Limit Load Analysis of Crack Contained Thick Walled Cylinders

Reliable limit load estimations for thick walled pressurized cylinders containing defects are required for the assessment of integrity of structures that experience significant plastic deformation prior to failure. Analytical and finite element analyses of limit load in thick walled cylinders containing defects are presented in this paper. FE analyses were conducted to obtain estimates of the limit state of loading for a range of combined loading schemes and loading sequences for open-end and closed-end cylinder. Part through shallow and deep hoop cracks in the cylinder for uniform radial, uniform axial and combined loading were examined. The results suggest that adjustments to the estimates of limit loads obtained from conventional methods reported in literature are needed in order to reflect the role of material response, crack configuration and boundary conditions on the limit loads of defected thick walled pipes and cylinders. These findings are very important and should be noted carefully, especially in the context of treatment of hoop and axial residual stresses in the integrity assessment of pipelines containing part through cracks.

Pressure-Plus-Moment Limit-Load Analysis for a Cylindrical Shell Nozzle

10.1115/1.3264867 ◽

1987 ◽

Vol 109 (3) ◽

pp. 297-301 ◽

Cited By ~ 5

Author(s):

C. J. Tabone ◽

R. H. Mallett

Keyword(s):

Cylindrical Shell ◽

Three Dimensional ◽

Limit Load ◽

Element Model ◽

Combined Loading ◽

Inelastic Behavior ◽

Limit Loads ◽

Out Of Plane ◽

Load Analysis ◽

The Moment

A finite element model of a nozzle in a cylindrical shell is analyzed for three cases; pressure, out-of-plane moment and combined pressure plus out-of-plane moment. The model uses three-dimensional finite elements and the analysis considers inelastic behavior at small displacements. Load versus displacement behavior is given for the three cases. Estimates of limit loads are obtained based upon extrapolation of load versus inverse displacement data curves. An interaction expression is used to show the effect of the combined loading for a case in which an internal pressure reduces the moment capability of the nozzle by 35 percent.

Limit Load Analysis of Cracked Components Using the Reference Volume Method

10.1115/1.2749288 ◽

2006 ◽

Vol 129 (3) ◽

pp. 391-399 ◽

Cited By ~ 2

Author(s):

R. Adibi-Asl ◽

R. Seshadri

Keyword(s):

Elastic Modulus ◽

Three Dimensional ◽

Local Limit ◽

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 sets 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 FEA. The procedures are applied to a practical component with crack 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.

Accelerated Limit Loads Using Repeated Elastic Finite Element Analyses

Computer Technology and Applications ◽

10.1115/pvp2003-1890 ◽

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.

Limit Analysis for Anisotropic Solids Using Variational Principle and Repeated Elastic Finite Element Analyses

Fitness for Service Evaluations and Non-Linear Analysis ◽

10.1115/pvp2002-1321 ◽

2002 ◽

Cited By ~ 2

Author(s):

L. Pan ◽

R. Seshadri

Keyword(s):

Finite Element ◽

Variational Principle ◽

Limit State ◽

Limit Load ◽

Anisotropic Materials ◽

Stress Fields ◽

Finite Element Analyses ◽

Structural Components ◽

Directionally Solidified ◽

Elastic Compensation Method

Many structural components, such as rolled sheets, directionally solidified superalloys and composites, are made of anisotropic materials. The knowledge of limit load is useful in the design and the sizing of these components and structures. This paper presents the extension of the modified mα-method to anisotropic materials. Mura’s variational principle is employed in conjunction with repeated elastic finite element analyses (FEA). The secant modulus of the discretized finite elements in the reference direction in successive elastic iterations is used to estimate the plastic flow parameter for the anisotropic components. The modified initial elastic properties are adopted to ensure the “elastic” stress fields satisfy the anisotropic yield surface. Using the notion of “leap-frogging” to limit state, improved lower-bound limit loads can be obtained. The formulation is applied to two anisotropic components, and the limit load estimates are compared with those using elastic compensation method and inelastic FEA.

Compliance with strength criteria for a model polymeric-composite grillage taking into account nonlinearity of the filler in different loading scenarios

TRANSACTIONS OF THE KRYLOV STATE RESEARCH CENTRE ◽

10.24937/2542-2324-2020-2-s-i-250-255 ◽

2020 ◽

Vol S-I (2) ◽

pp. 250-255

Author(s):

N. Sosnin ◽

Keyword(s):

