The use of an SQP algorithm in slope stability analysis

In the upper bound approach to limit analysis of slope stability based on the rigid finite element method, the search for the minimum factor of safety can be formulated as a non‐linear programming problem with equality constraints only based on a yield criterion, a flow rule, boundary conditions, an...

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Vydáno v:Communications in numerical methods in engineering Ročník 21; číslo 1; s. 23 - 37
Hlavní autoři: Chen, Jian, Yin, Jian-Hua, Lee, C. F.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Chichester, UK John Wiley & Sons, Ltd 01.01.2005
Wiley
Témata:
Applied sciences
Buildings. Public works
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Geotechnics
Inelasticity (thermoplasticity, viscoplasticity...)
limit analysis
non-linear programming
Physics
rigid finite element method
sequential quadratic programming
slope stability
Soil mechanics. Rocks mechanics
Solid mechanics
Structural and continuum mechanics
upper bound
limit analysis
Yield criterion
non-linear programming
Slope stability
Non linear programming
rigid finite element method
Quadratic programming
Modeling
Optimization
Finite element method
Energy balance
Upper bound
Safety factor
Sequential method
Non linear effect
sequential quadratic programming
Ultimate load
Non existence
ISSN:1069-8299, 1099-0887
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Shrnutí:In the upper bound approach to limit analysis of slope stability based on the rigid finite element method, the search for the minimum factor of safety can be formulated as a non‐linear programming problem with equality constraints only based on a yield criterion, a flow rule, boundary conditions, and an energy‐work balance equation. Because of the non‐linear property of the resulting optimization problems, a non‐linear mathematical programming algorithm has to be employed. In this paper, the relations between the numbers of nodes, elements, interfaces, and subsequent unknowns and constraints in the approach have been derived. It can be shown that in the large‐scale problems, the unknowns are subject to a highly sparse set of equality constraints. Because of the existence of non‐linear equalities in the approach, this paper applies first time a special sequential quadratic programming (SQP) algorithm, feasible SQP (FSQP), to obtain solutions for such non‐linear optimization problems. In FSQP algorithm, the non‐linear equality constraints are turned into inequality constraints and the objective function is replaced by an exact penalty function which penalizes non‐linear equality constraint violations only. Three numerical examples are presented to illustrate the potentialities and efficiencies of the FSQP algorithm in the slope stability analysis. Copyright © 2004 John Wiley & Sons, Ltd.
Bibliografie:Research Grants Council (RGC) - No. PolyU 5064/00E
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ArticleID:CNM723
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ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1069-8299
1099-0887
DOI:10.1002/cnm.723