A New Constitutively Accurate Lower Bound Direct Shakedown Method

2013 ◽  
Author(s):  
Alan Jappy ◽  
Donald Mackenzie ◽  
Haofeng Chen
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Lower Bound ◽  
Yield Surface ◽  
Direct Methods ◽  
Accurate Description ◽  
Element Analysis ◽  
Surface Plasticity ◽  
Fundamental Requirement ◽  
Linear Matching Method

Ensuring sufficient safety against shakedown or ratchet is a fundamental requirement of pressure vessel design. Determining the shakedown or ratchet boundary can however prove difficult when using a full elastic plastic finite element analysis and a number of direct methods have been proposed that overcome the difficulties associated with shakedown or ratchet boundary evaluation. Here a new direct lower bound shakedown method, which can be extended to a ratchet method, is proposed. The method maintains a constitutively accurate description of the assumed material response through the use of non-smooth multi yield surface plasticity models. The proposed shakedown method can consider arbitrary load cases and may be solved in a single analysis step in a standard finite element analysis with a user-programed non-smooth multi yield surface plasticity model. It is demonstrated that by maintaining a constitutively accurate description of the plastic strains the method is able to calculate strict lower bound shakedown boundaries. The resulting boundary is shown to give excellent agreement with the upper and lower bound linear matching method.

scholarly journals A Fully Implicit, Lower Bound, Multi-Axial Solution Strategy for Direct Ratchet Boundary Evaluation: Implementation and Comparison

2012 ◽  
Author(s):  
Alan Jappy ◽  
Donald Mackenzie ◽  
Haofeng Chen
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Hybrid Method ◽  
Direct Methods ◽  
Benchmark Problems ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Boundary Evaluation ◽  
Fully Implicit ◽  
Tangent Moduli

Ensuring sufficient safety against ratcheting is a fundamental requirement of pressure vessel design. However, determining the ratchet boundary using a full elastic plastic finite element analysis can be problematic and a number of direct methods have been proposed to overcome difficulties associated with ratchet boundary evaluation. This paper proposes a new approach, similar to the previously proposed Hybrid method but based on fully implicit elastic-plastic solution strategies. This method utilizes superimposed elastic stresses and modified radial return integration to converge on the residual state throughout, resulting in one Finite Element model suitable for solving the cyclic stresses (stage 1) and performing the augmented limit analysis to determine the ratchet boundary (stage 2). The modified radial return methods for both stages of the analysis are presented, with the corresponding stress update algorithm and resulting consistent tangent moduli. Comparisons with other direct methods for selected benchmark problems are presented. It is shown that the proposed method consistently evaluates a lower bound estimate of the ratchet boundary, which has not been demonstrated for the Hybrid method and is yet to be clearly shown for the UMY and LDYM methods. Limitations in the description of plastic strains and compatibility during the ratchet analysis are identified as being a cause for the differences between the proposed methods and other current upper bound methods.

Shakedown and Ratcheting Assessment of a Tubeplate Using the Linear Matching Method

2012 ◽  
Author(s):  
H. Reece-Barkell ◽  
M. Stevens ◽  
D. J. Tipping ◽  
J. Sole
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Power Plant ◽  
Finite Element Methods ◽  
Plastic Collapse ◽  
Matching Method ◽  
Element Analysis ◽  
Linear Finite Element ◽  
Non Linear ◽  
Linear Matching Method

Power plant components may be subject to severe ranges of pressure and temperature when in-service. As a result, significant pressure and thermal stresses may occur which are cyclic in nature. For such components it is necessary to demonstrate an acceptable creep and fatigue life. However, before any such assessment can take place it must first be demonstrated that the cyclic loading would not lead to incremental plasticity, also known as ratcheting, and ultimately plastic collapse. If ratcheting does occurs then the calculation of creep and fatigue lives based upon a steady cyclic behaviour is invalid. It is therefore useful for find out how close structures are to ratcheting. A power plant tubeplate has been analysed using non-linear finite element methods to assess its susceptibility to ratcheting and the potential for plastic collapse to occur. This is referred to as a shakedown assessment. Finite element analysis is a traditional method for assessing shakedown, however this approach is computationally expensive. An alternative method of assessing shakedown, which is significantly more efficient, although not as well validated, is the Linear Matching Method. In this work, both finite element analysis and the Linear Matching Method have been used on a real world problem. The objective of this work is to assess the advantages and disadvantages of the LMM when compared to traditional non-linear finite element methods.

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.

Assessment of the Twice-Yield Method for Elastic-Plastic Fatigue Analysis

2006 ◽  
Author(s):  
W. Reinhardt
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Yield Surface ◽  
Fatigue Analysis ◽  
Half Cycle ◽  
Proportional Loading ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Effective Yield ◽  
Von Mises

The twice-yield (2 Sy) method was proposed by Kalnins as a convenient method to perform an elastic-plastic fatigue analysis using Finite Element analysis. With this method, only a single loading half cycle needs to be run. However, since the shape of the effective yield surface used in this method deviates from the actual von Mises yield surface, the method may conceivably deviate from the solution obtained by elastic-plastic cycle-by-cycle analysis. This paper aims to evaluate the twice-yield method for elastic-plastic fatigue analysis, which is conventionally done cycle-by-cycle. It compares the predictions of plastic strain from the twice-yield method and cycle-by-cycle analysis using some generic examples with non-proportional loading histories as they are frequently encountered in practice.

scholarly journals A Fully Implicit, Lower Bound, Multi-Axial Solution Strategy for Direct Ratchet Boundary Evaluation: Theoretical Development

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Alan Jappy ◽  
Donald Mackenzie ◽  
Haofeng Chen
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Yield Strength ◽  
Stress Component ◽  
Direct Methods ◽  
Theoretical Development ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Boundary Evaluation ◽  
Fully Implicit

Ensuring sufficient safety against ratchet is a fundamental requirement in pressure vessel design. Determining the ratchet boundary can prove difficult and computationally expensive when using a full elastic–plastic finite element analysis and a number of direct methods have been proposed that overcome the difficulties associated with ratchet boundary evaluation. Here, a new approach based on fully implicit finite element methods, similar to conventional elastic–plastic methods, is presented. The method utilizes a two-stage procedure. The first stage determines the cyclic stress state, which can include a varying residual stress component, by repeatedly converging on the solution for the different loads by superposition of elastic stress solutions using a modified elastic–plastic solution. The second stage calculates the constant loads which can be added to the steady cycle while ensuring the equivalent stresses remain below a modified yield strength. During stage 2 the modified yield strength is updated throughout the analysis, thus satisfying Melan's lower bound ratchet theorem. This is achieved utilizing the same elastic plastic model as the first stage, and a modified radial return method. The proposed methods are shown to provide better agreement with upper bound ratchet methods than other lower bound ratchet methods, however limitations in these are identified and discussed.

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