scholarly journals Application of discontinuity layout optimization to three-dimensional plasticity problems

2013 ◽  
Vol 469 (2155) ◽  
pp. 20130009 ◽  
Author(s):  
Samuel Hawksbee ◽  
Colin Smith ◽  
Matthew Gilbert
Keyword(s):  
Upper Bound ◽  
Limit Analysis ◽  
Three Dimensional ◽  
Layout Optimization ◽  
Benchmark Problems ◽  
Cone Programming ◽  
Yield Criteria ◽  
Collapse Mechanisms ◽  
Second Order Cone ◽  
Programming Techniques

A new three-dimensional limit analysis formulation that uses the recently developed discontinuity layout optimization (DLO) procedure is described. With DLO, limit analysis problems are formulated purely in terms of discontinuities, which take the form of polygons when three-dimensional problems are involved. Efficient second-order cone programming techniques can be used to obtain solutions for problems involving Tresca and Mohr–Coulomb yield criteria. This allows traditional ‘upper bound’ translational collapse mechanisms to be identified automatically. A number of simple benchmark problems are considered, demonstrating that good results can be obtained even when coarse numerical discretizations are employed.

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.

scholarly journals Elastoplastic and limit analysis of 3D steel assemblies using second-order cone programming and dual finite-elements

2020 ◽  
Vol 221 ◽  
pp. 111041
Author(s):  
Chadi El Boustani ◽  
Jeremy Bleyer ◽  
Mathieu Arquier ◽  
Mohammed-Khalil Ferradi ◽  
Karam Sab
Keyword(s):  
Finite Elements ◽  
Limit Analysis ◽  
Second Order ◽  
Cone Programming ◽  
Second Order Cone Programming ◽  
Second Order Cone
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