Variational Method in Limit Load Analysis—A Review

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.

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.

Plastic Limit Load Analysis of Cylindrical Pressure Vessels with Different Nozzle Inclination

2015 ◽  
Vol 97 (2) ◽  
pp. 163-174
Author(s):  
Anupam Prakash ◽  
Harit Kishorchandra Raval ◽  
Anish Gandhi ◽  
Dipak Bapu Pawar
Keyword(s):  
Limit Load ◽  
Pressure Vessels ◽  
Plastic Limit ◽  
Plastic Limit Load ◽  
Load Analysis

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

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 ◽  
Load Analysis

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.

The Collapse Load of Plates by Hierarchical C0-Plate Element

2013 ◽  
Vol 405-408 ◽  
pp. 3147-3150
Author(s):  
Kwang Sung Woo ◽  
Yong Hwan Yeo ◽  
Dong Woo Lee ◽  
Seung Ho Yang
Keyword(s):  
Plate Theory ◽  
Limit Load ◽  
Mindlin Plate ◽  
Plate Element ◽  
Upper Bound Theorem ◽  
Linear Elastic ◽  
Yield Line Theory ◽  
Load Carrying ◽  
Line Theory ◽  
Bound Theorem

Although a structural analysis of plates based on the linear elastic theory yields good results for deformations and stresses produced by working loads, it fails to assess the real load-carrying capacities of plates on the verge of yielding. In the case of a limit analysis of plates, the yield line theory is widely used on the basis of the upper bound theorem and theoretically it overestimates the strength of plates. That is why the p-version of the finite element method has been proposed for determining the accurate limit load of plates causing collapse. In this method, the hierarchical Co -plate element for bending of elastic-plastic plates accounting for transverse shear effects has been formulated, and is based on the incremental theory of plasticity and the Reissner-Mindlin plate theory. The numerical results are presented for a variety of rectangular plate problems and are compared to the results obtained by the h-version software ADINA, as well as with the available analytical solutions in literature.

Numerical Simulation of Multiple Fatigue Crack Growth with Additional Crack Initiation

2011 ◽  
Vol 488-489 ◽  
pp. 444-447
Author(s):  
Dirk Holländer ◽  
Michael Wünsche ◽  
S. Henkel ◽  
Holger Theilig
Keyword(s):  
Numerical Simulation ◽  
Fatigue Crack ◽  
Crack Growth ◽  
Growth Process ◽  
Limit Load ◽  
Simulation Algorithm ◽  
Plastic Limit ◽  
Curved Crack ◽  
Bound Theorem ◽  
Plastic Limit Load

In this paper, advanced numerical simulations of curved crack growth in the case of mul­tiple crack systems in combination with the analysis of the plastic limit load by the lower bound theorem of plasticity are presented. In order to take additionally initiated cracks during the crack growth process into account, the numerical simulation algorithm has been extended by using the Smith-Watson-Topper (SWT) parameter in combination with a linear fatigue damage accumula­tion.

Evaluation of plastic limit load of piping branch junctions subjected to out-of-plane moment loadings

2003 ◽  
Vol 38 (5) ◽  
pp. 395-404 ◽  
Author(s):  
F-Z Xuan ◽  
P-N Li ◽  
S-T Tu
Keyword(s):  
Failure Mode ◽  
Limit State ◽  
Branch Pipe ◽  
Limit Load ◽  
Internal Force ◽  
Plastic Limit ◽  
Main Pipe ◽  
Out Of Plane ◽  
Plastic Limit Load ◽  
Global Collapse

Under out-of-plane moment loadings, the piping branch junctions (also called tees in engineering) exhibit three kinds of failure mode, namely collapse failure of the branch pipe, global collapse of the intersection due to plastic hinges forming along the intersection line and local instability of the main pipe at the flank. In this work, the common piping branch junctions utilized in petrochemical and power industries with a failure mode of global collapse were investigated, and a new approximate formula for an out-of-plane plastic limit moment was presented. The formula was built on the following process: firstly, an equation between the out-of-plane limit moment and internal force of the branch pipe along the intersection is set up on the basis of the force equilibrium condition. Regarding this internal force as an external load for the main pipe shell, the internal force and moment along the intersection of the main pipe, under the plastic limit state, are then obtained. Finally, referring to the von Mises yield criterion, the approximate plastic limit load of the piping branch junctions subjected to the out-of-plane moment is derived. The accuracy of the new formula is validated by comparison with finite element analysis and experimental results.

Plastic Limit Load Analysis of Tee Joint Containing Corner Cracks

2010 ◽  
Author(s):  
Lijie Chen ◽  
Yinghua Liu ◽  
Tieqiang Gang ◽  
Jane W. Z. Lu ◽  
Andrew Y. T. Leung ◽  
...  
Keyword(s):  
Limit Load ◽  
Plastic Limit ◽  
Plastic Limit Load ◽  
Load Analysis ◽  
Corner Cracks
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