Limit State ◽

Polymeric Composite ◽

Limit Load ◽

Failure Criteria ◽

Load Level ◽

Material Behaviour ◽

Stress Strain ◽

Limit Loads ◽

Strength Criteria ◽

Limit Stress

This study compares different strength criteria in static loading simulation of a polymeric-composite grillage for different loading scenarios, boundary conditions and models of physical material behaviour. The paper discusses a detailed, structurally similar model of grillage made up by three-layered parts taking into account contact interaction (not the joint one) at the boundaries of bearing layers and the filler, with consideration of physically linear and nonlinear model of filler behaviour. The study applies volume-shell FE idealization. The loading (distributed and local)is simulated as per a step-wise procedure until the selected failure criteria are met, i.e. until limit loads (according to various hypotheses) are achieved. The paper gives examples of limit load calculations and their respective states of grillage for different variants of bearing circuit fastening and different loading types. The study yielded the fields of stress-strain parameters and the four principal complex failure criteria. The study discusses the effect of overall grillage compliance, as well as the effect of local (i.e. not affecting the compliant areas of the flooring) and distributed loading upon the limit state pattern of the structure and the level of its bearing capacity. It also estimates the effect of soft non-linearity of the filler upon limit stress-strain state pattern and limit load level, as well as upon the localization of «triggering» zones for non-dimensional criteria.

Inf–sup conditions on convex cones and applications to limit load analysis

Mathematics and Mechanics of Solids ◽

10.1177/1081286519843969 ◽

2019 ◽

Vol 24 (10) ◽

pp. 3331-3353 ◽

Cited By ~ 1

Author(s):

Jaroslav Haslinger ◽

Stanislav Sysala ◽

Sergey Repin

Keyword(s):

Yield Criterion ◽

Failure Mechanisms ◽

Limit Load ◽

Convex Cones ◽

Mesh Adaptivity ◽

Limit Loads ◽

Perfectly Plastic ◽

Dual Cones ◽

Geotechnical Stability ◽

The paper is devoted to a family of specific inf–sup conditions generated by tensor-valued functions on convex cones. First, we discuss the validity of such conditions and estimate the value of the respective constant. Then, the results are used to derive estimates of the distance to dual cones, which are required in the analysis of limit loads of perfectly plastic structures. The equivalence between the static and kinematic approaches to limit analysis is proven and computable majorants of the limit load are derived. Particular interest is paid to the Drucker–Prager yield criterion. The last section exposes a collection of numerical examples including basic geotechnical stability problems. The majorants of the limit load are computed and expected failure mechanisms of structures are visualized using local mesh adaptivity.

Variational Method in Limit Load Analysis—A Review

10.1115/1.4041058 ◽

2018 ◽

Vol 140 (5) ◽

Author(s):

Reza Adibi-Asl ◽

R. Seshadri

Keyword(s):

Variational Method ◽

Limit State ◽

Limit Load ◽

Loading History ◽

Plastic Limit ◽

Upper Bound Theorem ◽

Bound Theorem ◽

General Limit ◽

Load Analysis ◽

Numerical Approaches

This paper reviews the literature on variational method in limit load analysis and presents both analytical and numerical approaches. One of the most successful applications of variational method in theory of plasticity is limit load analysis. The main objective of the limit load analysis is to estimate the load at the impending plastic limit state of a body. However, for complicated problems it may be very difficult to find the exact limit load. Therefore, based on the extremum principles of limit load analysis, the lower-bound theorem or the upper bound theorem is employed to estimate the limit load directly without considering the entire loading history. In general, limit load analysis plays an important role in design and fitness-for-service assessment of pressurized vessels and piping.

Local Limit-Load Analysis Using the mβ Method

10.1115/1.2716434 ◽

2006 ◽

Vol 129 (2) ◽

pp. 296-305 ◽

Cited By ~ 7

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 ◽

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

10.1115/1.1499960 ◽

2002 ◽

Vol 124 (4) ◽

pp. 433-439 ◽

Cited By ~ 15

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.

Limit Load Analysis of Cylindrical Vessels Under Internal Pressure and Axial Strain

ASME 2011 Pressure Vessels and Piping Conference: Volume 6, Parts A and B ◽

10.1115/pvp2011-57175 ◽

2011 ◽

Author(s):

Xian-Kui Zhu

Keyword(s):

Internal Pressure ◽

Carrying Capacity ◽

Pressure Vessel ◽

Axial Strain ◽

Limit State ◽

Limit Load ◽

Operating Pressure ◽

Load Carrying Capacity ◽

Load Carrying ◽

Strain-based design is a newer technology used in safety design and integrity management of oil and gas pipelines. In a traditional stress-based design, the axial stress is relatively small compared to the hoop stress generated by internal pressure in a line pipe, and the limit state in the pipeline is usually load-controlled. In a strain-based design, however, axial strain can be large and the load-carrying capacity of pipelines could be reduced significantly below an allowed operating pressure, where the limit state is controlled by an axial strain. In this case, the limit load analysis is of great importance. The present paper confirms that the stress, strain and load-carrying capacity of a thin-walled cylindrical pressure vessel with an axial force are equivalent those of a long pressurized pipeline with an axial tensile strain. Elastic stresses and strains in a pressure vessel are then investigated, and the limit stress, limit strain and limit pressure are obtained in terms of the classical Tresca criterion, von Mises criteria, and a newly proposed average shear stress yield criterion. The results of limit load solutions are analyzed and validated using typical experimental data at plastic yield.