An Improved Upper Bound Limit Load Solution for Weld Strength Anisotropic Overmatched Cracked Plates in Pure Bending

2008 ◽  
pp. 357-358
Author(s):  
N. Kontchakova ◽  
S. Alexandrov
Keyword(s):  
Upper Bound ◽  
Limit Load ◽  
Weld Strength ◽  
Pure Bending ◽  
Cracked Plates

scholarly journals A Limit Load Solution for Anisotropic Welded Cracked Plates in Pure Bending

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1764
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Alexander Pirumov ◽  
Dinh Kien Nguyen
Keyword(s):  
Numerical Method ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Bending Moment ◽  
Limit Load ◽  
Vertical Axis ◽  
Pure Bending ◽  
Cracked Plates ◽  
Base Materials ◽  
Assessment Procedures

The present paper’s main objective is to derive a simple upper bound solution for a welded plate in pure bending. The plate contains a crack located in the weld. Both the weld and base materials are orthotropic. Hill’s quadratic yield criterion is adopted. The solution is semi-analytic. A numerical method is only required for minimizing a function of two independent variables. Six independent dimensionless parameters classify the structure. Therefore, the complete parametric analysis of the solution is not feasible. However, for a given set of parameters, the numerical solution is straightforward, and the numerical method is fast. A numerical example emphasizes the effect of plastic anisotropy and the crack’s location on the bending moment at plastic collapse. In particular, the bending moment for the specimen having a vertical axis of symmetry is compared with that of the asymmetric specimen. It is shown that the latter is smaller for all considered cases. The solution found can be used in conjunction with flaw assessment procedures.

Limit Load Solutions for Surface Cracks in Plates Under Different Loading Types

2002 ◽  
Author(s):  
Peter Dillstro¨m ◽  
Iradj Sattari-Far
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Crack Length ◽  
Crack Depth ◽  
Limit Load ◽  
Surface Cracks ◽  
Pure Bending ◽  
Element Analysis ◽  
Linear Finite Element ◽  
Cracked Plates

Limit load solutions of plates containing surface cracks are determined using non-linear finite element analysis. The study covers both shallow and deep cracks with different crack length/crack depth ratios under different loading types. The crack configurations consist of semi-elliptical surface cracks with a/t = 0.20, 0.40, 0.60, 0.80 and l/a = 2, 5, 10. Also studied are plates containing infinite surface cracks with a/t = 0.00, 0.20, 0.40, 0.60, 0.80. The cracked plates are subjected to pure tension, pure bending and combined tension and bending. The finite element results obtained from this study are compared with some published limit load solutions in the literature. It is shown that the exiting solutions are in general overly conservative.

Effect of three-dimensional deformation on the limit load of highly weld strength undermatched specimens under tension

2008 ◽  
Vol 222 (2) ◽  
pp. 107-115 ◽  
Author(s):  
S Alexandrov ◽  
M Kocak
Keyword(s):  
Upper Bound ◽  
Metal Forming ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Limit Load ◽  
Weld Strength ◽  
Structural Applications ◽  
Analytical Formulae ◽  
Current Article ◽  
Assessment Procedures

In the case of welded structures with cracks, a number of parameters, such as those with units of length, makes it difficult to present the results of numerical solutions in a form convenient for direct engineering applications, such as flaw assessment procedures. For centre-cracked components under tension, it is shown in the current article that an effect of crack length on the limit load can be taken into account by means of an upper bound limit load for the corresponding structure with no crack without any additional numerical treatment. Using this result, it is sufficient to find an upper bound limit load for the structure with no crack and then to apply the analytical formulae for finding the corresponding limit load for the structure of interest. Welding of some aluminium alloys for structural applications usually leads to a significantly lower strength (undermatched) weld joint. The approach proposed is used to demonstrate an effect of three-dimensional deformation on an upper bound limit load for such highly strength undermatched centre-cracked welded specimens under tension. This result can also be used in metal-forming applications where upper bound solutions are more useful than lower bound solutions.

