A convex hull approach for the reliability-based design optimization of nonlinear transient dynamic problems

doi:10.1016/J.CMA.2006.12.008

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A convex hull approach for the reliability-based design optimization of nonlinear transient dynamic problems

Journal Article•DOI•

A convex hull approach for the reliability-based design optimization of nonlinear transient dynamic problems

Samy Missoum¹, Palaniappan Ramu², Raphael T. Haftka²•Institutions (2)

University of Arizona¹, University of Florida²

15 May 2007-Computer Methods in Applied Mechanics and Engineering (Elsevier)-Vol. 196, Iss: 29, pp 2895-2906

TL;DR: In this article, a convex hull approach is adopted to isolate the points corresponding to unwanted bifurcations in the design space, which is applied to a tube impacting a rigid wall representing a transient dynamic problem.

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About: This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2007-05-15. It has received 64 citations till now. The article focuses on the topics: Nonlinear programming & Convex hull.

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Journal Article•DOI•

Computational methods in optimization considering uncertainties – An overview

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Gerhart I. Schuëller¹, Hector A. Jensen²•Institutions (2)

University of Innsbruck¹, Valparaiso University²

15 Nov 2008-Computer Methods in Applied Mechanics and Engineering

TL;DR: In this article, the authors present a brief survey on some of the most relevant developments in the field of optimization under uncertainty, including reliability-based optimization, robust design optimization and model updating.

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487 citations

Journal Article•DOI•

A survey on approaches for reliability-based optimization

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Marcos A. Valdebenito¹, Gerhart I. Schuëller¹•Institutions (1)

University of Innsbruck¹

01 Nov 2010-Structural and Multidisciplinary Optimization

TL;DR: This contribution provides a survey on approaches for performing Reliability-based Optimization, with emphasis on the theoretical foundations and the main assumptions involved.

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Abstract: Reliability-based Optimization is a most appropriate and advantageous methodology for structural design. Its main feature is that it allows determining the best design solution (with respect to prescribed criteria) while explicitly considering the unavoidable effects of uncertainty. In general, the application of this methodology is numerically involved, as it implies the simultaneous solution of an optimization problem and also the use of specialized algorithms for quantifying the effects of uncertainties. In view of this fact, several approaches have been developed in the literature for applying this methodology in problems of practical interest. This contribution provides a survey on approaches for performing Reliability-based Optimization, with emphasis on the theoretical foundations and the main assumptions involved. Early approaches as well as the most recently developed methods are covered. In addition, a qualitative comparison is performed in order to provide some general guidelines on the range of applicability on the different approaches discussed in this contribution.

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329 citations

Cites background or methods from "A convex hull approach for the reli..."

...(1991); Moan and Song (2000); Petryna and Krätzig (2005); similarly, aspects on parallel computing are not treated in this contribution. Moreover, this contribution considers approaches using classical probabilities only; however, it should be noted that non-classical approaches (see, e.g. Moens and Vandepitte (2005); Möller and Beer (2007)) have been applied as well for problems of optimization under uncertainties, see e....
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...In Missoum et al (2007), it is proposed to approximate the limit state functions related to the failure event by means of a convex hull; such an approximation allows to apply direct MCS at low numerical costs, rendering a feasible means for performing RBO....
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...(1991); Moan and Song (2000); Petryna and Krätzig (2005); similarly, aspects on parallel computing are not treated in this contribution....
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Journal Article•DOI•

Response surface approximation of Pareto optimal front in multi-objective optimization

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Tushar Goel¹, Rajkumar Vaidyanathan¹, Raphael T. Haftka¹, Wei Shyy¹, Nestor V. Queipo², Kevin Tucker³ - Show less +2 more•Institutions (3)

University of Florida¹, University of Zulia², Marshall Space Flight Center³

01 Jan 2007-Computer Methods in Applied Mechanics and Engineering

TL;DR: A systematic approach to approximate the Pareto optimal front (POF) by a response surface approximation is presented, and the approximated POF can help visualize and quantify trade-offs among objectives to select compromise designs.

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269 citations

Journal Article•DOI•

Adaptive explicit decision functions for probabilistic design and optimization using support vector machines

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Anirban Basudhar¹, Samy Missoum¹•Institutions (1)

University of Arizona¹

01 Oct 2008-Computers & Structures

TL;DR: This article presents a methodology to generate explicit decision functions using support vector machines (SVM) and proposes an adaptive sampling scheme that updates the decision function.

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203 citations

Cites background from "A convex hull approach for the reli..."

