The Statement of Optimal Design Problem with the Cusp Catastrophe Theory Application

Aleksandr Vasilyevich Pitukhin; Igor Skobtsov

doi:10.4028/www.scientific.net/AMM.709.530

Paper Titles

The Design of a Multi-Functional Force Loading Device
p.496

Control and Optimization of Development Risk of the High-Tech Manufacturing and Measuring Product
p.503

Exploration on Creative Product Customization Design Based on 3D Printing Technology Research
p.509

Research on the Application Method of Intuitive Design
p.513

The Analysis of Intuition in Industrial Design
p.517

The Automobile Body Modelling Design Based on CATIA Surface Design Module
p.521

The Application of Folding Structure in the Draw-Bar Box Design
p.526

The Statement of Optimal Design Problem with the Cusp Catastrophe Theory Application
p.530

Design Optimization to Reduce Variation in Manufacturing Process
p.534

HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 709The Statement of Optimal Design Problem with the...

The Statement of Optimal Design Problem with the Cusp Catastrophe Theory Application

Abstract:

The purpose of this paper is to present the catastrophe theory method for the optimal design of machine components. A brief description of the cusp catastrophe is presented in the introduction. The statement of optimal design problem is given in the second part of the paper. A single criterion design is presented; the reliability function is used as the objective function. The last part is devoted to probability approach. Manage variables are viewed as stochastic quantities, analytical and statistical linearization methods are used for the reliability function evaluation.

You might also be interested in these eBooks

Designing and Researching of Machines and Technologies for Modern Manufacture

View Preview

Info:

Periodical:

Applied Mechanics and Materials (Volume 709)

Pages:

530-533

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.709.530

Citation:

Cite this paper

Online since:

December 2014

Authors:

Aleksandr Vasilyevich Pitukhin*, Igor Skobtsov

Keywords:

Cusp Catastrophe, Optimal Design, Stochastic Quantity

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

* - Corresponding Author

References

[1] R. Thom, Structural Stability and Morphogenesis, Benjamin, Massachusetts, (1975).

Google Scholar

[2] E.C. Zeeman, Catastrophe Theory: Selected Papers 1972-1977, Addison-Wesley, Massachusetts, (1977).

Google Scholar

[3] T. Poston, I.N. Stewart, Catastrophe Theory and its Applications, Pitman, London, (1978).

Google Scholar

[4] A.E.R. Woodcock, M Davis, Catastrophe Theory, E. P. Dutton, New York, (1978).

Google Scholar

[5] R. Gilmore, Catastrophe Theory for Scientists and Engineers, Dover, New York, (1993).

Google Scholar

[6] V.I. Arnold, Catastrophe Theory, third ed., Springer-Verlag, Berlin, (1992).

Google Scholar

[7] A.V. Pitukhin, Application of Cusp Catastrophe Theory in Engineering Design, The Third World Congress on Computational Mechanics, Chiba, Japan. Volume II (1994) 1259-1260.

Google Scholar

[8] A.V. Pitukhin, Stochastic Cusp Catastrophe and Engineering Design, Proceedings of the Fifth EPMESC Conference «Education, practice and Promotion of Computational methods in Engineering Using Small Computers», Macao, China. Volume 2 (1995) 897-902.

Google Scholar

[9] A.V. Pitukhin, Fracture Mechanics and Optimal Design, International Journal for Numerical Methods in Engineering. Volume 34 No3 (1992) 933-940.

DOI: 10.1002/nme.1620340316

Google Scholar

[10] A.V. Pitukhin, Optimal Design Problems Using Fracture Mechanics Methods, Computers and Structures. Volume 65 No4 (1997) 621-624.

DOI: 10.1016/s0045-7949(94)e0284-9

Google Scholar

[11] A.V. Pitukhin, I.G. Skobtsov, The Estimation of Reliability Function in Terms of the Catastrophe Theory, Applied Mechanics and Materials. 607 (2014) 817-820.

DOI: 10.4028/www.scientific.net/amm.607.817

Google Scholar