Limit Loads for Layered Structures Using Extended Variational Principles and Repeated Elastic Finite Element Analysis

2002 ◽  
Vol 124 (4) ◽  
pp. 425-432 ◽  
Author(s):  
L. Pan ◽  
R. Seshadri
Keyword(s):  
Finite Element ◽  
Flow Parameter ◽  
Variational Principles ◽  
Limit State ◽  
Limit Load ◽  
Layered Structures ◽  
Element Analysis ◽  
Element Discretization ◽  
Limit Loads ◽  
Strength Performance

Layered structures are used in industry due to their better cost-to-strength and weight-to-strength performance compared with conventional structures. This paper presents a simple and systematic procedure to estimate the limit load for those layered structures that can undergo plastic collapse. The extended Mura’s variational principle is used in conjunction with repeated elastic finite element analyses (FEA). The elastic parameters are modified in order to ensure that the repeated analyses lead to a stress distribution close to the limit state. The secant modulus of a given element within the finite element discretization scheme is employed to simulate the plastic flow parameter μ0, and rapid convergence of estimated multipliers to the exact value is achieved. By using the notion of “leap-frogging” to limit state, improved lower-bound values of limit loads have been obtained. The method has been applied to layered cylinders and beams.

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.

Simple Bounds on Limit Loads by Elastic Finite Element Analysis

1993 ◽  
Vol 115 (1) ◽  
pp. 27-31 ◽  
Author(s):  
D. Mackenzie ◽  
C. Nadarajah ◽  
J. Shi ◽  
J. T. Boyle
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Pressure Vessel ◽  
Limit Load ◽  
Analysis Procedure ◽  
Element Analysis ◽  
Elastic Continuum ◽  
Limit Loads ◽  
Simple Bounds ◽  
Elastic Compensation Method

A method for bounding limit loads by an iterative elastic continuum finite element analysis procedure, referred to as the elastic compensation method, is proposed. A number of sample problems are considered, based on both exact solutions and finite element analysis, and it is concluded that the method may be used to obtain limit-load bounds for pressure vessel design by analysis applications with useful accuracy.

ROBUST LIMIT LOADS OF SYMMETRIC AND NON-SYMMETRIC PLATE STRUCTURES

1995 ◽  
Vol 19 (3) ◽  
pp. 227-246 ◽  
Author(s):  
S.P. Mangalaramanan ◽  
R. Seshadri
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Limit Load ◽  
Robust Methods ◽  
Element Analysis ◽  
Construction Technique ◽  
Plate Structures ◽  
Limit Loads ◽  
Collapse Mechanisms

Robust methods for estimating limit loads of symmetric and non-symmetric plate structures are presented. The methods proposed in this paper for determining limit loads are (1) the r-node method and (2) the semi-circle construction technique. Analytical methods for estimating the limit loads of plate structures are feasible only for simple configurations. Also, determination of limit loads based on assumed collapse mechanisms may not always give upper bound estimates. Limit analysis using inelastic finite element analysis is often elaborate and time consuming. The methods described in this paper circumvent these difficulties. The methods are applied to several configurations of symmetric and non-symmetric plate structures and the limit load estimates are found to be satisfactory.

The M-Beta Multiplier Method for Limit Load Determination of Components With Local Plastic Collapse

2005 ◽  
Author(s):  
H. Indermohan ◽  
R. Seshadri
Keyword(s):  
Stress Distribution ◽  
Variational Principles ◽  
Limit State ◽  
Limit Load ◽  
Multiplier Method ◽  
Element Analysis ◽  
Reference Volume ◽  
Reference Stress ◽  
Reference Parameter

The mβ-multiplier method based on Mura’s extended variational principles in plasticity relies on a reference stress that is obtained from an entire stress distribution in a structure. The method is relatively insensitive to components that undergo localized plastic action and generates limit load bounds that are better than the classical and mα-multiplier methods. The multiplier mβ is determined by evaluating a reference parameter βR, which may be difficult to determine if the stress distribution obtained using elastic modulus adjustment procedures does not converge to a limit type of distribution. In this paper, physical insights relating to the reference parameter βR are provided by linking the concept of reference volume to the local collapse of the structure. As well, a systematic procedure to identify the converged limit state is presented. The mβ-multiplier method, developed in conjunction with the reference volume concept, is applied to a number of cracked component configurations. The results are compared with the corresponding inelastic finite element analysis.

Simplified Limit Load Estimation of Components With Cracks Using the Reference Two-Bar Structure

2007 ◽  
Author(s):  
R. Adibi-Asl ◽  
R. Seshadri
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Rapid Determination ◽  
Limit Load ◽  
Load Estimation ◽  
Element Analysis ◽  
Limit Loads ◽  
Scaling Relationships ◽  
Simple Scaling

Limit loads for different crack configurations are determined in this paper by invoking the concept of equivalence of “static indeterminacy” that relates a multidimensional component configuration to a “reference two-bar structure.” Simple scaling relationships are developed that enable rapid determination of limit loads. The method is applied to different crack configurations, and the limit loads are compared with corresponding results obtained from inelastic finite element analysis.