...The boundaries of the failure region (global buckling) were later defined with a convex hull which led to a more accurate and less conservative failure domain [13]....
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Journal Article•DOI•

Limit state function identification using Support Vector Machines for discontinuous responses and disjoint failure domains

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Anirban Basudhar¹, Samy Missoum¹, Antonio Harrison Sanchez¹•Institutions (1)

University of Arizona¹

01 Jan 2008-Probabilistic Engineering Mechanics

TL;DR: In this article, a method for the explicit construction of limit state functions using Support Vector Machines (SVM) is presented to handle the difficulties associated with the reliability assessment of problems exhibiting discontinuous responses and disjoint failure domains.

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142 citations

Additional excerpts

...The approach was later extended to the use of a convex hull for the definition of the boundaries of a failure region [8]....
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References

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Journal Article•DOI•

A K-Means Clustering Algorithm

[...]

J. A. Hartigan¹, M. A. Wong¹•Institutions (1)

Yale University¹

01 Mar 1979-Journal of The Royal Statistical Society Series C-applied Statistics

10,702 citations

Journal Article•DOI•

The quickhull algorithm for convex hulls

[...]

C. Bradford Barber¹, David P. Dobkin², Hannu Huhdanpaa•Institutions (2)

University of Minnesota¹, Princeton University²

01 Dec 1996-ACM Transactions on Mathematical Software

TL;DR: This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull algorithm with the general-dimension Beneath-Beyond Algorithm, and provides empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it used less memory.

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Abstract: The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull algorithm with the general-dimension Beneath-Beyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it used less memory. computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floating-point arithmetic, this assumption can lead to serous errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of “thick” facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.

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5,050 citations

"A convex hull approach for the reli..." refers background in this paper

...It is to be noted that a convex hull is not limited to two dimensions and can be easily extended to several dimensions (Barber et al., 1996)....
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...Qhull implements the Quickhull algorithm (Barber et al., 1996)....
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Book•

Nonlinear Finite Elements for Continua and Structures

[...]

Ted Belytschko, Wing Kam Liu, Brian Moran

12 Sep 2000

TL;DR: In this paper, the authors present a list of boxes for Lagrangian and Eulerian Finite Elements in One Dimension (LDF) in one dimension, including Beams and Shells.

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Abstract: Preface. List of Boxes. Introduction. Lagrangian and Eulerian Finite Elements in One Dimension. Continuum Mechanics. Lagrangian Meshes. Constitutive Models Solution Methods and Stability. Arbitrary Lagrangian Eulerian Formulations. Element Technology. Beams and Shells. Contact--Impact. Appendix 1: Voigt Notation. Appendix 2: Norms. Appendix 3: Element Shape Functions. Glossary. References. Index.

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3,928 citations

Book•

Structural Reliability: Analysis and Prediction

[...]

Robert E. Melchers

01 Jan 1987

TL;DR: Measures of Structural Reliability Assessment, including second-Moment and Transformation Methods, and Probabilistic Evaluation of Existing Structures.

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Abstract: Measures of Structural Reliability. Structural Reliability Assessment. Integration and Simulation Methods. Second-Moment and Transformation Methods. Reliability of Structural Systems. Time Dependent Reliability. Load and Load Effect Modelling. Resistance Modelling. Codes and Structural Reliability. Probabilistic Evaluation of Existing Structures. Appendices. References. Index.

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3,151 citations

"A convex hull approach for the reli..." refers methods in this paper

...Therefore, the assessment of a probability of failure in the context of reliability-based design optimization (RBDO) can be performed efficiently through, for instance, Monte-Carlo Simulations (Melchers, 1999)....
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Book•DOI•

Non-Linear Finite Element Analysis of Solids and Structures: de Borst/Non-Linear Finite Element Analysis of Solids and Structures

[...]

René de Borst, Mike A. Crisfield, Joris J.C. Remmers, Clemens V. Verhoosel

17 Aug 2012

TL;DR: De Borst et al. as mentioned in this paper present a condensed version of the original book with a focus on non-linear finite element technology, including nonlinear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity.

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Abstract: Built upon the two original books by Mike Crisfield and their own lecture notes, renowned scientist Rene de Borst and his team offer a thoroughly updated yet condensed edition that retains and builds upon the excellent reputation and appeal amongst students and engineers alike for which Crisfield's first edition is acclaimed. Together with numerous additions and updates, the new authors have retained the core content of the original publication, while bringing an improved focus on new developments and ideas. This edition offers the latest insights in non-linear finite element technology, including non-linear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity. The authors' integrated and consistent style and unrivalled engineering approach assures this book's unique position within the computational mechanics literature.

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2,568 citations