An Upper Bound Solution for Upsetting of Two-Layer Cylinder

2006 ◽  
Vol 505-507 ◽  
pp. 1303-1308 ◽  
Author(s):  
Gow Yi Tzou ◽  
Sergei Alexandrov
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Limit Load ◽  
Equivalent Strain ◽  
Industrial Applications ◽  
Upper Bound Theorem ◽  
Bound Solution ◽  
Upper Bound Solution ◽  
Perfectly Plastic ◽  
Plastic Materials

An upper bound solution for axisymmetric upsetting of two-layer cylinder made of rigid perfectly plastic materials is provided. An important feature of the solution is that the kinematically admissible velocity field, in addition to the necessary requirements of the upper bound theorem, satisfies the frictional boundary condition in stresses, the maximum friction law. The latter is archived by introducing a singular velocity field such that the equivalent strain rate approaches infinity at the friction surface. The dependence of the upper bound limit load on geometric parameters and the ratio of the yield stresses of the two materials is analyzed. The solution can be used in industrial applications for evaluating the load required to deform two-layer cylinders.

A Simplified Kinematic Method for 3D Limit Analysis

2016 ◽  
Vol 846 ◽  
pp. 342-347 ◽  
Author(s):  
J.P. Hambleton ◽  
Scott William Sloan
Keyword(s):  
Upper Bound ◽  
Limit Analysis ◽  
Three Dimensional ◽  
Yield Condition ◽  
Limit Load ◽  
Computational Techniques ◽  
Simple Formulation ◽  
Planar Velocity ◽  
Collapse Mechanisms ◽  
Second Order Cone

The kinematic (upper bound) method of limit analysis is a powerful technique for evaluating rigorous bounds on limit loads that are often very close to the true limit load. While generalized computational techniques for two-dimensional (e.g., plane strain) problems are well established, methods applicable to three-dimensional problems are relatively underdeveloped and underutilized, due in large part to the cumbersome nature of the calculations for analytical solutions and the large computation times required for numerical approaches. This paper proposes a simple formulation for three-dimensional limit analysis that considers material obeying the Mohr-Coulomb yield condition and collapse mechanisms consisting of sliding rigid blocks separated by planar velocity discontinuities. A key advantage of the approach is its reliance on a minimal number of unknowns, can dramatically reduce processing time. The paper focuses specifically on tetrahedral blocks, although extension to alternative geometries is straightforward. For an arbitrary but fixed arrangement of blocks, the procedure for computing the unknown block velocities that yield the least upper bound is expressed as a second-order cone programming problem that can be easily solved using widely available optimization codes. The paper concludes with a simple example and remarks regarding extensions of the work.

Limit Load Solutions of the Orthotropic Thick-Walled Pipe Subjected to Internal Pressure, Bending Moment and Torsion Moment

2019 ◽  
Author(s):  
Min Xu ◽  
Yujie Zhao ◽  
Binbin Zhou ◽  
Xiaohua He ◽  
Changyu Zhou
Keyword(s):  
Analytical Solution ◽  
Yield Strength ◽  
Internal Pressure ◽  
Yield Criterion ◽  
Bending Moment ◽  
Limit Load ◽  
Pure Bending ◽  
Pure Torsion ◽  
Torsion Moment ◽  
The Difference

Abstract Based on the Hill yield criterion, the analytical solutions of the limit load of orthotropic thick-walled pipes under pure internal pressure, bending moment and torsion are given respectively. The simplified Mises analytical solution and finite element results of limit load for isotropic thick-walled pipe are obtained. The solution verifies the reliability of the analytical solution. The paper discusses the difference of limit load of isotropic and orthotropic pipes under the conditions of pure internal pressure, pure bending moment and pure torsion moment. It is concluded that the influence of material anisotropy on the limit load is significant. The limit load of pipe under pure internal pressure is mainly determined by circumferential yield strength, pure bending is only related to axial yield strength and pure torsion moment is related to the yield strength in the 45° direction and radial yield strength.

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.

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