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

2019 ◽  
Vol 24 (10) ◽  
pp. 3331-3353 ◽  
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 ◽  
Load Analysis

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.

Incorporation of Strain Hardening Effect Into Limit Load Analysis

2010 ◽  
Author(s):  
P. S. Reddy Gudimetla ◽  
R. Adibi-Asl ◽  
R. Seshadri
Keyword(s):  
Strain Hardening ◽  
Limit Load ◽  
Active Volume ◽  
Limit Loads ◽  
Reference Volume ◽  
Perfectly Plastic ◽  
Tangent Method ◽  
Novel Method ◽  
Typical Strain ◽  
Load Analysis

In this paper a novel method for finding out limit loads in the components or structures by incorporating strain hardening effects is presented. This has been done by including certain amount of the strain hardening into limit load analysis, which normally idealizes the material to be perfectly plastic. The typical strain hardening curves including bilinear hardening and Ramberg-Osgood material models are investigated. The paper also concentrates on plastic reference volume correction concept to find the active volume participating in plastic collapse. The reference volume concept in combination with mα-Tangent method is used to estimate the lower bound limit load of different components.

A limit load solution for a thick-walled cylinder with a fully circumferential crack under axial tension

2009 ◽  
Vol 44 (6) ◽  
pp. 407-416 ◽  
Author(s):  
P J Budden ◽  
Y Lei
Keyword(s):  
Finite Element ◽  
Plastic Material ◽  
Yield Criterion ◽  
Limit Load ◽  
Cylinder Wall ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Inside Radius ◽  
Walled Cylinder

Limit loads for a thick-walled cylinder with an internal or external fully circumferential surface crack under pure axial load are derived on the basis of the von Mises yield criterion. The solutions reproduce the existing thin-walled solution when the ratio between the cylinder wall thickness and the inside radius tends to zero. The solutions are compared with published finite element limit load results for an elastic–perfectly plastic material. The comparison shows that the theoretical solutions are conservative and very close to the finite element data.

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.

Limit Load Analysis of Crack Contained Thick Walled Cylinders

2010 ◽  
Author(s):  
Saeid Hadidi-Moud ◽  
David John Smith
Keyword(s):  
Plastic Deformation ◽  
Limit State ◽  
Limit Load ◽  
Combined Loading ◽  
Finite Element Analyses ◽  
Limit Loads ◽  
Integrity Assessment ◽  
Crack Configuration ◽  
Load Analysis

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.

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 for thin‐walled piping branch junctions under combined pressure and in‐plane bending

2008 ◽  
Vol 43 (2) ◽  
pp. 87-108 ◽  
Author(s):  
Y‐J Kim ◽  
K‐H Lee ◽  
C‐Y Park
Keyword(s):  
Branch Pipe ◽  
Three Dimensional ◽  
Limit Load ◽  
Small Strain ◽  
Limit Loads ◽  
Perfectly Plastic ◽  
Dimensional Finite Element ◽  
Plane Bending ◽  
Elastic Perfectly Plastic ◽  
Three Dimensional Finite Element

Closed‐form yield loci are proposed for branch junctions under combined pressure and in‐plane bending, via small‐strain three‐dimensional finite element (FE) limit load analyses using elastic—perfectly plastic materials. Two types of bending loading are considered: bending on the branch pipe and that on the run pipe. For bending on the run pipe, the effect of the bending direction is further considered. Comparison with extensive FE results shows that predicted limit loads using the proposed solutions are overall conservative and close to FE results. The proposed solutions are believed to be valid for the branch‐to‐run pipe ratios of radius and of thickness from 0.0 to 1.0, and the mean radius‐to‐thickness ratio of the run pipe from 5.0 to 20.0.

The Doubly Nonlinear Limit Load Analysis of Space Grid Structure

2012 ◽  
Vol 166-169 ◽  
pp. 144-149
Author(s):  
Cao Xi ◽  
Yun Hong Hao
Keyword(s):  
Limit Load ◽  
Grid Structure ◽  
Limit Loads ◽  
Load Increment ◽  
Mechanics Model ◽  
Space Grid ◽  
Calculated Load ◽  
Doubly Nonlinear ◽  
Load Analysis ◽  
Complementary Equation

This paper first adopts variational inequation—the method of linear complementary equation. We use this method to analyses the elastoplastic limit load of space grid structure. This is a way to resolve the nonlinear question. Adopting this method to resolve the limit load of space grid structure avoid some drawback caused by adopting iteration method. We only need do some limited compute to a load-increment then we can obtain consequence, which fit in with all condition. Particularly, though adopting the method of linear complementary equation, we can control the value of limit load, make the calculated load can not exceed the limit load. Once exceeding, computer can decrease load- increment automatically and load again till getting the limit load of structure. Based on elastoplastic limit load analysis, this paper has considered big deformation impact on the limit load of bspace grid structure. We have made analysis of doubly nonlinear limit loads under the condition of coupling out of elastoplastic big deformation. The method and theory of this paper can combine with all kinds of single rod mechanics model.

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

1987 ◽  
Vol 109 (3) ◽  
pp. 297-301 ◽  
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 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]

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