A Numerical Approach for Lower Bound Limit Analysis

2014 ◽  
Vol 626 ◽  
pp. 474-481
Author(s):  
Ying Hua Liu ◽  
Bing Ye Xu ◽  
Xian He Du
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Limit Analysis ◽  
Yield Criterion ◽  
Numerical Procedure ◽  
Mathematical Programming Problem ◽  
Plastic Limit ◽  
Active Constraint ◽  
Plastic Limit Analysis ◽  
Lower Bound Limit Analysis

In this paper, a numerical procedure for plastic limit analysis of 3-D elastic-perfectly plastic bodies under complex loads is presented. The method is based on the lower-bound limit theorem and von Mises yield criterion so that the lower-bound limit analysis can be conducted by solving a nonlinear mathematical programming problem. A SQP algorithm and a dimension reduction-based technique are used to solve the discretized finite element optimization formulation. A conception of active constraint set is introduced, so that the number of constraints can be reduced greatly. The basis vectors of reduced residual stress spaces are constructed by performing an equilibrium iteration procedure of elasto-plastic finite element analysis. The numerical procedure is applied to carry out the plastic limit analysis of pipelines with part-through slots under internal pressure, bending moment and axial force. The effects of different sizes of part-through slots on the limit loads of pipelines are studied.

Study of Lower Bound Method for Plastic Limit Analysis of Wedge on Consideration of Anchor Bolt

2013 ◽  
Vol 444-445 ◽  
pp. 966-970
Author(s):  
Zhi Lin Liang ◽  
Ze Li
Keyword(s):  
Lower Bound ◽  
Limit Analysis ◽  
Programming Model ◽  
Yield Condition ◽  
Plastic Limit ◽  
Rocky Slope ◽  
Plastic Limit Analysis ◽  
Structural Surface ◽  
The Stability ◽  
Lower Bound Theory

The massive rock slope is made up of rocks and structural surface. The existence and strength of the structural surface decides the stability of the rock mass. By adopting the lower bound method for the plastic limit analysis of wedge slope, we can easily calculate the stability of the rocky slope under various circumstances. To apply this method, we first took the wedge-shaped slide block as a complex of rigid block and structural surface for the analysis of the slope stress under the function of anchor bolts, the integrated function of rocks and structural surfaces being considered. Then, on the basis of the lower bound theory for the plastic limit analysis, a mathematical programming model which takes safety factor of slope stability as the object function is established. This model has to meet the equilibrium condition of the bolt, the Mohr-Coulomb yield condition and the boundary condition of slope. In the end, a classic model of wedge is analyzed and its lower bound solution is worked out. This result is compared to the result worked out by limiting equilibrium to test the validity of the measure and procedure used in this paper.

Limit analysis using the ellipsoid yield surface

1994 ◽  
Vol 445 (1925) ◽  
pp. 519-527
Keyword(s):  
Mathematical Programming ◽  
Yield Surface ◽  
Limit Analysis ◽  
Iteration Process ◽  
Mathematical Programming Problem ◽  
Plastic Limit ◽  
Polyester Composite ◽  
Plastic Limit Analysis ◽  
Element Technique ◽  
Kinematic Theorem

The ellipsoid yield surface can be applied to many engineering materials, such as metal, concrete, polyester, composite, etc. It is essential to establish an efficient method to carry out the plastic limit analysis of such media. Based on the classical kinematic theorem of plasticity theory and the finite element technique, a discrete mathematical programming formula is presented to determine the collapse load for materials with ellipsoid yield surface. The mathematical programming problem is solved by an efficient algorithm including an iteration process. The convergency of the algorithm is guaranteed. Numerical examples are presented and the results are reasonable and satisfactory.

Limit Analysis of a Spherical Shell Under Axial Loading on Central Boss

1996 ◽  
Vol 118 (4) ◽  
pp. 454-459 ◽  
Author(s):  
D. J. Yeom ◽  
M. Robinson
Keyword(s):  
Finite Element ◽  
Spherical Shell ◽  
Limit Analysis ◽  
Axial Loading ◽  
Geometrical Parameters ◽  
Finite Element Code ◽  
Collapse Load ◽  
Plastic Limit ◽  
Plastic Limit Analysis ◽  
Analysis Package

The purpose of this study is to investigate the collapse load of a spherical shell under axial loading on a central boss. The investigation was carried out using an existing lower-bound plastic limit analysis package and the ABAQUS finite element code. Results are obtained for various geometrical parameters and compared with previous analytical and experimental results.

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