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.

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.

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 Loads Using Extended Variational Concepts in Plasticity

2000 ◽  
Vol 122 (3) ◽  
pp. 379-385
Author(s):  
R. Seshadri
Keyword(s):  
Lower Bound ◽  
Classical Method ◽  
Yield Criterion ◽  
Limit Load ◽  
Quadratic Equation ◽  
Limit Loads ◽  
Linear Elastic ◽  
Primary Stress ◽  
Component Design ◽  
Calculated Stress

Lower-bound limit load estimates are relevant from a standpoint of pressure component design, and are acceptable quantities for ascertaining primary stress limits. Elastic modulus adjustment procedures, used in conjunction with linear elastic finite element analyses, generate both statically admissible stress distributions and kinematically admissible strain distributions. Mura’s variational formulation for determining limit loads, originally developed as an alternative to the classical method, is extended further by allowing the elastic calculated stress fields to exceed yield provided they satisfy the “integral mean of yield” criterion. Consequently, improved lower-bound values for limit loads are obtained by solving a simple quadratic equation. The improved lower-bound limit load determination procedure, which is designated “the mα method,” is applied to symmetric as well as nonsymmetric components. [S0094-9930(00)01103-3]

Reference Volume Consideration in the mα-Tangent Method Based Linear Elastic Analysis

2011 ◽  
Author(s):  
R. Adibi-Asl ◽  
M. M. Hossain ◽  
S. L. Mahmood ◽  
P. S. R. Gudimetla ◽  
R. Seshadri
Keyword(s):  
Finite Element ◽  
Rapid Determination ◽  
Limit Load ◽  
Elastic Analysis ◽  
Element Analysis ◽  
Limit Loads ◽  
Linear Elastic ◽  
Reference Volume ◽  
Tangent Method

Limit loads for pressure components are determined on the basis of a single linear elastic finite element analysis by invoking the concept of kinematically active (reference) volume in the context of the “mα-tangent” method. The resulting technique enables rapid determination of lower bound limit load for pressure components by eliminating the kinematically inactive volume. This method is applied to a number of practical components with different percentages of inactive volume. The results are compared with the corresponding inelastic finite element results, or available analytical solutions.

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.

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.

Integral Mean of Yield Criterion in Design and Fitness for Service Assessment

2008 ◽  
Author(s):  
R. Adibi-Asl ◽  
R. Seshadri
Keyword(s):  
Lower Bound ◽  
Variational Formulation ◽  
Yield Criterion ◽  
Hot Spot ◽  
Corrosion Damage ◽  
Limit Load ◽  
Assessment Procedure ◽  
Limit Loads ◽  
Reference Volume ◽  
Volume Method

Mura’s variational formulation for determining limit loads, originally developed as an alternative to classical methods, is extended further by allowing the pseudo-elastic distributions of stresses to lie outside the yield surface provided they satisfy the “integral mean of yield” criterion. Consequently, improved lower-bound and upper-bound values for limit loads are obtained. The mα estimation limit load method, reference volume method and the fitness for service assessment procedure (including corrosion damage and thermal hot spot damage), are all applications and extensions of the “integral mean of yield” criterion.

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.

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