preliminary Design ◽  
Time Saving ◽  
Linear Elastic ◽  
Stress Concentration Factors ◽  
Ultimate Load Carrying Capacity ◽  
Cost Implications

Abstract Anchor flanges are interface items which are used to connect pipelines to subsea in-line and end termination structures. They are forged and tend to be long-lead items; therefore, the design of an anchor flange should be completed at a very early project stage, possibly even during the tender phase. An optimised, analytical method for preliminary design would result in reduced design time overall and have beneficial cost implications. The analytical notch methods (i.e. Neuber’s and Glinka’s) that are presented utilise linear-elastic stress concentration factors to make realistic predictions of the ultimate load carrying capacity of an anchor flange in the non-linear regime. The linear-elastic stress concentration factor values are calculated with simple analytical formulae and graphs. The analytical notch methods are deployed to predict the anchor flange limit load and peak plastic strain and thereby ensure that the plastic strain remains within the allowable limits of design codes. The cost and time saving associated with the analytical notch methods, and the accuracy that is maintained, are assessed by comparison with the predictions results obtained from detailed finite element analyses.

Local Limit-Load Analysis Using the mβ Method

2006 ◽  
Vol 129 (2) ◽  
pp. 296-305 ◽  
Author(s):  
R. Adibi-Asl ◽  
R. Seshadri
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Local Limit ◽  
Limit Load ◽  
Element Analysis ◽  
Limit Loads ◽  
Linear Elastic ◽  
Reference Volume ◽  
Component Design ◽  
Load Analysis

Several upper-bound limit-load multipliers based on elastic modulus adjustment procedures converge to the lowest upper-bound value after several linear elastic iterations. However, pressure component design requires the use of lower-bound multipliers. Local limit loads are obtained in this paper by invoking the concept of “reference volume” in conjunction with the mβ multiplier method. The lower-bound limit loads obtained compare well to inelastic finite element analysis results for several pressure component configurations.

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.

Upper and lower bound limit and shakedown loads for hollow tubes with axisymmetric internal projections under axial loading

2001 ◽  
Vol 36 (6) ◽  
pp. 595-604 ◽  
Author(s):  
S. J Hardy ◽  
A. R Gowhari-Anaraki ◽  
M. K Pipelzadeh
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Axial Loading ◽  
Limit Load ◽  
Analysis Procedure ◽  
Elastic Analysis ◽  
Elastic Plastic ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Elastic Compensation Method

In this paper, the elastic compensation method proposed by Mackenzie and Boyle is used to estimate the upper and lower bound limit (collapse) loads and the upper and lower bound shakedown loads for hollow tubes with axisymmetric internal projections subjected to axial loading. The method is based on an iterative elastic analysis procedure and the application of lower and upper bound limit load theorems. Four different geometries with a range of stress concentration factors (from low to high) are considered. Elastic-plastic finite element predictions for collapse and shakedown pressure are found to be within these upper and lower bound estimates. The method is particularly useful because it is founded on an iterative elastic approach and does not require extensive and complex elastic-plastic finite element computations.

Stress Analysis and Design for Cyclic Loading

2000 ◽  
Vol 122 (4) ◽  
pp. 427-430
Author(s):  
P. Carter
Keyword(s):  
Thermal Loading ◽  
Limit Load ◽  
Elastic Analysis ◽  
Analysis And Design ◽  
Linear Elastic ◽  
Inelastic Analysis ◽  
Nonlinear Elastic Analysis ◽  
Comprehensive Framework ◽  
Nonlinear Elastic ◽  
Effective Design

A finite element implementation of rapid cycle analysis is described and demonstrated. It forms part of a comprehensive framework for static structural analysis which consists of: linear elastic analysis, limit load or nonlinear elastic analysis, and rapid cycle analysis. This approach allows for complex material and loading behavior, but is computationally more efficient and easier to perform than full inelastic analysis. It indicates more complex behavior than can be inferred from linear elastic analysis. The objective of this paper is to calculate shakedown, reverse plasticity, ratcheting, and the increase in strain rate as a result of cyclic mechanical and thermal loading. Results are presented in the form of interaction diagrams, similar to the O’Donnell-Porowski plot in the ASME BPV Code, which are effective design tools. [S0094-9930(00)01604-8]

Fitness-for-Service Methodology Based on Variational Principles in Plasticity

2004 ◽  
Author(s):  
H. Indermohan ◽  
R. Seshadri
Keyword(s):  
Lower Bound ◽  
Hot Spots ◽  
Variational Formulation ◽  
Variational Principles ◽  
Limit Load ◽  
Pressure Vessels ◽  
Load Estimation ◽  
Estimation Technique ◽  
Simplified Procedures

A variational formulation in plasticity has been used to develop improved limit load estimation technique, such as the m-alpha method. Lower bound limit load estimates are especially germane to design and fitness-for-service assessments. The concept of “integral mean of yield” has been applied to problems involving locally thin areas (LTA) and local hot spots in the context of industrial pressure vessels and piping. Simplified procedures for “fitness-for-service” assessment, suitable for use by plant engineers, have been developed. The results are compared with the corresponding inelastic finite elastic analyses.

scholarly journals Effects of Material Nonlinearities on Design of Composite Constructions—Elasto-Plastic Behaviour

Materials ◽  
2020 ◽  
Vol 13 (7) ◽  
pp. 1792 ◽  
Author(s):  
Aleksander Muc
Keyword(s):  
Cylindrical Shell ◽  
Composite Structures ◽  
Pressure Vessels ◽  
Experimental Results ◽  
Matrix Cracking ◽  
Elastic Analysis ◽  
Limit States ◽  
Numerical Examples ◽  
Linear Elastic ◽  
Linear Behaviour

Usually, the design of composite structures is limited to the linear elastic analysis only. The experimental results discussed in the paper demonstrate the physical non-linear behaviour both for unidirectional and woven roving composites. It is mainly connected with the micromechanical damages in composite structures, particularly with the effects of matrix cracking modeled in the form of elastic-plastic physical relations. In the present paper, the effects of both physical and geometrical non-linearities are taken into account. Their influence on the limit states (understood in the sense of buckling or failure/damage) of composite structures is discussed. The numerical examples deal with the behaviour of composite pressure vessels components, such as a cylindrical shell and the reinforcement of the junction of shells. The optimisation method of the reinforcement thickness is also formulated and solved herein.

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