Assessment Techniques Using the R6 Procedure: Investigation of Limit Load Approach for Pipe Branch Connections

2010 ◽  
Author(s):  
Peter A. Frost
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Surface Defect ◽  
Surface Defects ◽  
Local Limit ◽  
Limit Load ◽  
Elliptic Surface ◽  
Element Analysis ◽  
Limit Loads ◽  
Failure Assessment

The R6 Revision 4 Procedure ‘Assessment of the Integrity of Structures Containing Defects’, states that the use of the finite element ‘global’ limit load derived for pipe branch components can be non-conservative when used with the Option 1 and 2 failure assessment curves but that ‘local’ limit loads, based on the spread of plasticity through the pipe wall, should lead to conservative results. The current advice of R6 is based on separate studies by Fox and Connors of pipe branch components with fully extended surface defects. Their studies provide two distinct methods for calculating a suitably conservative local limit load. However, there is concern that these two methods may provide an overly conservative local limit load with therefore a less realistic prediction of defect tolerance. Furthermore, typical defectiveness is perhaps most commonly characterised as a semi-elliptic surface defect and it is therefore necessary to adapt both these methods in order to accommodate such defects. The purpose of this study was therefore to investigate local limit load approaches for pipe branch components with postulated semi-elliptic surface defects. A typical pipe branch component was chosen for assessment during this study, as part of a series of separate studies on a variety of pipe branch components. Local limit loads were calculated using two approaches. The first approach adapted the ‘Connors’ method by applying an adjustment to allow for the semi-elliptic surface defect; this is referred to as the ‘Modified Connors’ approach. The second approach used cracked body finite element analysis and evaluated the local limit load by consideration of the onset of plasticity at the crack ligament. The global limit load was also derived from the cracked body finite element analysis. Assessment points were developed using global and local limit loads, both obtained by cracked body finite element analysis, and also by using the ‘Modified Connors’ local limit load approach. R6 Option 3 failure assessment curves were produced for each limit load approach in order to investigate the extent of any non-conservatism in the Option 1 and 2 failure assessment curves with the chosen limit load approach.

Limit Load Analysis of Cracked Components Using the Reference Volume Method

2006 ◽  
Author(s):  
R. Adibi-Asl ◽  
R. Seshadri
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Elastic Modulus ◽  
Limit Load ◽  
Multiple Cracks ◽  
Element Analysis ◽  
Limit Loads ◽  
Integrity Assessment ◽  
Reference Volume ◽  
Volume Method

Cracks and flaws occur in mechanical components and structures, and can lead to catastrophic failures. Therefore, integrity assessment of components with defects is carried out. This paper describes the Elastic Modulus Adjustment Procedures (EMAP) employed herein to determine the limit load of components with cracks or crack-like flaw. On the basis of linear elastic Finite Element Analysis (FEA), by specifying spatial variations in the elastic modulus, numerous set of statically admissible and kinematically admissible distributions can be generated, to obtain lower and upper bounds limit loads. Due to the expected local plastic collapse, the reference volume concept is applied to identify the kinematically active and dead zones in the component. The Reference Volume Method is shown to yield a more accurate prediction of local limit loads. The limit load values are then compared with results obtained from inelastic finite element analysis. The procedures are applied to some practical components with cracks in order to verify their effectiveness in analyzing crack geometries. The analysis is then directed to geometries containing multiple cracks and three-dimensional defect in pressurized components.

Simplified Limit Load Determination Using the mα-Tangent Method

2008 ◽  
Author(s):  
R. Seshadri ◽  
M. M. Hossain
Keyword(s):  
Finite Element ◽  
Rapid Determination ◽  
Limit Load ◽  
Finite Element Analyses ◽  
Element Analysis ◽  
Limit Loads ◽  
Linear Elastic ◽  
Tangent Method ◽  
Mechanical Components

Limit load determination of mechanical components and structures by the mα-tangent method is proposed herein. The proposed technique is a simplified method that enables rapid determination of limit loads for a general class of mechanical components and structures. The method makes use of statically admissible stress field based on a linear elastic finite element analysis to estimate the limit loads. The method is applied to a number of mechanical component configurations and the results compare well with those obtained by the corresponding elastic-plastic finite element analyses results.

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.

Simplified Limit Load Estimation of Components With Cracks Using the Reference Two-Bar Structure

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
R. Adibi-Asl ◽  
R. Seshadri
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Rapid Determination ◽  
Limit Load ◽  
Load Estimation ◽  
Element Analysis ◽  
Limit Loads ◽  
Scaling Relationships ◽  
Simple Scaling

Limit loads are determined in this paper by invoking the concept of equivalence of “static indeterminacy” that relates a multidimensional component configuration (with cracks) to a “reference two-bar structure.” Simple scaling relationships are developed that enable rapid determination of limit loads. The method is applied to different crack configurations, and the limit loads are compared with corresponding results obtained from inelastic finite element analysis.

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