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.

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

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Alan Jappy ◽  
Donald Mackenzie ◽  
Haofeng Chen
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Direct Methods ◽  
Element Model ◽  
Benchmark Problems ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Boundary Evaluation ◽  
Fully Implicit ◽  
Tangent Moduli

Ensuring sufficient safety against ratcheting is a fundamental requirement in 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 lower bound ratchet analysis approach, similar to the previously proposed hybrid method but based on fully implicit elastic-plastic solution strategies. The 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 evaluates a consistent lower bound estimate of the ratchet boundary, which has not previously been clearly demonstrated for other lower bound approaches. 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 current upper bound methods.

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.

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

2012 ◽  
Author(s):  
Alan Jappy ◽  
Donald Mackenzie ◽  
Haofeng Chen
Keyword(s):  
Lower Bound ◽  
Yield Strength ◽  
Stress Component ◽  
Direct Methods ◽  
Theoretical Development ◽  
Implicit Methods ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Boundary Evaluation ◽  
Fully Implicit

Ensuring sufficient safety against ratchet is a fundamental requirement of pressure vessel design. Determining the 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 ratchet boundary evaluation. Here, a new approach based on fully implicit 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 whilst ensuring the equivalent stresses remain below a modified yield strength. During stage 2 the modified yield strength used is updated throughout the analysis thus satisfying Melans Lower bound ratchet theorem. This is achieved through the same elastic plastic model as the first stage, using a modified radial return method. The methods that have been proposed here are shown to provide better agreement with upper bound ratchet method than the Hybrid method, however some limitations in this type of method have been identified and are discussed.

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.

Elastic-Shakedown Analysis of Axisymmetric Nozzles

2003 ◽  
Vol 125 (4) ◽  
pp. 365-370 ◽  
Author(s):  
Martin Muscat ◽  
Donald Mackenzie
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Lower Bound ◽  
Pressure Vessel ◽  
Element Analysis ◽  
Shakedown Analysis ◽  
Elastic Plastic ◽  
Section Viii ◽  
Elastic Shakedown ◽  
Division 2

An investigation of the shakedown behavior of axisymmetric nozzles under internal pressure is presented. The analysis is based on elastic-plastic finite element analysis and Melan’s lower bound shakedown theorem. Calculated shakedown pressures are compared with values from the literature and with the ASME Boiler and Pressure Vessel Code Section VIII Division 2 primary plus secondary stress limits. Results obtained by the lower bound method are also verified by cyclic elastic-plastic finite element analysis.

Buckling characteristics of cut-out borne composite stiffened hyperbolic paraboloid shell panel

2021 ◽  
pp. 146442072110058
Author(s):  
Sarmila Sahoo
Keyword(s):  
Finite Element ◽  
Orientation Angle ◽  
Buckling Load ◽  
Benchmark Problems ◽  
Hyperbolic Paraboloid ◽  
Element Analysis ◽  
Load Effect ◽  
Global Buckling ◽  
Fiber Orientation Angle ◽  
Shell Panel

The present study investigates buckling characteristics of cut-out borne stiffened hyperbolic paraboloid shell panel made of laminated composites using finite element analysis to evaluate the governing differential equations of global buckling of the structure. The finite element code is validated by solving benchmark problems from literature. Different parametric variations are studied to find the optimum panel buckling load. Laminations, boundary conditions, depth of stiffener and arrangement of stiffeners are found to influence the panel buckling load. Effect of different parameters like cut-out size, shell width to thickness ratio, degree of orthotropy and fiber orientation angle of the composite layers on buckling load are also studied. Parametric and comparative studies are conducted to analyze the buckling strength of composite hyperbolic paraboloid shell panel with cut-out.

Effect of Defect on Elastic/Plastic and Creep Behavior of Bone: A Finite Element Study

2007 ◽  
Author(s):  
A. Ajdari ◽  
P. K. Canavan ◽  
H. Nayeb-Hashemi ◽  
G. Warner
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Trabecular Bone ◽  
Fatigue Loading ◽  
Dimensional Structure ◽  
Plastic Behavior ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Local Bone ◽  
Osteoporotic Vertebral Fractures

Three-dimensional structure of trabecular bone can be modeled by 2D or 3D Voronoi structure. The effect of missing cell walls on the mechanical properties of 2D honeycombs is a first step towards understanding the effect of local bone resorption due to osteoporosis. In patients with osteoporosis, bone mass is lost first by thinning and then by resorption of the trabeculae [1]. Furthermore, creep response is important to analyze in cellular solids when the temperature is high relative to the melting temperature. For trabecular bone, as body temperature (38 °C) is close to the denaturation temperature of collagen (52 °C), trabecular bone creeps [1]. Over the half of the osteoporotic vertebral fractures that occur in the elderly, are the result of the creep and fatigue loading associated with the activities of daily living [2]. The objective of this work is to understand the effect of missing walls and filled cells on elastic-plastic behavior of both regular hexagonal and non-periodic Voronoi structures using finite element analysis. The results show that the missing walls have a significant effect on overall elastic properties of the cellular structure. For both regular hexagonal and Voronoi materials, the yield strength of the structure decreased by more than 60% by introducing 10% missing walls. In contrast, the results indicate that filled cells have much less effect on the mechanical properties of both regular hexagonal and Voronoi materials.

A Study of Wall Ironing by the Finite Element Technique

1978 ◽  
Vol 100 (1) ◽  
pp. 31-36 ◽  
Author(s):  
E. I. Odell
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Cone Angle ◽  
Reduction Ratio ◽  
Operating Parameters ◽  
Finite Element Technique ◽  
Elastic Plastic ◽  
Maximum Reduction ◽  
Load Displacement ◽  
Element Technique

Wall ironing has been analyzed using an elastic-plastic finite element technique. The effects that the ironing ring semi-cone angle and friction have on the maximum reduction ratio are studied in detail. Stress contours are given for a typical set of operating parameters. Several ram load/displacement curves are provided and compared with upper and lower bound loads.

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